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Recommended Books

Here is a list of books that we would recommended for young people who are interested in mathematics. They are grouped into three different categories:

History of Mathematics

Recreational, thinking mathematically.

We have given each book a lower age band based on the content and language used in the book and have presented them in ascending order of age. This is merely a guideline and you are welcome to make your own judgements on whether or not a book is suitable.

If you'd like to see some book recommendations for younger learners, take a look at the list of books compiled by our Primary team .

Students considering studying Maths or a related subject at university might be interested in the Cambridge Mathematical Reading List , which contains a wide range of suggested books including historical, recreational and technical maths books.

There are lots of maths podcasts you can listen to. Why not try: BBC's More or Less podcast Numberphile 's videos and postcasts.

The Boy Who Loved Math: The Improbable Life of Paul Erdős

Age 7+ Most people think of mathematicians as solitary, working away in isolation. And, it's true, many of them do. But Paul Erdős never followed the usual path. At the age of four, he could ask you when you were born and then calculate the number of seconds you had been alive in his head. But he didn't learn to butter his own bread until he turned twenty. Instead, he traveled around the world, from one mathematician to the next, collaborating on an astonishing number of publications. With a simple, lyrical text and richly layered illustrations, this is a beautiful introduction to the world of math and a fascinating look at the unique character traits that made "Uncle Paul" a great man.

Blockhead: The Life of Fibonacci

Infinity and Me

Uma can't help feeling small when she peers up at the night sky. She begins to wonder about infinity. Is infinity a number that grows forever? Is it an endless racetrack? Could infinity be in an ice cream cone? Uma soon finds that the ways to think about this big idea may just be . . . infinite.

On a Beam of Light: A Story of Albert Einstein

Travel along with Einstein on a journey full of curiosity, laughter, and scientific discovery. Parents and children alike will appreciate this moving story of the powerful difference imagination can make in any life.

50 Mathematical Ideas You Really Need to Know by Tony Crilly

In this book, Professor Tony Crilly explains in 50 clear and concise essays the mathematical concepts - ancient and modern, theoretical and practical, everyday and esoteric - that allow us to understand and shape the world around us. Packed with diagrams, examples and anecdotes, this book is the perfect overview of this often daunting but always essential subject. For once, mathematics couldn't be simpler.

The Math Book by Clifford A Pickover

Mathematic's infinite mysteries and beauty unfold in this book. Beginning millions of years ago with ancient ant odometers and moving through time to our modern-day quest for new dimensions, prolific polymath Clifford Pickover covers 250 milestones in mathematical history. Among the numerous concepts readers will encounter as they dip into this inviting anthology: cicada-generated prime numbers, magic squares, the discovery of pi and calculus, and the butterfly effect. Each topic is presented in a lavishly illustrated spread, including formulas, fascinating facts about scientists' lives and real-world applications of the theorems.

Alex's Adventures in Numberland by Alex Bellos

The world of maths can seem mind-boggling, irrelevant and, sometimes, boring. This groundbreaking book reclaims maths from the geeks. Mathematical ideas underpin just about everything in our lives: from the surprising geometry of the 50p piece to how probability can help you win in any casino. In search of weird and wonderful mathematical phenomena, Alex Bellos travels across the globe and meets the world's fastest mental calculators in Germany and a startlingly numerate chimpanzee in Japan. Packed with fascinating, eye-opening anecdotes, Alex's Adventures in Numberland is an exhilarating cocktail of history, reportage and mathematical proofs that will leave you awestruck.

The Monty Hall Problem: Beyond Closed Doors by Rob Deaves

This short book explores the Monty Hall dilemma, a well known mathematical puzzle. The original problem, the controversy surrounding it and its solution are discussed. Further, the boundaries of the problem are expanded to consider prior knowledge and host intention. This book should be of interest to those who enjoy problem solving.

The Language of Mathematics by Keith Devlin

In The Language of Mathematics, award-winning author Keith Devlin reveals the vital role mathematics plays in our eternal quest to understand who we are and the world we live in. More than just the study of numbers, mathematics provides us with the eyes to recognize and describe the hidden patterns of life. Devlin shows us what keeps a jumbo jet in the air, explains how we can see and hear a football game on TV, allows us to predict the weather, the behavior of the stock market, and the outcome of elections. Far from a dry and esoteric subject, mathematics is a rich and living part of our culture. An exploration of an often woefully misunderstood subject, this book celebrates the simplicity, the precision, the purity, and the elegance of mathematics.

The Music of the Primes by Marcus Du Sautoy

How can one predict when the next prime number will occur? Is there a formula which could generate primes? These apparently simple questions have confounded mathematicians ever since the Ancient Greeks. In 1859, the brilliant German mathematician Bernhard Riemann put forward a hypothesis which finally seemed to reveal a magical harmony at work in the numerical landscape. The promise that these eternal, unchanging numbers would finally reveal their secret thrilled mathematicians around the world. Yet Riemann never publicly provided a proof for his hypothesis and his housekeeper burned most of his personal papers on his death. Whoever cracks Riemann's hypothesis will go down in history, for it has implications far beyond mathematics. In business, it plays a central role in security and e-commerce. In science, it brings together vastly different areas, with critical ramifications in Quantum Mechanics, Chaos Theory and the future of computing. Pioneers in each of these fields are racing to crack the code and a prize of $1 million has been offered to the winner. As yet, it remains unsolved.

Journey Through Genius: The Great Theorems of Mathematics by William Dunham

In this book Dunham treats mathematical theorems as creative works of art. He places each theorem within its historical context and explores the very human and often turbulent life of the creator. He studies such great mathematicians as Archimedes, Gerolamo Cardano and Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.

The Mathematical Universe: Alphabetical Journey Through the Great Proofs, Problems & Personalities by William Dunham

In this book, Dunham takes us through a tantalizing selection of the great proofs, notorious disputes, and intriguing unsolved mysteries of the mathematical universe. Subjects range from the golden age of Greek geometry to the furthest frontier of infinite series. Dunham explores more than five thousand years of mathematical history, digging into the earliest records in Egypt, Babylon, India, and China, and turning up surprising tales and tidbits from modern times. All along the way, Dunham portrays the great masters of mathematics at their work. In colorful anecdotes, the brilliant - often eccentric - luminaries chart the course of mathematical progress. This book is accessible to any reader with a basic knowledge of algebra and geometry. You will come away from this exhilarating book with a keen sense of the power and splendor of the magical mathematical world.

Chaos by James Gleick

Chaos is what happens when the behaviour of a system gets too complicated to predict; the most familiar example is the weather, which apparently cannot be forecast accurately more than five days ahead. This book tells the story so far in the study of this new field of Physics.

Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace by Leonard Mlodinow

Anyone who thought geometry was boring or dry should prepare to be amazed. Despite its worthy cover this book is exactly what its title says - a story - and the plot of this story involves life, death and revolutions of understanding and belief. It stars the some of the most famous names in history, from Euclid who laid the logical foundations, to Albert Einstein, who united space and time in a single non-Euclidean geometry. It offers an alternative history of mathematics, revealing how simple questions anyone might ask about space - in the living room or in some other galaxy - have been the hidden engines of the highest achievements in science and technology.

Closing the Gap: The Quest to Understand Prime Numbers by Vicky Neale

Prime numbers have intrigued, inspired and infuriated mathematicians for millennia. Every school student studies prime numbers and can appreciate their beauty, and yet mathematicians' difficulty with answering some seemingly simple questions about them reveals the depth and subtlety of prime numbers. In this book, Vicky Neale charts the recent progress towards proving the famous Twin Primes Conjecture, and the very different ways in which the breakthroughs have been made: a solo mathematician working in isolation and obscurity, and a large collaboration that is more public than any previous collaborative effort in mathematics. Interleaved with this story are highlights from a significantly older tale, going back two thousand years and more, of mathematicians' efforts to comprehend the beauty and unlock the mysteries of the prime numbers.

Fermat's Last Theorem by Simon Singh

The story of the solving of a puzzle that has confounded mathematicians since the 17th century. In 1963, a schoolboy browsing in his local library stumbled across the world's greatest mathematical problem: Fermat's Last Theorem, a puzzle that every child can understand but which has baffled mathematicians for over 300 years. Aged just ten, Andrew Wiles dreamed that he would crack it. Wiles's lifelong obsession with a seemingly simple challenge set by a long-dead Frenchman is an emotional tale of sacrifice and extraordinary determination. In the end, Wiles was forced to work in secrecy and isolation for seven years, harnessing all the power of modern maths to achieve his childhood dream. Many before him had tried and failed, including a 18-century philanderer who was killed in a duel. An 18-century Frenchwoman made a major breakthrough in solving the riddle, but she had to attend maths lectures at the Ecole Polytechnique disguised as a man since women were forbidden entry to the school.

The Code Book by Simon Singh

The Code Book is a history of man's urge to uncover the secrets of codes, from Egyptian puzzles to modern day computer encryptions. As in Fermat's Last Theorem, Simon Singh brings life to an astonishing story of puzzles, codes, languages and riddles that reveals man's continual pursuit to disguise and uncover, and to work out the secret languages of others. Codes have influenced events throughout history, both in the stories of those who make them and those who break them. The betrayal of Mary Queen of Scots and the cracking of the enigma code that helped the Allies in World War II are major episodes in a continuing history of cryptography. In addition to stories of intrigue and warfare, Simon Singh also investigates other codes, the unravelling of genes and the rediscovery of ancient languages and most tantalisingly, the Beale ciphers, an unbroken code that could hold the key to a 20 million dollar treasure.

The Penguin Dictionary of Curious and Interesting Numbers by David Wells

Look up 1729 to see why it is 'among the most famous of all numbers'. Look up 0.7404 ($= \frac{\pi}{18}$) to discover that this is the density of closely packed identical spheres in what is believed by many mathematicians (though it was at that time an unproven hypothesis) and is known by all physicists and greengrocers to be the optimal packing. Look up Graham's number (the last one in the book), which is inconceivably big: even written as a tower of powers ($9 ^{9^ {9 ^\cdots}}$) it would take up far more ink than could be made from all the atoms in the universe. It is an upper bound for a quantity in Ramsey theory whose actual value is believed to be about 6. A book to be dipped into at leisure.

Calculus has a fierce reputation as complicated, abstract and difficult, but Steven Strogatz tells the true story of its beauty and simplicity. Starting with the Ancient Greeks, calculus has tantilised and fascinated humanity for millenia. Its applications grew from teaching us how to determine the area of a circle with only sand and a stick to safely launching rockets into space. Without it, we wouldn’t have mobile phones, TV, GPS, or ultrasound. This book explains the history of our relationship with calculus, and its relationship with infinity.

Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter

Douglas Hofstadter's book is concerned directly with the nature of maps or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

The Great Mathematical Problems by Ian Stewart

There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics. This book explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincaré Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and problems which, like the Riemann Hypothesis, remain baffling after centuries. Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.

Can you Solve my Problems? by Alex Bellos

This book contains 125 of the world's best brainteasers from the last two millennia, taking us from ancient China to medieval Europe, Victorian England to modern-day Japan, with stories of espionage, mathematical breakthroughs and puzzling rivalries along the way. Some solutions rely on a touch of cunning, others call for creativity, others need mercilessly logical thought. All are guaranteed to sharpen your mind!

Snowflake Seashell Star by Alex Bellos and Edmund Harriss

This book is the first in a series of mathematical colouring books by Alex Bellos and mathematical artist, Edmund Hariss. It is full of intricate and divinely beautiful illustrations, using patterns such as loops, waves and spirals. Stretch your artistic talents and embrace mathematics' aesthetic and conceptual exquisiteness. In 80 glorious images, Alex will teach you how to convey the wonder of mathematics through colour and design. Snowflake, Seashell, Star is an incredible celebration of the overlaps between mathematics and art, learning and play, concentration and calm.

A Mathematical Pandora's Box by Brian Bolt

Through his own experience, Brian Bolt has discovered a worldwide interest in mathematical puzzles. Bolt not only uses them to stimulate creative thinking, but also to open up new areas of mathematics to the reader. This book contains 142 activities: in addition to puzzles, there are games, tricks, models and explanation of various phenomena. They range from number manipulation, through happy and amicable numbers, coin puzzles, picnicking bears and pentominoes, to building shapes with cubes. There is a detailed commentary at the end of the book, giving solutions and explanations, together with the occasional follow-up problem.

The Number Devil by Hans Magnus Enzensberger

The quirky and unusual story of a young boy who hates maths at school, but who discovers a new side to the subject when he meets an unusual mathematician in a dream. This book takes you on an adventure through creative mathematical thinking, with great illustrations along the way.

The Indisputable Existence of Santa Claus by Hannah Fry and Thomas Oléron Evans

How do you apply game theory to select who should be on your Christmas shopping list? Can you predict Her Majesty's Christmas Message? Will calculations show Santa is getting steadily thinner - shimmying up and down chimneys for a whole night - or fatter - as he tucks into a mince pie and a glass of sherry in billions of houses across the world? Full of diagrams, sketches and graphs, beautiful equations, Markov chains and matrices, this book brightens up the bleak midwinter with stockingfuls of mathematical marvels. Mathematics has never been merrier.

Aha! Insight & aha! Gotcha by Martin Gardner

Previously published separately, the two books aha! Gotcha and aha! Insight have been combined as a single volume. The aha! books, as they are referred to by fans of Martin Gardner, contain 144 wonderful puzzles from the reigning king of recreational mathematics. In this combined volume, you will find puzzles ranging over geometry, logic, probability, statistics, number, time, combinatorics, and word play. Gardner calls these puzzles aha! problems, that 'seem difficult, and indeed are difficult if you go about trying to solve them in traditional ways. But if you can free your mind from standard problem solving techniques, you may be receptive to an aha! reaction that leads immediately to a solution. Don't be discouraged if, at first, you have difficulty with these problems. After a while you will begin to catch the spirit of offbeat, nonlinear thinking, and you may be surprised to find your aha! ability improving.'

My Best Mathematical and Logic Puzzles by Martin Gardner

Over a period of 25 years as author of the Mathematical Games column for Scientific American, Martin Gardner devoted a column every six months or so to short math problems or puzzles. This volume contains a rich selection of 70 of the best of these brain teasers, in some cases including references to new developments related to the puzzle. Now enthusiasts can challenge their solving skills and rattle their egos with such stimulating mind-benders as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, The Fork in the Road, Bronx vs. Brooklyn, Touching Cigarettes, and 64 other problems involving logic and basic math. Solutions are included.

The Thrilling Adventures of Lovelace and Babbage by Sydney Padua

In this book Sydney Padua transforms one of the most compelling scientific collaborations into a hilarious set of adventures, starring Ada Lovelace and Charles Babbage. This book presents a delightful alternate reality in which Lovelace and Babbage build the Difference Engine and use it to create runaway economic models, battle the scourge of spelling errors, explore the wider realms of mathematics and, of course, fight crime - for the sake of both London and science. Extremely funny and utterly unusual, this book comes complete with historical curiosities, extensive footnotes and never-before-seen diagrams of Babbage's mechanical, steam-powered computer. And ray guns.

The 'Uncle Albert' Series by Russell Stannard

A best selling science/adventure series, beginning with 'The Time and Space of Uncle Albert'. Uncle Albert and his intrepid niece, Gedanken, enter the dangerous and unknown world of a thought bubble. Their mission: to unlock the deep mysteries of Time and Space... Discover why you can't break the ultimate speed barrier, how to become older than your mother, how to put on weight without getting fat, and how to live forever without even knowing it. Other books in the series include: 'Black Holes and Uncle Albert' and 'Uncle Albert and the Quantum Quest'.

Professor Stewart's Cabinet of Mathematical Curiosities by Ian Stewart

A selection of mathematical puzzles, stories, tricks and short articles - great to read all in one go, or to dip into. The content varies between simple logic puzzles to introductions to more advanced topics such as the Four Colour Theorem, which tells us that we can colour in any map using only four colours, so that no bordering countries have the same colour.

Book of Curious & Interesting Mathematics by David Wells

A collection of strange mathematical facts and stories. This anthology covers a whole range of ages, maths and mathematicians, and includes probability paradoxes, jumbled Shakespearean sonnets, record-breaking monkeys and typewriters, and theories of big game hunting. Also featured are stories of people who looked for logical loopholes in the American Constitution or calmed their nerves with algebra.

Book of Curious & Interesting Puzzles by David Wells

This collection by best-selling author David Wells, a Cambridge math scholar and teacher, includes more than 560 puzzles, from the "mind sharpeners" of a medieval monk to the eitheenth-century Ladies' Diary, the Hindu Bhakshali manuscript, and riddles and popular rhymes. None require any mathematics beyond the most elementary algebra and geometry - and few require even that. Complete answers appear at the end.

Mathematics, Magic and Mystery by Martin Gardner

Famed puzzle expert Martin Gardner explains the mathematics behind a multitude of mystifying tricks: card tricks, stage "mind reading," coin and match tricks, counting out games, geometric dissections, etc. Each of these are actually demonstrations of probability, sets, number theory, topology and other braches of mathematics. No skill at sleight of hand is needed to perform the more than 500 tricks described in this book because mathematics guarantees their success.

How Many Socks Make a Pair? by Rob Eastaway

Can maths be creative? This book sets out to prove that it can, through a selection of short articles on surprising maths in everyday life. Through lots of intriguing problems, involving card tricks, polar bears and, of course, socks, Rob Eastaway shows shows how maths can demonstrate its secret beauties in even the most mundane of everyday objects.

Why do Buses Come in Threes? by Rob Eastaway and Jeremy Wyndham

With a foreword by Tim Rice, this book will change the way you see the world. Why is it better to buy a lottery ticket on a Friday? Why are showers always too hot or too cold? And what's the connection between a rugby player taking a conversion and a tourist trying to get the best photograph of Nelson's Column? These and many other fascinating questions are answered in this entertaining and highly informative book, which is ideal for anyone wanting to remind themselves - or discover for the first time - that maths is relevant to almost everything we do. Dating, cooking, travelling by car, gambling and even life-saving techniques have links with intriguing mathematical problems, as you will find explained here. Whether you have a PhD in astrophysics or haven't touched a maths problem since your school days, this book will give you a fresh understanding of the world around you.

Flatterland by Ian Stewart

In 1884, Edwin A. Abbott published “Flatland”; a brilliant novel about mathematics and philosophy that charmed and fascinated all of England. Now, Ian Stewart has written a fascinating, modern sequel to Abbott's book. Through larger-than-life characters and an inspired story line, "Flatterland" explores our present understanding of the shape and origins of the universe, the nature of space, time, and matter, as well as modern geometries and their applications.

The Liar Paradox and the Towers of Hanoi: 10 Greatest Math Puzzles of All Time by Marcel Danesi

Ever since the Sphinx asked his legendary riddle of Oedipus, riddles, conundrums, and puzzles of all sizes have kept humankind perplexed and amused. The Liar Paradox and the Towers of Hanoi takes die-hard puzzle experts on a tour of the world's most enduringly intriguing braintwisters, from Königsberg's Bridges and the Hanoi Towers to Fibonacci's Rabbits, the Four Color Problem, and the Magic Square. Each chapter introduces the basic puzzle, discusses the mathematics behind it, and includes exercises and answers plus additional puzzles similar to the one under discussion. Here is a veritable kaleidoscope of puzzling labyrinths, maps, bridges, and optical illusions that will keep aficionados entertained for hours.

The Number Mysteries by Marcus du Sautoy

An exploration of surprising ways maths occurs in our everyday lives, centred around five famous unsolved problems in mathematics. Topics include how to detect an art forgery, winning strategies in Monopoly, and how to crack a code. Sprinkled with games and links to interactive online content so you can try out some of the ideas for yourself!

Things to Make and Do in the Fourth Dimension by Matt Parker

This is the complete guide to exploring the fascinating world of maths you were never told about at school. Stand-up comedian and mathematician Matt Parker uses bizarre Klein Bottles, unimaginably small pizza slices, knots no one can untie and computers built from dominoes to reveal some of the most exotic and fascinating ideas in mathematics. Starting with simple numbers and algebra, this book goes on to deal with inconceivably big numbers in more dimensions than you ever knew existed. And always with something for you to make or do along the way.

How to Cut a Cake: and Other Mathematical Conundrums by Ian Stewart

In this book are twenty more curious puzzles and fantastical mathematical stories from one of the world's most popular and accessible writers on mathematics. This is a strange world of never-ending chess games, empires on the moon, furious fireflies, and, of course, disputes over how best to cut a cake. Each chapter - with titles such as, "How to Play Poker By Post" and "Repealing the Law of Averages" - presents a fascinating mathematical puzzle that is challenging, fun, and introduces the reader to a significant mathematical problem in an engaging and witty way. Illustrated with clever and quirky cartoons, each tale will delight those who love puzzles and mathematical conundrums.

Games and Mathematics by David Wells

The appeal of games and puzzles is timeless and universal. In this book, David Wells explores the fascinating connections between games and mathematics, proving that mathematics is not just about tedious calculation but imagination, insight and intuition. The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. This thought-provoking book is perfect for anyone with a thirst for mathematics and its hidden beauty; a good high school grounding in mathematics is all the background that is required, and the puzzles and games will suit pupils from 14 years.

Mathematical Puzzles: A Connoisseur's Collection by Peter Winkler

Collected over several years by Peter Winkler, dozens of elegant, intriguing challenges are presented in this book. The answers are easy to explain, but without this book, devilishly hard to find. Creative reasoning is the key to these puzzles. No involved computation or higher mathematics is necessary, but your ability to construct a mathematical proof will be severly tested - even if you are a professional mathematician. For the truly adventurous, there is even a chapter on unsolved puzzles.

Elastic Numbers by Daniel Griller

Beautifully crafted and immensely enjoyable, the problems in this book require minimal technical knowledge, being accessible to young secondary school pupils. However, there is an astonishing range in difficulty; while some of the problems are fairly straightforward, others are significantly tougher, with a great deal of ingenuity and clarity of thought needed to make progress. Whether you are a student preparing for a maths competition, an educational establishment seeking to supplement your problem solving resources, or an individual looking for a different sort of challenge, Elastic Numbers is a unique collection, and will push you to the very edge of your abilities.

Thinking Mathematically by Mason, Burton & Stacey

Thinking Mathematically is perfect for anyone who wants to develop their powers to think mathematically, whether at school, at university or just out of interest. This book is invaluable for anyone who wishes to promote mathematical thinking in others or for anyone who has always wondered what lies at the core of mathematics. Thinking Mathematically reveals the processes at the heart of mathematics and demonstrates how to encourage and develop them. Extremely practical, it involves the reader in questions so that subsequent discussions speak to immediate experience.

Finding Moonshine: A Mathematician's Journey Through Symmetry by Marcus Du Sautoy

This book tells the story of one of the biggest adventures in mathematics: the search for symmetry. This is the story of how humankind has come to its understanding of the bizarre world of symmetry - a subject of fundamental significance to the way we interpret the world around us. Our eyes and minds are drawn to symmetrical objects, from the sphere to the swastika, from the pyramid to the pentagon. 'Symmetry' is all-pervasive: in chemistry the concept of symmetry explains the structure of crystals; in evolutionary biology, the natural world exploits symmetry in the fight for survival; symmetry and the breaking of symmetry are central to ideas in art, architecture and music; the mathematics of symmetry is even exploited in industry, for example to find efficient ways to store more music on a CD or to keep your mobile phone conversation from cracking up through interference.

Mathematics for the Curious by Peter Higgins

When do the hands of a clock coincide? How likely is it that two children in the same class will share a birthday? How do we calculate the volume of a doughnut? Mathematics for the Curious provides anyone interested in mathematics with a simple and entertaining account of what it can do. Author Peter Higgins gives clear explanations of the more mysterious features of childhood mathematics as well as novelties and connections that prove that mathematics can be enjoyable and full of surprises. Topics include: the truth about fractions, ten questions and their answers, and the golden ratio. Higgins poses entertaining puzzles and questions tempting the reader to ponder math problems with imagination instead of dread. Mathematics for the Curious is an accessible introduction to basic mathematics for beginning students and a lively refresher for adults.

Mathematics for the Imagination by Peter Higgins

Mathematics for the Imagination provides an accessible and entertaining investigation into mathematical problems in the world around us. From world navigation, family trees, and calendars to patterns, tessellations, and number tricks, this informative and fun book helps you to understand the maths behind real-life questions and rediscover your arithmetical mind. This is a highly involving book which encourages the reader to enter into the spirit of mathematical exploration.

Mathematics and the Physical World by Morris Kline

A stimulating account of development of basic mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations and non-Euclidean geometries. Also describes how maths is used in optics, astronomy, motion under the law of gravitation, acoustics, electromagnetism, and other aspects of physics.

Mathematics: A Very Short Introduction by Timothy Gowers

Tim Gowers is a Fields Medalist (the Fields medal is the mathematical equivalent of the Nobel prize), so it is not at all surprising that what he writes is worth reading. What is surprising is the ease and charm of his writing. He touches lightly many areas of mathematics, some that will be familiar (Pythagoras) and some that may not be (manifolds) and has something illuminating to say about all of them.

Excursions in Geometry by C. Stanley Ogilvy

In this book, Professor Ogilvy demonstrates the mathematical challenege and satisfaction to be had from geometry, the only requirement being two simple implements (straight-edge and compass) and a little thought. Topics including harmonic division and Apollonian circles, inversive geometry, the hexlet, conic sections, projective geometry, the Golden Section and angle trisection are addressed in a way that brings out the true intellectual excitement inherent in each. Also included are some unsolved problems of modern geometry.

Excursions in Mathematics by C. Stanley Ogilvy

This book offers a fascinating glimpse into the world of mathematics and mathematicians. It is designed for the reader who has no advanced mathematical background of special aptitude, but who wants to acquaint him or herself with the intellectually stimulating and aesthetically satisfying aspects of the subject. After illuminating the role of the mathematician and dispelling several popular misconceptions about the nature of mathematics, Professor Ogilvy takes you on a lively tour of the four basic branches of the subject: number theory, algebra, geometry and analysis. Focusing on the interesting, and even amusing, aspects of mathematics, he points out the interconnections between the branches and presents mathematics as a vital subject whose frontiers are continually expanding. Many illustrations and examples illuminate classic aspects of the subject as well as recent advances.

Excursions in Number Theory by C. Stanley Ogilvy and John Anderson

This delightful volume, by two well-known mathematicians, invites readers to join a challenging expedition into the mystery and magic of number theory. No special training is needed - just high school mathematics, a fondness for figures and an inquisitive mind. Beginning with familiar notions, the authors skillfully transport the reader to higher realms of mathematics, developing the necessary concepts along the way. Included are thorough discussions of prime numbers, number patterns, irrationals and iterations and calculating prodigies, among other topics.

Q.E.D. - Beauty in Mathematical Proof by Burkard Polster

Which famous proof did Archimedes inscribe on his tombstone? How and why do knots make perfect pentagons? Have you ever seen a proof so completely that it is just obvious? In this delicious little book, top down-under mathemagician Dr. Polster presents many of the most visually intuitive and exciting proofs from the dusty annuals of mathematical history. You can test your ability to follow the logic, leap into mathemagnosis and experience eureka-moment after eureka-moment.

How to Solve It by George Polya

A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out - from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft - indeed, brilliant - instructions on stripping away irrelevancies and going straight to the heart of the problem.

The Joy of X: A Guided Tour of Mathematics from One to Infinity by Steven Strogatz

Maths is everywhere, often where we don't even realise. Award-winning professor Steven Strogatz acts as our guide as he takes us on a tour of numbers that - unbeknownst to the unitiated - connect pop culture, literature, art, philosophy, current affairs, business and even every day life. In The Joy of X, Strogatz explains the great ideas of maths - from negative numbers to calculus, fat tails to infinity - with clarity, wit and insight. He is the maths teacher you never had and this book is perfect for the smart and curious, the expert and the beginner.

Problem-Solving Strategies In Mathematics: From Common Approaches To Exemplary Strategies by Alfred S Posamentier and Stephen Krulik

This book introduces ten problem-solving strategies by first presenting the strategy and then applying it to problems in elementary mathematics. In so doing, the common less efficient approach is first mentioned and then the effective strategy is shown. Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics.

1089 and All That: A Journey into Mathematics by David Acheson

David Acheson's extraordinary little book makes mathematics accessible to everyone. From very simple beginnings he takes us on a thrilling journey to some deep mathematical ideas. On the way, via Kepler and Newton, he explains what calculus really means, gives a brief history of pi, and even takes us to chaos theory and imaginary numbers. Every short chapter is carefully crafted to ensure that no one will get lost on the journey. Packed with puzzles and illustrated by world famous cartoonists, this is one of the most readable and imaginative books on mathematics ever written.

An Introduction to Mathematical Reasoning by Peter Eccles

The purpose of this book is to introduce the basic ideas of mathematical proof to students. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the classic proofs.

Can the study of mathematics enrich the heart as well as the mind? Francis Su explains how humans crave logic, beauty, truth and play, and that searching for these in mathematics is not only rewarding, but builds virtues in us that help us be better individuals and members of society. The book includes puzzles to draw everyone in to the enjoyment of mathematics, as part of his vision that mathematics should be shared by everyone.

What is Mathematics? by Richard Courant, Herbert Robbins and Ian Stewart

Written for beginners and scholars, for students and teachers, for philosophers and engineers, this book is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.

Towards Higher Mathematics: A Companion by Richard Earl

Containing a large and varied set of problems, this rich resource will allow students to stretch their mathematical abilities beyond the school syllabus, and bridge the gap to university-level mathematics. Many proofs are provided to better equip students for the transition to university. The author covers substantial extension material using the language of sixth-form mathematics, thus enabling students to understand the more complex material. There are over 1500 carefully graded exercises, with hints included in the text, and solutions available online. Historical and contextual asides highlight each area of mathematics and show how it has developed over time.

The Art of the Infinite by Robert and Ellen Kaplan

This book unlocks the secrets of maths - revealing it to be our lost, native language, as much a part of us as the words we use every day. Number and form are the essence of our world: from the patterns of the stars to the pulses of the market, from the beats of our hearts to catching a ball or tying our shoelaces. Drawing on science, literature, history and philosophy, this book makes the rich patterns of maths brilliantly clear.

Algorithmic Puzzles by Anany & Maria Levitin

In this book, Anany and Maria Levitin use many classic brainteasers as well as newer examples from job interviews with major corporations to show readers how to apply analytical thinking to solve puzzles requiring well-defined procedures. The book's unique collection of puzzles is supplemented with carefully developed tutorials on algorithm design strategies and analysis techniques intended to walk the reader step-by-step through the various approaches to algorithmic problem solving. Mastery of these strategies - exhaustive search, backtracking, and divide-and-conquer, among others - will aid the reader in solving not only the puzzles contained in this book, but also others encountered in interviews, puzzle collections, and throughout everyday life. Each of the 150 puzzles contains hints and solutions, along with commentary on the puzzle's origins and solution methods. Readers with only middle school mathematics will develop their algorithmic problem-solving skills through puzzles at the elementary level, while seasoned puzzle solvers will enjoy the challenge of thinking through more difficult puzzles.

The Mathematics of Games and Gambling by Edward Packel

This book introduces and develops some of the important and beautiful elementary mathematics needed for rational analysis of various gambling and game activities. Most of the standard casino games (roulette, craps, blackjack, keno), some social games (backgammon, poker, bridge) and various other activities (state lotteries, horse racing) are treated in ways that bring out their mathematical aspects. The mathematics developed ranges from the predictable concepts of probability, expectation, and binomial coefficients to some less well-known ideas of elementary game theory. Game-related exercises are included and solutions to some appear at the end of the book.

How to Study for a Mathematics Degree by Lara Alcock

Every year, thousands of students go to university to study mathematics. Many of these students are extremely intelligent and hardworking, but even the best will, at some point, struggle with the demands of making the transition to advanced mathematics. The mathematics shifts in focus from calculation to proof, so students are expected to interact with it in different ways. These changes need not be mysterious - mathematics education research has revealed many insights into the adjustments that are necessary - but they are not obvious and they do need explaining. This book translates these research-based insights into practical advice for a student audience. It covers every aspect of studying for a mathematics degree, from the most abstract intellectual challenges to the everyday business of interacting with lecturers and making good use of study time.

How to Think Like a Mathematician by Kevin Houston

Looking for a head start in your undergraduate degree in mathematics? This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.

All The Math Books You’ll Ever Need (Updated 2023)

Countless math books are published each year, however, only a tiny percentage of these titles are destined to become the kind of classics that are loved the world over by students and mathematicians.

Within this page, you’ll find an extensive list of math books that have sincerely earned the reputation that precedes them.

For many of the most important branches of mathematics, we’ve provided what we consider to be the best math books for the subject at hand. We aimed for a list of titles that were either introductory in nature or that fall into the category of “must-have” math reference books.

Naturally, a universal consensus doesn’t exist but the books below are as close as it gets to a wish list for any aspiring mathematician or person who’s interested in mathematics. We highly recommend each and every one of these titles and hope that you’ll enjoy them, too.

Please note, this list will constantly be updated so as to keep it current.

Math Books Menu

Abstract algebra books, contemporary abstract algebra.

by Joseph Gallian

Abstract Algebra

by David S. Dummit and Richard M. Foote

Algorithms Books

Introduction to algorithms, third edition.

by Thomas H. Cormen, Charles E. Leiserson and Ronald L. Rivest

The Art of Computer Programming, Volumes 1-3 Boxed Set

by Donald E. Knuth

Calculus Helpers Books

The calculus lifesaver: all the tools you need to excel at calculus.

by Adrian Banner

Calculus Made Easy

by Silvanus P. Thompson

Calculus I Books

Calculus, vol. 1.

by Tom M. Apostol

by Michael Spivak

Calculus II/III Books

Calculus, vol. 2, calculus on manifolds, coffee table math books, mathematicians: an outer view of the inner world.

by Mariana Cook

Sacred Mathematics: Japanese Temple Geometry

by Fukagawa Hidetoshi and Tony Rothman

Combinatorics Books

Principles and techniques in combinatorics.

by Chen Chuan-Chong and Koh Khee-Meng

Combinatorics and Graph Theory (2nd edition)

by John Harris, Jeffry L. Hirst, and Michael Mossinghoff

Differential Equations Books

Differential equations and their applications.

by Martin Braun

Encyclopedias of Mathematics Books

The princeton companion to mathematics.

by Timothy Gowers, June Barrow-Green and Imre Leader (Editors)

Encyclopedia of Mathematics

by James Stuart Tanton

Foundations of Mathematics Books

A mathematical introduction to logic, second edition.

by Herbert Enderton

Classic Set Theory for Guided Independent Study

by Derek C. Goldrei

Categories for the Working Mathematician

by Saunders Mac Lane

History of Mathematics Books

Mathematics: from the birth of numbers.

by Jan Gullberg

What Is Mathematics? An Elementary Approach to Ideas and Methods

by Richard Courant and Herbert Robbins

Mathematics and its History

by John Stillwell

Information Theory Books

Computational science and engineering.

by Gilbert Strang

Information Science

by David G. Luenberger

Introduction to Coding and Information Theory

by Steve Roman

Linear Algebra and Geometry Books

Linear algebra done right.

by Sheldon Axler

The Four Pillars of Geometry

Mathematical methods books, mathematical methods: for students of physics and related fields.

by Sadri Hassani

Mathematical Methods in the Physical Sciences

by Mary L. Boas

Number Theory Books

Elementary number theory.

by Gareth A. Jones and Josephine M. Jones

An Invitation to Modern Number Theory

by Steven J. Miller and Ramin Takloo-Bighash

An Introduction to the Theory of Numbers

by G. H. Hardy, Edward M. Wright and Andrew Wiles

Numerical Analysis Books

Numerical analysis with cd-rom.

by Timothy Sauer

Numerical Recipes 3rd Edition: The Art of Scientific Computing

by William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery

Precalculus Books

Precalculus mathematics in a nutshell: geometry, algebra, trigonometry.

by George F. Simmons

Basic Mathematics

by Serge Lang

Probability Books

Introduction to probability models, tenth edition.

by Sheldon M. Ross

An Introduction to Probability Theory and Its Applications

by William Feller

Probability Theory: The Logic of Science

by E.T Jaynes

Fifty Challenging Problems in Probability with Solutions

by Frederick Monsteller

Real and Complex Analysis Books

Principles of mathematical analysis, third edition.

by Walter Rudin

Real Analysis

by N.L Carothers

Real and Complex Analysis

A first course in complex analysis with applications.

by Dennis Zill and Patrick Shanahan

Visual Complex Analysis

by Tristan Needham

Statistics Books

Statistics in plain english, third edition.

by Timothy C. Urdan

Review : Just as the title implies, the author has submitted an unequivocal and palpable exposition on statistics. Statistics in Plain English is regarded by many as the most appropriate statistics primer for undergraduates. Urdan has managed to compress everything one needs to know about statistics into a compact 250 page book that doesn’t feel hurried or unfulfilling. The text is general enough to be used in a variety of mathematical areas yet retains its comprehensiveness and accuracy. Urdan masterfully moves through essential concepts without losing the reader the way many professors would. Students harboring apprehension towards statistics will tremendously enjoy this book. More info .

Introductory Statistics

by Neil A. Weiss

Statistics, 4th Edition

by David Freedman, Robert Pisani and Roger Purves

Topology Books

Introduction to topology and modern analysis, introduction to topology: third edition.

by Bert Mendelson

Feel free to get in touch if you think the list is really missing out by not listing a specific book. If you are a publisher and feel that we’re missing a great book of yours, drop us a line. Please understand that we recommend only what we consider to be the best books on the market today. No exceptions.

Disclaimer: Here at Math-Blog.com we believe in full disclosure. The links to Amazon.com, have our referral id which earns us a tiny commission every time you buy from these links. Think of it as a tip that won’t cost you a cent, to reward us for our time investment. We appreciate your support.

Book series

Problem Books in Mathematics

About this book series.

• Peter Winkler

Book titles in this series

Selection tests in number theory for mathematical olympiads.

• Corneliu Ma'nescu-Avram
• Copyright: 2024

Available Renditions

Functional Analysis and Operator Theory

• Volodymyr Brayman
• Andrii Chaikovskyi
• Oleksii Konstantinov
• Alexander Kukush

Creative Puzzles to Ignite Your Mind

• Shyam Sunder Gupta
• Copyright: 2023

Applying Power Series to Differential Equations

An Exploration through Questions and Projects

• James Sochacki
• Anthony Tongen
• Copyright: 2022

An Excursion Through Partial Differential Equations

• Svetlin G. Georgiev

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Abstracted and indexed in.

• Mathematical Reviews
• Norwegian Register for Scientific Journals and Series

Definitive resource hub on everything higher math

Bonus guides and lessons on mathematics and other related topics

• Definitive Guide to Learning Higher Mathematics
• Ultimate LaTeX Reference Guide
• Comprehensive List of Mathematical Symbols
• Math Tutoring / Consulting
• Higher Math Proficiency Test
• 10 Commandments of Higher Math Learning
• Math Vault Linear Algebra Ebook Series
• Recommended Math Books
• Recommended Math Websites
• Recommended Online Tools

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Join us in contributing to the glory of mathematics

Recommended Books on Higher Mathematics

Epic textbooks , manuals and guides for the mathematically-inclined, along with other less mathy masterpieces here and there.

Recreational Mathematics

Arithmetics, math puzzles, mathematical initiation and all that goodness

Secrets of Mental Math : The Mathematgician's Guide to Lightning Calculation and Amazing Math Tricks

— By Arthur Benjamin and Michael Shermer

A step-by-step guide on how the mathemagician Arthur Benjamin, a mathematician and a professional magician himself, manages to pull off gigantic arithmetic calculations off of top of his head through a combination of smart tricks and mnemonic techniques .  

COVERED TOPICS

• Substraction
• Multiplication
• Memorizing large numbers
• Calendar-related calculation
• Guess-estimation
• Vedic division

A Mathematician's Lament : How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

— By Paul Lockhart

In this 140-page essay, Paul Lockhart decries the deplorable state of the traditional U.S. K-12 math educational system, and passionately calls for the need to teach mathematics as a creative endeavour  and an  artform .

FEATURED THESES

• Mathematics is primarily an  artform , not a tool.
• U.S. K-12 math education  has lost touch with what mathematics is, and what mathematicians do. 
• By teaching math without the  whys and the contexts , mathematics is in effect reduced to an empty shell.
• The esse n ce of mathematics is  abstraction — not the memorization or applications of facts and figures.

Thinking Mathematically   (2nd Edition)

— By John Mason , Leone Burton and  Kaye Stacey 

A book dedicated to taking one from the mere act of exercise solving to the core of mathematics — mathematical thinking . It showcases the different mental processes for dissecting a problem, and discusses how one can go from a master of tricks into an actual, standalone mathematical thinker.

NOTABLE FEATURES

• A thorough treatment on mathematical investigation
• A mental framework for dealing with intellectual plateaus
• Illustrative, beginner-level problems (with guidance or hints)
• An integrated approach to problem solving and the associated mental processes

What is Mathematics?  An Elementary Approach to Ideas and Methods (2nd Edition)

— By Richard Courant and Herbert Robbins

An all-time cl a ssic in mathematical initiation . Written in a quasi-literary style by two prominent 20th-century mathematicians. It encourages the use of problem solving to develop new insight and understanding, and takes its readers gently to the different branches of higher mathematics.

• Elementary number theory
• Analytic geometry

The Mathematical Experience   (Study Edition)

— By Philip Davis and Reuben Hersh

A collection of humanistic , semi-technical essays about some of most fundamental questions and philosophical issues in mathematics, along with the historical development of the various subtopics and peripheral topics in mathematics. Some experience with undergrad math is recommended.

FEATURED TOPICS

• Mathematical creation vs. discovery
• Mathematical beauty and elegance
• Math as an intermediate reality between the physical and the subjective
• Intro into Fourier analysis , non-Cantorian set theory , finite group theory , non-standard calculus and other topics

Applied   College Mathematics

College algebra,  calculus, linear algebra, differential equations and the like.

Introduction to Linear Algebra (5th Edition)

— By Gilbert Strang

A 500-page linear algebra classic by one of most sought-after educator in the field. It features conversational-style narratives, review sections and challenge problems, all of the while maintaining a focus on geometric intuition and real-life applications.

• System of linear equations
• Vector space
• Orthogonality
• Determinant
• Eigenvector
• Singular value decomposition
• Linear transformation

Calculus (8th Edition)

— By James Stewart

An accessible, ultra-comprehensive textbook on almost everything calculus has to offer . 30 years in the making, and strikes a balance between applicability and rigor. Each section comes with a motivating discussion, followed by several solved examples and many problem sets afterwards.

• Derivatives
• Derivative applications
• Integration techniques
• Partial derivatives
• Multiple integrals
• Lagrange multipliers
• Divergence / Curl
• Applications of integrals
• Differential equations

Probability   & Statistics

Discrete/continuous distributions,  hypothesis testing, analysis of variance, Bayesian inference and more.

Statistics (13th Edition)

— By James McClave and Terry Sincich

A comprehensive, time-tested, non-calculus-based textbook on much of what applied statistics has to offer. It's accessible to almost anyone with a background in high-school math, and features a wide range of explanations, examples, sample problems and exercises to choose from.

• Descriptive statistics
• Basic probability
• Probability distributions
• Confidence interval
• Hypothesis testing
• Analysis of variance
• Linear regression
• Categorical data analysis
• Non-parametric statistics

Mathematical Statistics with Applications (7th Edition)

— By Dennis Wackerly , William Mendenhall and Richard Scheaffer

A solid, calculus-based textbook on probability and statistics from the mathematical point of view. It strikes a good balance between theory and applications, while featuring a wide range of problems to further solidify the mechanics and the understanding of concepts and theorems.

• Moment-generating functions
• Law of large numbers
• Central Limit Theorem
• Methods of estimation
• Bayesian inference

Introduction to Proof

Basic logic,  proof techniques and their applications in higher mathematics.

How to Read and Do Proof : An Introduction to Mathematical Thought Processes (6th Edition)

— By Daniel Solow

A unique, 170-page book with a systematic approach in identifying, categorizing and explaining a mathematical proof and its making. Written in accessible conversational style, it also features 15 video lectures and the solution manual on its student companion website .

• Forward-backward method
• Construction method
• Choose method
• Generalisation
• Unification
• Dual representation
• Abstraction

How to Prove It : A Structured Approach (2nd Edition)

— By Daniel Velleman

A 300-page classic which takes a reader from not knowing what a proof is, to being able to carry out one proficiently. Notable features include conversational-style instructions, extensive proof illustrations and gently-crafted exercise sets. Accessible to high school students and beyond.

• Basic logic
• Elementary set theory
• Proof techniques
• Mathematical induction
• Infinite sets
• Schröder–Bernstein theorem

Proof-Based  Algebra

Abstract algebra,  proof-based linear algebra and other goodness.

Elements of Modern Algebra   (8th Edition)

— By Linda Gilbert

An accessible, time-tested textbook on first-year abstract algebra , featuring neat formatting, clear presentation, and a surprising amount of examples both within and after a section. Ideal for both self-study and reference purpose.

• Integral domain
• Complex number

Linear Algebra Done Right  (3rd Edition)

— By Sheldon Axler

A unique 250-page textbook covering second-year linear algebra through a non-standard route (i.e., without resorting to determinant — which is only covered in the last chapter of the book). The 3rd edition represents a major improvement in terms of both formatting and exercise set expansion.

• Linear mapping
• Inner product space
• Spectral theorem

Geometry &  Topology

Platonic solids,  fractals, manifolds and other highly-visual math.

Introduction to Geometry  (2nd Edition)

— By Richard Rusczyk

A standalone, 500-page textbook on introductory geometry — written by a former winner of USA Mathematical Olympiad. Aside from the concise explanations, it also features 900+ problems which are Useful for developing one's geometric intuition and spatial reasoning skill.

• Similar / Congruent triangles
• Quadrilaterals
• Power of a point
• 3D geometry
• Transformations

Discrete  Mathematics

Number theory,  combinatorics, graph theory... Very discrete.

Discrete Mathematics with Applications (5th Edition)

— By Suzanna Epp

A modern, ultra-comprehensive textbook on much of what discrete mathematics has to offer, featuring clear, accessible explanations along with numerous solved examples and exercise sets.

• Recurrence relation
• Cardinality
• Counting techniques
• Logic c i rcuit
• Algorithmic efficiency
• Finite-state automata

Discrete Mathematics and its Applications (8th Edition)

— By Kenneth Rosen

The de-facto bible in discrete mathematics. Accessible, application-driven and rich in visuals and problem sets.

• Set and logic
• Algorithmic complexity
• Cryptography
• Recursive structure
• Spanning tree
• Boolean algebra
• Logic circuit
• Turing machine
• Structural induction
• Modular arithmetic
• Recurrent relation
• Generating function

Continuous   Mathematics

Real analysis,  complex analysis, numerical analysis — among other "continuous math".

Understanding Analysis (2nd Edition)

— By Stephen Abbott

A solid and accessible textbook that provides a unifying view of first-year real analysis . Each section starts with some historical motivation behind the topic, followed by many engaging examples and thought processes through which a problem can be solved.

• Sequence 
• Point-set topology
• Uniform convergence

Schaum's Outline of Advanced Calculus (3rd Edition)

— By Robert Wrede and Murray Spiegel

A 400-page review guide with 1370+ solved and unsolved problems in anything advanced calculus . While not suitable as a first text, it's nonetheless very useful for people who want to hone in their advanced calculus skill in a very efficient and cost-effective manner.

• Sequence and series
• Function and limit
• Partial derivative
• Multiple integral
• Line integral
• Surface integral
• Integral theorems
• Improper integral
• Fourier series
• Gamma / Beta functions
• Complex-variable function

Complex Variables with Applications (3rd Edition)

— By David Wunsch

A unique textbook which demystifies complex analysis through a series of clear presentations, accessible discussions,  solved examples and problem sets. Ideal for students in engineering and other applied sciences.

• Complex transcendental functions
• Analyticity 
• Contour integration
• Cauchy integral formula
• Laurent series
• Residue mapping
• Conformal mapping

Numerical Analysis (3rd Edition)

— By Timothy Sauer

A neatly-formatted, well-organized textbook on the various aspects of numerical analysis . It strikes a fine balance between theory and applicability, and features clear expositions, solved examples and relevant MATLAB codes throughout the text.

• Numerical root-finding
• Interpolation 
• Least-square methods
• Numerical differentiation
• Numerical integration
• Numerical ODE methods
• Numerical PDE methods

Set Theory & Mathematical Logic

First-order logic,  proof systems, meta-theory and other foundation stuffs.

A Concise Introduction to Logic   (12th Edition)

— By Patrick Hurley

A comprehensive, mostly-non-technical survey on critical thinking and the various forms of logic in our daily routines, with Part II of the book dedicated to the development of formal logic and other math-based reasoning.

• Propositional logic
• Predicate logic
• Natural deduction
• Rules of inference
• Inductive reasoning
• Legal reasoning
• Probabilistic reasoning
• Statistical reasoning

Language, Proof and Logic  (2nd Edition)

— By David Barker-Plummer , Jon Barwise  and John Etchemendy  

A comprehensive, accessible textbook on first-order logic and its associated meta-theory. It's based on the proof system Fitch and covers logic at both introductory and intermediate levels (for students majoring in philosophy).

• Formal / informal translations
• Truth table
• Fitch system
• Axiomatic set theory
• Löwenheim-Skolem Theorem
• Compactness theorem
• Gödel's Incompleteness Theorems

The awesome document-preparation system for typesetting math and other scientific goodness.

LaTeX Beginner's Guide

— By Stefan Kottwitz

A standalone, 300-page guide that teaches introductory LaTeX  through short explanations and examples. It strikes a good balance between breadth and depth, and ensures that by the end of the book, the reader will be able to produce a professionally-typeset document on their own.

• Installing LaTeX distribution
• Formatting text
• Designing page layout
• Customizing lists
• Float environments
• Cross - reference
• Typesetting math
• Adjusting font

More Math Into LaTeX  (5th Edition)

— By George Grätzer

A most up-to-date ( ours aside of course ), comprehensive LaTeX manual that goes into the nuts and bolts of mathematical typesetting . Two decades in the making, with some notable features being the amount of examples (e.g., code vs. its output) and the dos and don'ts.

• Page layout
• Math expressions
• Proclamation
• Bibliography

• Grades 6-12
• School Leaders

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58 Amazing Math Books for Young Mathematicians

You can count on them loving these reads.

Math students often have a hard time understanding abstract math concepts. Enhancing your lessons with books about math for kids will help make connections while having fun in the process. Motivate your students while introducing new concepts, reinforcing ideas, and talking about all things math with some of our favorite books. We have you covered through the year with lots of elementary math topics using these children’s math books.

Sorting & Patterns

1. The Animals Would Not Sleep! by Sara Levine

Marco needs to get his stuffed animals organized before bedtime. He tries sorting them in lots of different ways, but they just won’t settle down. Kids will be clamoring to give him ideas!

Buy it: The Animals Would Not Sleep! at Amazon

2. Seeing Symmetry by Loreen Leedy

A beautifully illustrated book about math that shows how flips, slides, and turns can create amazing symmetrical images.

Buy it: Seeing Symmetry at Amazon

3. Pitter Pattern by Joyce Hesselberth

Definitely add this to your list of children’s math books to introduce patterns. This fiction and nonfiction hybrid covers many types of patterns, including simple visual patterns, sound patterns, patterns in nature, and more.

Buy it: Pitter Pattern at Amazon

4. Math at the Art Museum by Group Majoongmul

A little boy thinks his dad is telling a tall tale when he says elements of math are found in the art world. His mind is blown when he visits his local art museum with his family. Children’s math books help prove math is everywhere!

Buy it: Math at the Art Museum at Amazon

Addition & Subtraction

5. Ten on a Twig by Lo Cole

Ten adorably colorful birds sit happily on a branch—until they begin to fall off one by one! Subtraction is a hard concept to introduce to young kids, but this story makes it nice and concrete.

Buy it: Ten on a Twig  at Amazon

6. Six-Dinner Sid by Inga Moore

If you are a cat person, you know felines are smart little creatures. Sid tricks six separate neighbors into thinking he belongs to each household, receiving six dinners every night. Will they figure out his little secret?

Buy it: Six-Dinner Sid at Amazon

7. Monster Math by Anne Miranda

This cute children’s math book starts with a little monster patiently waiting for guests to arrive at the birthday party. As more and more arrive, kids can use addition skills to keep track. Once there are 50 guests, Monster Mom has had enough, and they begin to leave. This, of course, lends to using subtraction skills.

Buy it: Monster Math at Amazon

8. If You Were a Minus Sign by Trisha Speed Shaskan

This cute, colorful book meets the objective of teaching young students to comprehend their signs in math. This book is a great introduction to subtraction, which is necessary to continue building on throughout students’ math careers.

Buy it: If You Were a Minus Sign at Amazon

9., 10., & 11.: Math Is CATegorical Series by Brian P. Cleary

Rhyming text filled with funny, countable examples introduces basic math concepts for young readers and reveals that sometimes math is easier to show than explain. Pairing clever rhyming verse with comical cartoon cats, Brian P. Cleary and illustrator Brian Gable help children add up just how fun math can be.

Buy it: The Action of Subtraction , The Mission of Addition , How Long or How Wide? A Measuring Guide at Amazon

12. Money Math: Addition and Subtraction by David A. Adler

In this fun introduction to American currency, multiple past presidents introduce themselves and their denominations. Readers will learn about who is on each coin and bill, and what they’re worth—and how many of one it takes to add up to another.

Buy it: Money Math: Addition and Subtraction at Amazon

13. Alexander, Who Used To Be Rich Last Sunday by Judith Viorst

Alexander is given a dollar by his grandparents. As he stretches his imagination on how to spend it, count along with him. Kids will laugh while seeing the obstacles he faces along the way!

Buy it: Alexander, Who Used To Be Rich Last Sunday at Amazon

14. Lemonade in Winter: A Book About Two Kids Counting Money by Emily Jenkins

Follow a brother and sister team as they set out to make some money on a cold winter’s day. While lemonade may not be the best idea for the weather, they learn a good lesson about buying and selling goods. Count along with them as they try to make a profit.

Buy it: Lemonade in Winter: A Book About Two Kids Counting Money at Amazon

15. A Dollar, a Penny, How Much and How Many? by Brian P. Cleary

Learn all about different coins and bills in our currency system. Then count along with the help of fun rhymes and silly mathematician cat characters!

Buy it: A Dollar, a Penny, How Much and How Many? at Amazon

16., 17., & 18. Triangle, Square, and Circle by Mac Barnett

Kids love the humor and whimsical illustrations in the sassy stories in the Shapes trilogy. Great for talking about the attributes of different geometric shapes in a fun context.

Buy it: Triangle , Square , and Circle at Amazon

19. The Greedy Triangle by Marilyn Burns 

Triangle is a busy shape! However, he is bored with the same routines. He asks the shapeshifter for another side and goes on adventures. This pattern continues until he no longer can keep track of himself. This is a great geometry book, and it also teaches a valuable life lesson. 

Buy it: The Greedy Triangle at Amazon

20. Grandfather Tang’s Story by Ann Tompert

This Chinese folktale uses tangram shapes to bring the animal characters to life. Grab a class set of tangram puzzles and have your students create the different animals in the story as you read it.

Buy it: Grandfather Tang’s Story at Amazon

21. Circle Loves Pi: A Pi Day Story by Vea Lewis 

Circle is a tough shape to measure. However, when his buddy Pi is around, circumference, volume, and area are a breeze to compute!

Buy it: Circle Loves Pi: A Pi Day Story at Amazon

22. Which One Doesn’t Belong? by Christopher Danielson

Keep the mathematical talk going by talking about attributes of shapes and how they are the same and different. Observations about the shapes on each page can go in many different directions.

Buy it: Which One Doesn’t Belong? at Amazon

23. Sir Cumference and the First Round Table  by Cindy Neuschwander

Brave knights, a strong ruler, and a dilemma that needs to be solved using math. Great for introducing geometry concepts in a fun and accessible way.

Buy it: Sir Cumference and the First Round Table at Amazon

24. Two of Everything by Lily Toy Hong

Mr. Haktuk is working in his garden when he digs up an ancient pot. He and his wife soon learn it is a magical pot. They fill their hut with gold, excited that their luck has changed. When they both fall into the pot, the real trouble begins!

Buy it: Two of Everything at Amazon

25. How Many? (Talking Math) by Christopher Danielson

This really is “a different kind of counting book”! Each page has a thought-provoking photo in which readers decide what and how to count. If you’re looking for children’s math books to get interesting number talks flowing, this is it!

Buy it: How Many? (Talking Math) at Amazon

26. Billions of Bricks: A Counting Book About Building by Kurt Cyrus

Watch as this busy construction crew creates impressive structures by grouping bricks by twos, fives, and tens. Kids will love the catchy repetitive verse and charming illustrations.

Buy it: Billions of Bricks: A Counting Book About Building at Amazon

27. Counting on Fall by Lizann Flatt

As young readers journey into the natural world, they will discover numbers, patterns, shapes, and more. The colorful, collage style of the book will engage both children and adults.

Buy it: Counting on Fall at Amazon

28. Mrs. Wiggles and the Numbers by Lisa Konkol

Mrs. Wiggles is the best way to introduce children to the world of math. Bold and vibrant numbers combined with catchy rhymes make it easy to keep children entertained.

Buy it: Mrs. Wiggles and the Numbers at Amazon

29. Pebbles and the Biggest Number by Joey Benun

A daring butterfly travels the world searching for the biggest number in a picture book filled with fun and facts. This is an entertaining way to teach kids about numbers larger than they could even imagine.

Buy it: Pebbles and the Biggest Number at Amazon

Measurement

30. Inch by Inch by Leo Lionni

Follow the adventures of an adorable inchworm as he measures different body parts of his animal friends. When a bird threatens to eat the inchworm if he can’t measure an intangible item, he gets creative. Kids love the colorful and whimsical artwork common to Lionni’s books.

Buy it: Inch by Inch at Amazon

31. How Tall? Wacky Ways To Compare Height by Mark Weakland

This wacky, laugh-out-loud introduction to height shows kids an easier way to understand measuring. The rhyming text makes it perfect for a read-aloud or to entertain young ones.

Buy it: How Tall? Wacky Ways To Compare Height at Amazon

Place Value

32. Place Value by David A. Adler

Love the story about monkeys jumping on the bed? You’ll adore this version that tells the story of the monkeys at Banana Cafe making one very large banana cupcake.

Buy it: Place Value at Amazon

33. Sir Cumference and All the King’s Tens: A Math Adventure by Cindy Neushwander 

Sir Cumference and his friends are back! This time, they are busy working with place value and counting by tens. When tens, hundreds, and eventually thousands of unanticipated guests show up for King Arthur’s birthday, they need to figure out how to feed everyone ASAP!

Buy it: Sir Cumference and All the King’s Tens: A Math Adventure at Amazon

Area and Perimeter

34. Spaghetti and Meatballs for All! by Marilyn Burns

Mr. and Mrs. Comfort are having a family reunion and need to arrange the tables so that everyone in the family can enjoy their fabulous spaghetti and meatballs. A witty tale by math guru Marilyn Burns.

Buy it: Spaghetti and Meatballs for All! at Amazon

35. Perimeter, Area, and Volume: A Monster Book of Dimensions by David A. Adler

Let’s go to the movies! Find the perimeter, area, and volume of movie theater staples with assistance from a cast of cute movie monster friends. 

Buy it: Perimeter, Area, and Volume at Amazon

Number Sense

36. Infinity and Me by Kate Hosford

Delightful illustrations and a dreamy young girl pondering the vastness of the universe make a very difficult concept approachable and interesting.

Buy it: Infinity and Me at Amazon

37. A Very Improbable Story by Edward Einhorn

Ethan wakes up one morning with a strange cat on his head, and the only way it will agree to get off is if Ethan agrees to play a game of probability with it. This kooky book will entertain your students as it teaches a difficult concept.

Buy it: A Very Improbable Story at Amazon

38. Zero the Hero by Joan Holub

Kids will love this fun story with delightful cartoon illustrations by Tom Lichtenheld that teach the importance of zero as a placeholder in our number system. Without Zero the Hero, we wouldn’t be able to count beyond the number nine!

Buy it: Zero the Hero at Amazon

39. Equal Shmequal by Virginia Kroll

Mouse and her friends want to play a game of tug-of-war but have a hard time making the sides fair. This charming story teaches the concept of balance and equality.

Buy it: Equal Shmequal at Amazon

40. & 41. One Odd Day and My Even Day by Doris Fisher and Dani Sneed

Two more rhyming tales with colorful, busy illustrations that kids will love. In each of these children’s math books, a boy wakes up one day and finds that things are kookily out of order. Great as read-alouds or for independent readers who will love hunting through the detailed pictures to find the odd or even items.

Buy it: One Odd Day and My Even Day at Amazon

42. How Much Is a Million? by David M. Schwartz

Children’s math books are especially helpful when demonstrating very large numbers since it shows a visual picture. Kids love hearing about the numbers in the millions, billions, and trillions, so this book will add to the excitement. With a mystical main character named Marvelossissimo the Magician and illustrations by Steven Kellogg, this book is beyond memorable.

Buy it: How Much Is a Million? at Amazon

Telling Time

43. A Second, a Minute, a Week With Days in It: A Book About Time by Brian P. Cleary

A playful book with silly characters and perfect rhyming that teaches not just the basics of telling time but the tricky concept of relative time.

Buy it: A Second, a Minute, a Week With Days in It at Amazon

44. If You Were a Minute by Tricia Speed Shaskan

How long is a minute, really, when trying to make sense of time? Kids can look at a clock and read the time, but this book helps them understand what can be done in different amounts of time to build deeper meaning. It is never too early to introduce time management skills.

Buy it: If You Were a Minute at Amazon

Division and Fractions

45. A Remainder of One by Elinor Pinczes

The 25th Beetle Army Corp is trying to solve the problem of how to divide their troops into equal groups for the parade march without leaving any stragglers. A fun rhyming book about math that will get kids thinking about how numbers are put together and pulled apart.

Buy it: A Remainder of One  at Amazon

46. The Great Divide: A Mathematical Marathon by Dayle Ann Dodds

At the beginning of the story, 80 contestants are ready to compete in the Great Divide. Dangers lie ahead at every turn, causing more and more runners to leave the competition. Who will be left at the end and survive the obstacles?

Buy it: The Great Divide: A Mathematical Marathon at Amazon

47. The Hershey’s Milk Chocolate Fractions Book by Jerry Pallotta

Incorporating children’s math books with tasty treats is a surefire way to get kids’ attention. Hershey’s chocolate bars are made up of 12 rectangles. Pass out a chocolate bar to each student. Then, use them with this book for a delicious, hands-on fractions lesson.

Buy it: The Hershey’s Milk Chocolate Fraction Book at Amazon

48. If You Were a Divided-By Sign by Trisha Speed Shaskan 

Celebrate a love of language and math with this book that includes a whimsical cast of characters to engage curious minds. Each set of problems introduces basic concepts using simple text and enhances the learning with silly and unexpected examples.

Buy it: If You Were a Divided-By Sign at Amazon

49. Fractions in Disguise by Edward Einhorn 

If you are looking for a fun way to teach your students about reducing fractions, look no further. When a valuable fraction goes missing, George Cornelius Factor (aka GCF) immediately is on the case. He knows if he continues to reduce fractions, he will eventually solve the mystery.

Buy it: Fractions in Disguise at Amazon

50. Math for Minecrafters: Adventures in Multiplication & Division by Amanda Brack

This kid-friendly workbook features well-loved video game characters and concepts to reinforce the development of 3rd and 4th grade math skills. Puzzles use familiar items from Minecraft like diamond swords, suits of armor, zombies, and magical potions to encourage math practice in gamers.

Buy it: Math for Minecrafters: Adventures in Multiplication & Division at Amazon

Problem-Solving

51. The Grapes of Math by Greg Tang

Good children’s math books hone in on problem-solving, identifying patterns, symmetry, and grouping. This one uses all four concepts to help students count in groups, instead of going one by one. Your students will think out of the box as they come up with ways to solve each math riddle. Watch the enthusiasm grow bigger with each turn of the page!

Buy it: The Grapes of Math at Amazon

52. One Grain of Rice: A Mathematical Folktale by Demi

In this Indian folktale, a greedy raja keeps all of the rice for himself. As the rest of the village starves, a clever girl named Rani devises a plan. She makes a deal to receive one grain of rice, doubled, for 30 days. As time passes, over 1 billion grains of rice become available for all of the villagers to share. Problem-solving, along with multiplication, are a big part of this book. At the same time, the valuable lessons of fairness and sharing shine through.

Buy it: One Grain of Rice at Amazon

53. Seven Golden Rings by Rajani LaRocca

This story of a clever young boy in ancient India can be enjoyed on many levels. Bhagat must figure out how to stretch his family’s only fortune, seven golden rings, as far as possible—which leads to some creative mathematical thinking! To engage older students, use the afterword to introduce how to write numbers in binary.

Buy it: Seven Golden Rings at Amazon

54. Math-terpieces: The Art of Problem-Solving by Greg Tang

Help students master important skills while also gaining exposure to some of the world’s most famous paintings. This book focuses on grouping numbers and creating different combinations using visuals.

Buy it: Math-terpieces: The Art of Problem-Solving at Amazon

55. Math Curse by Jon Scieszka

The main character of this children’s math book wakes up one morning only to find she has been placed under a math curse! Follow her through her day as she faces a different math problem everywhere she goes, while just carrying on with ordinary, daily activities. 

Buy it: Math Curse at Amazon

56. The Chicken Problem by Jennifer Oxley

Peg and Cat are enjoying a picnic lunch on the farm, until it is interrupted by chaos; the chickens have escaped the coop! Help them solve mathematical problems in order to restore the peace. 

Buy it: The Chicken Problem at Amazon

57. Problem-Solving Ninja by Mary Nhin

The Ninja Life Hacks series introduces pint-size characters in comedic books easy enough for young readers, yet witty enough for adults. This colorful book is perfect to teach about a growth mindset.

Buy it: Problem-Solving Ninja at Amazon

58. The Best of Times: Math Strategies That Multiply by Greg Tang

In this book, author Greg Tang takes on the times tables, teaching kids innovative ways to multiply numbers and derive answers without the need for memorization. This is one of the best children’s math books because it uses a simple, sing-song formula to allow kids to understand clever math strategies.

Buy it: The Best of Times: Math Strategies That Multiply at Amazon

Did you love these books about math for kids? Check out Second Grade Math Word Problems of the Day .

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20 Effective Math Strategies To Approach Problem-Solving 

Katie Keeton

Math strategies for problem-solving help students use a range of approaches to solve many different types of problems. It involves identifying the problem and carrying out a plan of action to find the answer to mathematical problems.  

Problem-solving skills are essential to math in the general classroom and real-life. They require logical reasoning and critical thinking skills.  students must be equipped with strategies to help them find solutions to problems.

This article explores mathematical problem solving strategies, logical reasoning and critical thinking skills to help learners with solving math word problems independently in real-life situations. 

What are problem-solving strategies?

Problem-solving strategies in math are methods students can use to figure out solutions to math problems. Some problem-solving strategies: 

• Draw a model
• Use different approaches
• Check the inverse to make sure the answer is correct

Students need to have a toolkit of math problem-solving strategies at their disposal to provide different ways to approach math problems. This makes it easier to find solutions and understand math better. 

Strategies can help guide students to the solution when it is difficult ot know when to start.

The ultimate guide to problem solving techniques

Download these ready-to-go problem solving techniques that every student should know. Includes printable tasks for students including challenges, short explanations for teachers with questioning prompts.

20 Math Strategies For Problem-Solving

Different problem-solving math strategies are required for different parts of the problem. It is unlikely that students will use the same strategy to understand and solve the problem. 

Here are 20 strategies to help students develop their problem-solving skills. 

Strategies to understand the problem

Strategies that help students understand the problem before solving it helps ensure they understand: 

• The context
• What the key information is
• How to form a plan to solve it

Following these steps leads students to the correct solution and makes the math word problem easier .

Here are five strategies to help students understand the content of the problem and identify key information. 

1. Read the problem aloud

Read a word problem aloud to help understand it. Hearing the words engages auditory processing. This can make it easier to process and comprehend the context of the situation.

2. Highlight keywords 

When keywords are highlighted in a word problem, it helps the student focus on the essential information needed to solve it. Some important keywords help determine which operation is needed.  For example, if the word problem asks how many are left, the problem likely requires subtraction.  Ensure students highlight the keywords carefully and do not highlight every number or keyword. There is likely irrelevant information in the word problem.

3. Summarize the information

Read the problem aloud, highlight the key information and then summarize the information. Students can do this in their heads or write down a quick summary.  Summaries should include only the important information and be in simple terms that help contextualize the problem.

4. Determine the unknown

A common problem that students have when solving a word problem is misunderstanding what they are solving. Determine what the unknown information is before finding the answer.  Often, a word problem contains a question where you can find the unknown information you need to solve. For example, in the question ‘How many apples are left?’ students need to find the number of apples left over.

5. Make a plan

Once students understand the context of the word problem, have dentified the important information and determined the unknown, they can make a plan to solve it.  The plan will depend on the type of problem. Some problems involve more than one step to solve them as some require more than one answer.  Encourage students to make a list of each step they need to take to solve the problem before getting started.

Strategies for solving the problem 

1. draw a model or diagram.

Students may find it useful to draw a model, picture, diagram, or other visual aid to help with the problem solving process.  It can help to visualize the problem to understand the relationships between the numbers in the problem. In turn, this helps students see the solution.

Similarly, you could draw a model to represent the objects in the problem:

2. Act it out

This particular strategy is applicable at any grade level but is especially helpful in math investigation in elementary school . It involves a physical demonstration or students acting out the problem using movements, concrete resources and math manipulatives .  When students act out a problem, they can visualize and contectualize the word problem in another way and secure an understanding of the math concepts.  The examples below show how 1st-grade students could “act out” an addition and subtraction problem:

3. Work backwards

Working backwards is a popular problem-solving strategy. It involves starting with a possible solution and deciding what steps to take to arrive at that solution.  This strategy can be particularly helpful when students solve math word problems involving multiple steps. They can start at the end and think carefully about each step taken as opposed to jumping to the end of the problem and missing steps in between.

For example,

To solve this problem working backwards, start with the final condition, which is Sam’s grandmother’s age (71) and work backwards to find Sam’s age. Subtract 20 from the grandmother’s age, which is 71.  Then, divide the result by 3 to get Sam’s age. 71 – 20 = 51 51 ÷ 3 = 17 Sam is 17 years old.

4. Write a number sentence

When faced with a word problem, encourage students to write a number sentence based on the information. This helps translate the information in the word problem into a math equation or expression, which is more easily solved.  It is important to fully understand the context of the word problem and what students need to solve before writing an equation to represent it.

5. Use a formula

Specific formulas help solve many math problems. For example, if a problem asks students to find the area of a rug, they would use the area formula (area = length × width) to solve.   Make sure students know the important mathematical formulas they will need in tests and real-life. It can help to display these around the classroom or, for those who need more support, on students’ desks.

Strategies for checking the solution 

Once the problem is solved using an appropriate strategy, it is equally important to check the solution to ensure it is correct and makes sense. 

There are many strategies to check the solution. The strategy for a specific problem is dependent on the problem type and math content involved.

Here are five strategies to help students check their solutions. 

1. Use the Inverse Operation

For simpler problems, a quick and easy problem solving strategy is to use the inverse operation. For example, if the operation to solve a word problem is 56 ÷ 8 = 7 students can check the answer is correct by multiplying 8 × 7. As good practice, encourage students to use the inverse operation routinely to check their work. 

2. Estimate to check for reasonableness

Once students reach an answer, they can use estimation or rounding to see if the answer is reasonable.  Round each number in the equation to a number that’s close and easy to work with, usually a multiple of ten.  For example, if the question was 216 ÷ 18 and the quotient was 12, students might round 216 to 200 and round 18 to 20. Then use mental math to solve 200 ÷ 20, which is 10.  When the estimate is clear the two numbers are close. This means your answer is reasonable. 

3. Plug-In Method

This method is particularly useful for algebraic equations. Specifically when working with variables.  To use the plug-in method, students solve the problem as asked and arrive at an answer. They can then plug the answer into the original equation to see if it works. If it does, the answer is correct.

If students use the equation 20m+80=300 to solve this problem and find that m = 11, they can plug that value back into the equation to see if it is correct. 20m + 80 = 300 20 (11) + 80 = 300 220 + 80 = 300 300 = 300 ✓

4. Peer Review

Peer review is a great tool to use at any grade level as it promotes critical thinking and collaboration between students. The reviewers can look at the problem from a different view as they check to see if the problem was solved correctly.   Problem solvers receive immediate feedback and the opportunity to discuss their thinking with their peers. This strategy is effective with mixed-ability partners or similar-ability partners. In mixed-ability groups, the partner with stronger skills provides guidance and support to the partner with weaker skills, while reinforcing their own understanding of the content and communication skills.  If partners have comparable ability levels and problem-solving skills, they may find that they approach problems differently or have unique insights to offer each other about the problem-solving process.

5. Use a Calculator

A calculator can be introduced at any grade level but may be best for older students who already have a foundational understanding of basic math operations. Provide students with a calculator to allow them to check their solutions independently, accurately, and quickly. Since calculators are so readily available on smartphones and tablets, they allow students to develop practical skills that apply to real-world situations.  

Step-by-step problem-solving processes for your classroom

In his book, How to Solve It , published in 1945, mathematician George Polya introduced a 4-step process to solve problems. 

Polya’s 4 steps include:

• Understand the problem
• Devise a plan
• Carry out the plan

Today, in the style of George Polya, many problem-solving strategies use various acronyms and steps to help students recall. 

Many teachers create posters and anchor charts of their chosen process to display in their classrooms. They can be implemented in any elementary, middle school or high school classroom. 

Here are 5 problem-solving strategies to introduce to students and use in the classroom.

How Third Space Learning improves problem-solving 

Resources .

Third Space Learning offers a free resource library is filled with hundreds of high-quality resources. A team of experienced math experts carefully created each resource to develop students mental arithmetic, problem solving and critical thinking. 

Explore the range of problem solving resources for 2nd to 8th grade students. 

One-on-one tutoring 

Third Space Learning offers one-on-one math tutoring to help students improve their math skills. Highly qualified tutors deliver high-quality lessons aligned to state standards. 

Former teachers and math experts write all of Third Space Learning’s tutoring lessons. Expertly designed lessons follow a “my turn, follow me, your turn” pedagogy to help students move from guided instruction and problem-solving to independent practice. 

Throughout each lesson, tutors ask higher-level thinking questions to promote critical thinking and ensure students are developing a deep understanding of the content and problem-solving skills.

Problem-solving

Educators can use many different strategies to teach problem-solving and help students develop and carry out a plan when solving math problems. Incorporate these math strategies into any math program and use them with a variety of math concepts, from whole numbers and fractions to algebra. 

Teaching students how to choose and implement problem-solving strategies helps them develop mathematical reasoning skills and critical thinking they can apply to real-life problem-solving.

READ MORE : 8 Common Core math examples

There are many different strategies for problem-solving; Here are 5 problem-solving strategies: • draw a model  • act it out  • work backwards  • write a number sentence • use a formula

Here are 10 strategies of problem-solving: • Read the problem aloud • Highlight keywords • Summarize the information • Determine the unknown • Make a plan • Draw a model  • Act it out  • Work backwards  • Write a number sentence • Use a formula

1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back

Some strategies you can use to solve challenging math problems are: breaking the problem into smaller parts, using diagrams or models, applying logical reasoning, and trying different approaches.

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Differentiated Instruction: 9 Differentiated Curriculum And Instruction Strategies For Teachers 

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12 Best Problem Solving Books to Read in 2024

You found our list of top problem solving books .

Problem solving books are guides that improve critical thinking capability and the ability to resolve issues in the workplace. These works cover topics like bias and logical fallacies, problem prevention, and prioritizing. The purpose of these books is to help workers remain calm under pressure and come up with solutions more quickly.

These guides are similar to decision making books , negotiation books , and conflict resolution books . To improve competency in this area, one can also play problem solving games .

This list includes:

• problem solving books for adults
• creative problem solving books
• business problem solving books
• problem solving books for programmers

Here we go!

List of problem solving books

Here is a list of books to improve problem solving skills in the workplace.

1. Fixed: How to Perfect the Fine Art of Problem Solving by Amy E Herman

Fixed is one of the most useful new books on problem solving. The book calls for problem solvers to look beyond instinctual and obvious answers and provides a framework for more creative thinking. While most folks think about problem solving in terms of logic, reason, and disciplines like math and science, this book shows the role that art and imagination play in the process. Amy Herman consulted on leadership training with Silicon Valley companies and military organizations and brings this expertise into the text to train readers on how to adopt a more innovative critical thinking approach.

Notable Quote: “Working through problems is critical for productivity, profit, and peace. Our problem-solving skills, however, have been short-circuited by our complicated, technology-reliant world.”

Read Fixed .

2. Cracked it!: How to solve big problems and sell solutions like top strategy consultants by Bernard Garrette, Corey Phelps, and Olivier Sibony

Cracked it! is one of the best creative problem solving books. Drawing inspiration from the tactics of consultants, this guide is a practical playbook for approaching business problems. The authors outline a “4S” method– State – Structure – Solve – Sell– to tackle obstacles and get support from stakeholders. While many problem solving books simply focus on how to think through issues, this guide also demonstrates how to gain approval for ideas and get others onboard with the solution. The book explains how to best use these techniques, and presents case studies that show the theories in action. Cracked it! is a handy reference for any professional that faces tough challenges on the regular.

Notable Quote: “If you want to know how a lion hunts, don’t go to a zoo. Go to the jungle.”

Read Cracked it!

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3. Upstream: The Quest to Solve Problems Before They Happen by Dan Heath

Upstream takes a proactive approach to problem solving. The book urges readers to not only be responsive to issues, but also try to prevent obstacles from occurring. The guide opens with an exploration of “problem blindness,” and the psychological factors that cause folks to be oblivious to issues, along with a reminder that many problems are more controllable and avoidable than first assumed. The pages that follow outline a series of questions leaders can ask to fine-tune the system and steer clear of major headaches, for instance, “How Will You Unite the Right People?” and “How Will You Avoid Doing Harm?” Upstream is full of real world examples of how minor tweaks achieved major results and allowed organizations to sidestep serious holdups.

Notable Quote: “The postmortem for a problem can be the preamble to a solution.”

Read Upstream .

4. Problem Solving 101: A Simple Book for Smart People by Ken Watanabe

Problem Solving 101 is one of the most fun problem solving books for adults. Written by Ken Watanabe, the guide draws on Japanese philosophy as well as the author’s experience as a consultant at McKinsey to help readers understand and approach problems in productive ways. The pages provide blueprints for problem-solving methods such as logic trees and matrixes, and include scenarios and illustrations that help readers visualize the process more clearly. Problem Solving 101 breaks down the problem solving procedure into the most basic parts and lays out step-by-step instructions for choosing the best action in any situation.

Notable Quote: “When you do take action, every result is an opportunity to reflect and learn valuable lessons. Even if what you take away from your assessment seems to be of small consequence, all of these small improvements taken together make a huge difference in the long term.”

Read Problem Solving 101 .

5. What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve by Thomas Wedell-Wedellsborg

What’s Your Problem? insists that the most important step in the problem solving process is to start by honing in on the correct problem. The root of much frustration and wasted efforts is that professionals often pick the wrong points to focus on. This book teaches readers how to reframe and approach issues from a different perspective. The guide outlines a repeatable three step process “Frame, Reframe, and Move Forward” to ensure that workers prioritize effectively and stay on track to achieve desired results. What’s Your Problem? teaches professionals of all levels how to be less rigid and more results-focused and adopt a more agile approach to fixing issues.

Notable Quote: “The problems we’re trained on in school are often quite different from the ones we encounter in real life.”

Read What’s Your Problem?

6. Sprint: How to Solve Big Problems and Test New Ideas in Just Five Days by Jake Knapp, John Zeratsky, et al

Sprint is one of the best problem solving books for programmers. The authors are the creators of the five-day-process at Google. This guide describes best practices for conducting sprints and solving problems in limited timeframes. The book provides a day-by-day breakdown of tasks for each day of the workweek, with the final steps being designing a prototype and a plan for implementation. Though this idea originated in the tech world and is most widely used in the software industry, this problem-solving and product design approach can be useful for any position that needs to find fixes in a time crunch.

Notable Quote: “We’ve found that magic happens when we use big whiteboards to solve problems. As humans, our short-term memory is not all that good, but our spatial memory is awesome. A sprint room, plastered with notes, diagrams, printouts, and more, takes advantage of that spatial memory. The room itself becomes a sort of shared brain for the team.”

Read Sprint , and check out this guide to virtual hackathons and this list of product design books .

7. Think Like a Rocket Scientist: Simple Strategies You Can Use to Make Giant Leaps in Work and Life by Ozan Varol

Think Like a Rocket Scientist lays out formulas and instructions for thinking more strategically. The guide reveals common problem solving approaches used by rocket scientists when exploring the unknown and testing new technology. The book is split into three sections– launch, accelerate, and achieve– with deep dives into concepts such as moonshot thinking and overcoming failure. The anecdotes revolve around space exploration and rocket science yet the methods can be applied to more commonplace and less complex problems as well. Think Like a Rocket Scientist proves that one does not need to be a genius to be a genius problem solver and lets readers learn tricks from one of the most complex professions on the planet.

Notable Quote: “Critical thinking and creativity don’t come naturally to us. We’re hesitant to think big, reluctant to dance with uncertainty, and afraid of failure. These were necessary during the Paleolithic Period, keeping us safe from poisonous foods and predators. But here in the information age, they’re bugs.”

Read Think Like a Rocket Scientist .

8. Bulletproof Problem Solving: The One Skill That Changes Everything by Charles Conn and Robert McLean

Bulletproof Problem Solving is one of the best business problem solving books. This workbook-style-guide breaks down a “bulletproof” method of problem solving favored by consultants at McKinsey. The authors distill the process into seven simple steps–define the problem, disaggregate, prioritize, workplan, analyze, synthesize, and communicate– and give numerous examples of how to follow this cycle with different dilemmas. The chapters explore each stage in depth and outline the importance and finer points of each phase. The book also provides practical tools for readers to build skills, including an appendix with exercise worksheets.

Notable Quote: “Problem solving doesn’t stop at the point of reaching conclusions from individual analyses. Findings have to be assembled into a logical structure to test validity and then synthesized in a way that convinces others that you have a good solution. Great team processes are also important at this stage.”

Read Bulletproof Problem Solving .

9. Think Like a Programmer: An Introduction to Creative Problem Solving by by V. Anton Spraul

Think Like a Programmer is one of the top problem solving books for programmers. The guide lays out methods for finding and fixing bugs and creating clean, workable code. The text emphasizes that programming is not merely a matter of being competent in the language, but also knowing how to troubleshoot and respond to unexpected occurrences. The chapters present examples of problems and puzzles and work through the answers to help strengthen professional competencies. The book provides an introductory crash course and practical toolkit for beginning coders, with a focus on C++. Yet since the text outlines general theory and approach, the book is also helpful for dealing with other programming languages, or for solving problems in non-tech industries as well. The point of the text is to provide a proper mindset and attitude for reacting to these developments, and the book can be a benefit for folks in any field.

Notable Quote: “Don’t Get Frustrated The final technique isn’t so much a technique, but a maxim: Don’t get frustrated. When you are frustrated, you won’t think as clearly, you won’t work as efficiently, and everything will take longer and seem harder. Even worse, frustration tends to feed on itself, so that what begins as mild irritation ends as outright anger.”

Read Think Like a Programmer .

10. The Founder’s Dilemmas: Anticipating and Avoiding the Pitfalls That Can Sink a Startup by by Noam Wasserman

The Founder’s Dilemmas lays out the most common problems entrepreneurs face and gives advice on how to avoid or solve these issues. The book tackles topics such as managing relationships, hiring, and rewarding or correcting employees. The chapters outline the mistakes inexperienced leaders often make and offer strategies for handling these tough situations with more smarts and skill. By reading this book, founders can learn from predecessors and avoid making obvious and avoidable errors in judgment. The Founder’s Dilemmas is a problem-solving resource for startup leaders and team members who lack more traditional guidance.

Notable Quote: “Ideas are cheap; execution is dear.”

Read The Founder’s Dilemmas , and check out more entrepreneurial books .

11. The Scout Mindset: Why Some People See Things Clearly and Others Don’t by Julia Galef

The Scout Mindset challenges readers to move beyond gut reactions and preconceptions and rethink problems. The book offers instructions for overcoming bias and central beliefs to gather more objective data. Julia Galef encourages readers to act more like scouts than soldiers and gather information without judging to make more informed decisions. The text outlines the common reasons folks jump to conclusions and offers advice on how to avoid incorrect assumptions and conduct level-headed analyses. The Scout Mindset is a call to action for objectivity and an instruction manual for breaking away from unhelpful mental patterns that can lead to poor choices.

Notable Quote: “Discovering you were wrong is an update, not a failure, and your worldview is a living document meant to be revised.”

Read The Scout Mindset .

12. Super Thinking: The Big Book of Mental Models by Gabriel Weinberg and Lauren McCann

Super Thinking is a comprehensive resource that explains various mental models for problem solving. The book identifies logical fallacies and shows readers how to avoid these pitfalls. The pages also lay out appropriate strategies, tools, techniques to use in different situations, such as matrices, pointed questions, and philosophies. The point of the guide is to teach readers how to evaluate information and make quick yet accurate judgements. The guide helps readers decide the best approach to use for each circumstance. Though packed with information, the pages also contain images and humor that prevent the material from getting too dry. Super Thinking is the ultimate cheat sheet for thinking rationally and acting with intention.

Notable Quote: “Unfortunately, people often make the mistake of doing way too much work before testing assumptions in the real world.”

Read Super Thinking .

Final Thoughts

Problem solving is one of the most essential skills for modern industry. With the breakneck pace at which the current business world changes, there is no shortage of new developments that professionals must contend with on a daily basis. Operating the same way for years at a time is impossible, and it is almost guaranteed that workers at every level will have issues to unravel at some point in their careers.

Books about problem solving help professionals predict, prevent, and overcome issues and find more viable and sustainable solutions. These guides not only provide skills, but also methods for survival in a highly competitive business landscape. These texts show workers that they are more capable than may first appear and that sometimes, seemingly insurmountable obstacles are beatable with a combination of creativity, teamwork, and proper process.

For more ways to beat the odds, check out this list of books on innovation and this list of books on business strategy .

We also have a list of the best communication books .

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FAQ: Problem solving books

Here are answers to common questions about problem solving books.

What are problem solving books?

Problem solving books are guides that teach critical thinking skills and strategies for resolving issues. The purpose of these works is to help professionals be more creative and strategic in problem solving approaches.

What are some good problem solving books for work?

Some good problem solving books for work include Sprint by Jake Knapp, John Zeratsky, et al, Upstream by Dan Heath, and Think Like a Rocket Scientist by Ozan Varol.

Author: Angela Robinson

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Climate change more like ecosocial crisis, openmind books, scientific anniversaries, kary mullis, the genius of a scientist, the eccentricity of a celebrity, featured author, latest book, solving problems visually.

What’s the best way to approach (and successfully solve) a mathematical problem statement? Perhaps by drawing a picture? That, at least, is the conclusion of a striking new study by researchers at the Universities of Geneva and Burgundy.

It’s not a trivial assumption. It is thought that when we face a mathematical problem that contains both mathematical information (numbers and arithmetic operations) and non-mathematical information (the context of the problem and the characteristics of the entities involved), our brains process this combination of verbal and numerical information and convert it into a mental representation in order to identify the best strategy for solving it. On the other hand, more and more studies suggest that the schematic drawings that are usually made to solve this type of problem are a reflection of these mental representations.

Game 1: Not a game, an experiment

In the study, participants were asked to solve 12 simple arithmetic problems in as few steps as possible and to draw a picture that would help them understand and solve the problem.

Here are two of these problems, and we invite you to solve them in the same way: in as few steps as possible, and with a drawing to help you understand the problem.

Problem 1 : Paul has five red marbles and also has some blue marbles. In total he has eleven marbles. Julie’s marbles are green and blue. Julie has as many blue marbles as Paul and also has two fewer green marbles than Paul has red marbles. How many marbles does Julie have?

Problem 2 : Lisa takes the train during the day, travels for 5 hours and arrives at her destination at 11am. Fred got on the train at the same time as Lisa and his trip took 2 hours less. What time did Fred arrive at his destination?

Independently of the above, many studies postulate that relying on drawings, diagrams or other types of graphical representations when processing information has numerous benefits: it improves our ability to learn and remember, it helps us to understand complex concepts, it reinforces critical and scientific thinking, and it fosters a transversal and interdisciplinary interpretation. And from a mathematical point of view, using these representations makes it easier to establish the relationships between different data, to visualise the information implicit in the statement and to identify the most direct and simplest solution strategy.

Use the drawings to answer these complex and hieroglyphic questions.

A recent study goes a step further by suggesting that the verbal information in the problem statement influences the type of diagram shown and also the strategy chosen to solve the problem. More specifically, the study has found that the type of diagram preferentially chosen depends on whether the statement is cardinal or ordinal in nature.

Thus, when the context alludes to the cardinal properties of the quantities involved—the number of elements in a set—a drawing based on groupings of entities (crosses, circles, etc.) that sometimes overlap (or intersect) is usually chosen. This in turn leads to a three-step arithmetic strategy. On the other hand, when the statement of the problem focuses on the ordinal properties of numbers—the position they occupy in a set—we usually opt for drawings based on axes, graduations or intervals, which lead to a more direct and simpler one-step solution strategy.

And this is observed even when the problems are analogous from a mathematical point of view: they have the same structure, the same numerical values and can be solved with the same strategy (as in the case of the two problems in Game 1).

But perhaps the most interesting reflection is that, knowing this, it is possible to guide and train the student to apply this second type of diagram, thereby facilitating the identification of the best way to solve it.

Game 3:  A high-flying challenge

Sara wants to travel from Madrid to Tokyo. To do so, she flies first to New York, from where she takes a plane to London and from there to Tokyo.

Paul also wants to go from Madrid to Tokyo, but in his case he flies directly from Madrid to London and then takes a flight to Tokyo.

If Sara flies for a total of 27hrs 15min and Paul for 14hrs 30min, and given that the flight from New York to London takes 4hrs 45min longer than the flight from Madrid to London, and the flight from London to Tokyo takes 12 hours, how long is the flight from Madrid to New York?

And if both Sara and Paul lose only one hour at each stopover, what will the local time be when they each arrive in Tokyo if they both depart Madrid at 2pm?

            M                                 NY    M-L + 4:45   L                    12:00 h                   T

                                                   M           L                                       12:00 h                    T 

14 hrs 30 min

The Madrid-London flight takes 2hrs 30min. New York to London is 2hrs 30min + 4hrs 45min = 7hrs 15min. And the Madrid to New York flight is 27hrs 15min – 12hrs – 7hrs 15min = 8 hours.

With this, and bearing in mind that each stopover only takes one hour:

If Sara leaves at 2pm from Madrid then: 2pm + 8hrs – 6hrs (time difference) + 1hr (at NY airport) + 7hrs 15min + 5hrs (time difference) + 1hr + 12hrs + 8hrs (time difference) = 2:15am on day 3.

In Paul’s case: 2pm + 2hrs 30min – 1hr (time difference) + 1hr + 12hrs + 8hrs (time difference) = 12:30pm on day 2.

Miguel Barral

Related publications.

• What Purpose Do the Great Mathematical Problems Serve?
• David Hilbert: The Architect of Modern Mathematics
• Magic Squares: When Art is Squared With Mathematics

More about Science

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