mathematics for phd students

Guide to Graduate Studies

The PhD Program The Ph.D. program of the Harvard Department of Mathematics is designed to help motivated students develop their understanding and enjoyment of mathematics. Enjoyment and understanding of the subject, as well as enthusiasm in teaching it, are greater when one is actively thinking about mathematics in one’s own way. For this reason, a Ph.D. dissertation involving some original research is a fundamental part of the program. The stages in this program may be described as follows:

• Acquiring a broad basic knowledge of mathematics on which to build a future mathematical culture and more detailed knowledge of a field of specialization.
• Choosing a field of specialization within mathematics and obtaining enough knowledge of this specialized field to arrive at the point of current thinking.
• Making a first original contribution to mathematics within this chosen special area.

Students are expected to take the initiative in pacing themselves through the Ph.D. program. In theory, a future research mathematician should be able to go through all three stages with the help of only a good library. In practice, many of the more subtle aspects of mathematics, such as a sense of taste or relative importance and feeling for a particular subject, are primarily communicated by personal contact. In addition, it is not at all trivial to find one’s way through the ever-burgeoning literature of mathematics, and one can go through the stages outlined above with much less lost motion if one has some access to a group of older and more experienced mathematicians who can guide one’s reading, supplement it with seminars and courses, and evaluate one’s first attempts at research. The presence of other graduate students of comparable ability and level of enthusiasm is also very helpful.

University Requirements

The University requires a minimum of two years of academic residence (16 half-courses) for the Ph.D. degree. On the other hand, five years in residence is the maximum usually allowed by the department. Most students complete the Ph.D. in four or five years. Please review the program requirements timeline .

There is no prescribed set of course requirements, but students are required to register and enroll in four courses each term to maintain full-time status with the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Qualifying Exam

The department gives the qualifying examination at the beginning of the fall and spring terms. The qualifying examination covers algebra, algebraic geometry, algebraic topology, complex analysis, differential geometry, and real analysis. Students are required to take the exam at the beginning of the first term. More details about the qualifying exams can be found here .

Students are expected to pass the qualifying exam before the end of their second year. After passing the qualifying exam students are expected to find a Ph.D. dissertation advisor.

Minor Thesis

The minor thesis is complementary to the qualifying exam. In the course of mathematical research, students will inevitably encounter areas in which they have gaps in knowledge. The minor thesis is an exercise in confronting those gaps to learn what is necessary to understand a specific area of math. Students choose a topic outside their area of expertise and, working independently, learns it well and produces a written exposition of the subject.

The topic is selected in consultation with a faculty member, other than the student’s Ph.D. dissertation advisor, chosen by the student. The topic should not be in the area of the student’s Ph.D. dissertation. For example, students working in number theory might do a minor thesis in analysis or geometry. At the end of three weeks time (four if teaching), students submit to the faculty member a written account of the subject and are prepared to answer questions on the topic.

The minor thesis must be completed before the start of the third year in residence.

Language Exam

Mathematics is an international subject in which the principal languages are English, French, German, and Russian. Almost all important work is published in one of these four languages. Accordingly, students are required to demonstrate the ability to read mathematics in French, German, or Russian by passing a two-hour, written language examination. Students are asked to translate one page of mathematics into English with the help of a dictionary. Students may request to substitute the Italian language exam if it is relevant to their area of mathematics. The language requirement should be fulfilled by the end of the second year. For more information on the graduate program requirements, a timeline can be viewed at here .

Non-native English speakers who have received a Bachelor’s degree in mathematics from an institution where classes are taught in a language other than English may request to waive the language requirement.

Upon completion of the language exam and eight upper-level math courses, students can apply for a continuing Master’s Degree.

Teaching Requirement

Most research mathematicians are also university teachers. In preparation for this role, all students are required to participate in the department’s teaching apprenticeship program and to complete two semesters of classroom teaching experience, usually as a teaching fellow. During the teaching apprenticeship, students are paired with a member of the department’s teaching staff. Students attend some of the advisor’s classes and then prepare (with help) and present their own class, which will be videotaped. Apprentices will receive feedback both from the advisor and from members of the class.

Teaching fellows are responsible for teaching calculus to a class of about 25 undergraduates. They meet with their class three hours a week. They have a course assistant (an advanced undergraduate) to grade homework and to take a weekly problem session. Usually, there are several classes following the same syllabus and with common exams. A course head (a member of the department teaching staff) coordinates the various classes following the same syllabus and is available to advise teaching fellows. Other teaching options are available: graduate course assistantships for advanced math courses and tutorials for advanced undergraduate math concentrators.

Final Stages

How students proceed through the second and third stages of the program varies considerably among individuals. While preparing for the qualifying examination or immediately after, students should begin taking more advanced courses to help with choosing a field of specialization. Unless prepared to work independently, students should choose a field that falls within the interests of a member of the faculty who is willing to serve as dissertation advisor. Members of the faculty vary in the way that they go about dissertation supervision; some faculty members expect more initiative and independence than others and some variation in how busy they are with current advisees. Students should consider their own advising needs as well as the faculty member’s field when choosing an advisor. Students must take the initiative to ask a professor if she or he will act as a dissertation advisor. Students having difficulty deciding under whom to work, may want to spend a term reading under the direction of two or more faculty members simultaneously. The sooner students choose an advisor, the sooner they can begin research. Students should have a provisional advisor by the second year.

It is important to keep in mind that there is no technique for teaching students to have ideas. All that faculty can do is to provide an ambiance in which one’s nascent abilities and insights can blossom. Ph.D. dissertations vary enormously in quality, from hard exercises to highly original advances. Many good research mathematicians begin very slowly, and their dissertations and first few papers could be of minor interest. The ideal attitude is: (1) a love of the subject for its own sake, accompanied by inquisitiveness about things which aren’t known; and (2) a somewhat fatalistic attitude concerning “creative ability” and recognition that hard work is, in the end, much more important.

PhD Program

During their first year in the program, students typically engage in coursework and seminars which prepare them for the  Qualifying Examinations .  Currently, these two exams test the student’s breadth of knowledge in algebra and real analysis. Starting in Autumn 2023, students will choose 2 out of 4 qualifying exam topics: (i) algebra, (ii) real analysis, (iii) geometry and topology, (iv) applied mathematics.

Current Course Requirements: To qualify for candidacy, the student must have successfully completed 27 units of Math graduate courses numbered between 200 and 297.

Within the 27 units, students must satisfactorily complete a course sequence. This can be fulfilled in one of the following ways:

Math 215A, B, & C: Algebraic Topology, Differential Topology, and Differential Geometry

• Math 216A, B, & C: Introduction to Algebraic Geometry
• Math 230A, B, & C: Theory of Probability
• 3 quarter course sequence in a single subject approved in advance by the Director of Graduate Studies.

Course Requirements for students starting in Autumn 2023 and later: 

To qualify for candidacy, the student must have successfully completed 27 units of Math graduate courses numbered between 200 and 297. (The course sequence requirement is discontinued for students starting in Autumn 2023 and later.)

By the end of Spring Quarter of their second year in the program, students must have a dissertation advisor and apply for Candidacy.

During their third year, students will take their Area Examination, which must be completed by the end of Winter Quarter. This exam assesses the student’s breadth of knowledge in their particular area of research. The Area Examination is also used as an opportunity for the student to present their committee with a summary of research conducted to date as well as a detailed plan for the remaining research.

Typically during the latter part of the fourth or early part of the fifth year of study, students are expected to finish their dissertation research. At this time, students defend their dissertation as they sit for their University Oral Examination. Following the dissertation defense, students take a short time to make final revisions to their actual papers and submit the dissertation to their reading committee for final approval.

All students continue through each year of the program serving some form of Assistantship: Course, Teaching or Research, unless they have funding from outside the department.

Our graduate students are very active as both leaders and participants in seminars and colloquia in their chosen areas of interest.

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Georgia Institute of Technology College of Sciences

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PhD in Mathematics

Here are the requirements for earning the PhD degree in Mathematics offered by the School of Math. For requirements of other PhD programs housed within the School, please see their specific pages at  Doctoral Programs . The requirements for all these programs consist of three components:  coursework ,  examinations , and  dissertation  in accordance to the guidelines described in the  GT Catalogue .

Completion of required coursework, examinations, and dissertation normally takes about five years. During the first one or two years, students concentrate on coursework to acquire the background necessary for the comprehensive examinations. By the end of their third year in the program, all students are expected to have chosen a thesis topic, and begin work on the research and writing of the dissertation.

The program of study must contain at least 30 hours of graduate-level coursework (6000-level or above) in mathematics and an additional 9 hours of coursework towards a minor. The minor requirement consists of graduate or advanced undergraduate coursework taken entirely outside the School of Mathematics, or in an area of mathematics sufficiently far from the students area of specialization.

Prior to admission to candidacy for the doctoral degree, each student must satisfy the School's comprehensive examinations (comps) requirement. The first phase is a written examination which students must complete by the end of their second year in the graduate program. The second phase is an oral examination in the student's proposed area of specialization, which must be completed by the end of the third year.

Research and the writing of the dissertation represent the final phase of the student's doctoral study, and must be completed within seven years of the passing of comps. A final oral examination on the dissertation (theses defense) must be passed prior to the granting of the degree.

The Coursework

The program of study must satisfy the following  hours ,  minor , and  breadth  requirements. Students who entered before Fall 2015 should see  the old requirements , though they may opt into the current rules described below, and are advised to do so.

Hours requirements.  The students must complete 39 hours of coursework as follows:

• At least 30 hours must be in mathematics courses at the 6000-level or higher.
• At least 9 hours must form the doctoral minor field of study.
• The overall GPA for these courses must be at least 3.0.
• These courses must be taken for a letter grade and passed with a grade of at least C.

Minor requirement.  The minor field of study should consist primarily of 6000-level (or higher) coursework in a specific area outside the School of Math, or in a mathematical subject sufficiently far from the student’s thesis work. A total of 9 credit hours is required and must be passed with a grade of B or better. These courses should not include MATH 8900, and must be chosen in consultation with the PhD advisor and the Director of Graduate Studies to ensure that they form a cohesive group which best complements the students research and career goals. A student wishing to satisfy the minor requirement by mathematics courses must petition the Graduate Committee for approval.  Courses used to fulfill a Basic Understanding breadth requirement in Analysis or Algebra should not be counted towards the doctoral minor. Upon completing the minor requirement, a student should immediately complete the  Doctoral Minor form .

Breadth requirements.  The students must demonstrate:

• Basic understanding of 2 subjects must be demonstrated through passing the subjects' written comprehensive exams.  At least 1 of these 2 exams must be in Algebra or Analysis.
• Basic understanding of the third subject may be demonstrated either by completing two courses in the subject (with a grade of A or B in each course) or by passing the subject's written comprehensive exam.
• A basic understanding of both subjects in Area I (analysis and algebra) must be demonstrated.
• Earning a grade of A or B in a one-semester graduate course in a subject demonstrates exposure to the subject.
• Passing a subject's written comprehensive exam also demonstrates exposure to that subject.

The subjects.  The specific subjects, and associated courses, which can be used to satisfy the breadth requirements are as follows.

• Area I subjects:​
• Area II subjects:​

Special Topics and Reading Courses.

• Special topics courses may always be used to meet hours requirements.
• Special topics courses may be used to meet breadth requirements, subject to the discretion of the Director of Graduate Studies.
• Reading courses may be used to meet hours requirements but not breadth requirements.

Credit Transfers

Graduate courses completed at other universities may be counted towards breadth and hours requirements (courses designated as undergraduate or Bachelors' level courses are not eligible to transfer for graduate credit).  These courses do not need to be officially transferred to Georgia Tech. At a student’s request, the Director of Graduate Studies will determine which breadth and hours requirements have been satisfied by graduate-level coursework at another institution.  

Courses taken at other institutions may also be counted toward the minor requirement, subject to the approval of the Graduate Director; however, these courses must be officially transferred to Georgia Tech.

There is no limit for the transfer of credits applied toward the breadth requirements; however, a maximum of 12 hours of coursework from other institutions may be used to satisfy hours requirements. Thus at least 27 hours of coursework must be completed at Georgia Tech, including at least 18 hours of 6000-level (or higher) mathematics coursework.

Students wishing to petition for transfer of credit from previous graduate level work should send the transcripts and syllabi of these courses, together with a list of the corresponding courses in the School of Math, to the Director of Advising and Assessment for the graduate program.

Comprehensive Examinations

The comprehensive examination is in two phases. The first phase consists of passing two out of seven written examinations. The second phase is an oral specialty examination in the student's planned area of concentration. Generally, a student is expected to have studied the intended area of research but not necessarily begun dissertation research at the time of the oral examination.

Written examinations.  The written examinations will be administered twice each year, shortly after the beginning of the Fall and Spring semesters. The result of the written examination is either pass or fail. For syllabi and sample exams see the  written exams page .

All students must adhere to the following rules and timetables, which may be extended by the Director of Graduate Studies, but only at the time of matriculation and only when certified in writing. Modifications because of leaves from the program will be decided on a case-by-case basis.

After acceptance into the PhD Program in Mathematics, a student must pass the written examinations no later than their fourth administration since the student's doctoral enrollment. The students can pass each of the two written comprehensive exams in separate semesters, and are allowed multiple attempts.

The Director of Graduate Studies (DGS) will be responsible for advising each new student at matriculation of these rules and procedures and the appropriate timetable for the written portion of the examination. The DGS will also be responsible for maintaining a study guide and list of recommended texts, as well as a file of previous examinations, to be used by students preparing for this written examination.

Oral examination.  A student must pass the oral specialty examination within three years since first enrolling in the PhD program, and after having passed the written portion of the comprehensive exams. The examination will be given by a committee consisting of the student's dissertation advisor or probable advisor, two faculty members chosen by the advisor in consultation with the student, and a fourth member appointed by the School's Graduate Director. The scope of the examination will be determined by the advisor and will be approved by the graduate coordinator. The examining committee shall either (1) pass the student or (2) fail the student. Within the time constraints of which above, the oral specialty examination may be attempted multiple times, though not more than twice in any given semester. For more details and specific rules and policies see the  oral exam page .

Dissertation and Defense

A dissertation and a final oral examination are required. For details see our  Dissertation and Graduation  page, which applies to all PhD programs in the School of Math.

Department of Mathematics

Mathematics phd program.

The Ph.D. program in the Department of Mathematics provides students with in-depth knowledge and rigorous training in all the subject areas of mathematics. A core feature is the first-year program, which helps bring students to the forefront of modern mathematics. Students work closely with faculty and each other and participate fully in both research and student-run seminars.

Questions? Email [email protected]

• The firm deadline for applications for Autumn 2024, is December 4, 2023.
• The (general and advanced) GRE tests are no longer accepted. Please do not submit these scores.

PhD in Mathematics

The PhD in Mathematics provides training in mathematics and its applications to a broad range of disciplines and prepares students for careers in academia or industry. It offers students the opportunity to work with faculty on research over a wide range of theoretical and applied topics.

Degree Requirements

The requirements for obtaining an PhD in Mathematics can be found on the associated page of the BU Bulletin .

• Courses : The courses mentioned on the BU Bulletin page can be chosen from the graduate courses we offer here . Half may be at the MA 500 level or above, but the rest must be at the MA 700 level or above. Students can also request to use courses from other departments to satisfy some of these requirements. Please contact your advisor for more information about which courses can be used in this way. All courses must be passed with a grade of B- or higher.
• Analysis (examples include MA 711, MA 713, and MA 717)
• PDEs and Dynamical Systems (examples include MA 771, MA 775, and MA 776)
• Algebra and Number Theory (examples include MA 741, MA 742, and MA 743)
• Topology (examples include MA 721, MA 722, and MA 727)
• Geometry (examples include MA 725, MA 731, and MA 745)
• Probability and Stochastic Processes (examples include MA 779, MA 780, and MA 783)
• Applied Mathematics (examples include MA 750, MA 751, and MA 770)
• Comprehensive Examination : This exam has both a written and an oral component. The written component consists of an expository paper of typically fifteen to twenty-five pages on which the student works over a period of a few months under the guidance of the advisor. The topic of the expository paper is chosen by the student in consultation with the advisor. On completion of the paper, the student takes an oral exam given by a three-person committee, one of whom is the student’s advisor. The oral exam consists of a presentation by the student on the expository paper followed by questioning by the committee members. A student who does not pass the MA Comprehensive Examination may make a second attempt, but all students are expected to pass the exam no later than the end of the summer following their second year.
• Oral Qualifying Examination: The topics for the PhD oral qualifying exam correspond to the two semester courses taken by the student from one of the 3 subject areas and one semester course each taken by the student from the other two subject areas. In addition, the exam begins with a presentation by the student on some specialized topic relevant to the proposed thesis research. A student who does not pass the qualifying exam may make a second attempt, but all PhD students are expected to pass the exam no later than the end of the summer following their third year.
• Dissertation and Final Oral Examination: This follows the GRS General Requirements for the Doctor of Philosophy Degree .

Admissions information can be found on the BU Arts and Sciences PhD Admissions website .

Financial Aid

Our department funds our PhD students through a combination of University fellowships, teaching fellowships, and faculty research grants. More information will be provided to admitted students.

More Information

Please reach out to us directly at [email protected] if you have further questions.

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Graduate Program

Thinking of applying to graduate school in mathematics.

Penn was ranked 8th among all US universities in a leading national study , and our mathematics graduate program was recently highest in a study of graduate programs in arts and sciences at Penn. We have a very active and involved mathematics faculty , diverse course offerings and a broad seminar schedule , with a variety of research projects and strengths in algebra, analysis, geometry-topology, combinatorics, logic, probability, and mathematical physics. We have a supportive atmosphere, with personal attention from the faculty and extensive interaction among graduate students. Our grad students can take courses not only in the Mathematics Department but also elsewhere at Penn, and the wide resources of the university are available. Our former graduate students have gone on to mathematical careers both in academia and in industry.

Our full-time Ph.D. students receive a generous and competitive support package including

• five years of funding with a combination of fellowships and teaching assistantships;
• a stipend and a full tuition scholarship;
• no teaching responsibilities for at least two years (generally including the first and fourth year);
• health insurance coverage provided at no cost to the student.

We invite you to learn about our graduate program, our math department, our university and living in Philadelphia, a cosmopolitan city and a true mathematical hub, with easy access to nearby mathematics departments and research institutes.

We are looking for interested, mathematically talented and dedicated students to be a part of our group of excellent future mathematicians. Consider applying to Penn for your graduate education. Questions?

PhD in Mathematics

The PhD in Mathematics consists of preliminary coursework and study, qualifying exams, a candidacy exam with an adviser, and creative research culminating in a written dissertation and defense. All doctoral students must also do some teaching on the way to the PhD. There are minimal course requirements, and detailed requirements and procedures for the PhD program are outlined in the  PhD Handbook .

Please note that our department alternates recruiting in-coming classes that are focused on either applied or pure mathematics. For the Fall 2024 admissions (matriculation in September 2024), we are focusing on students interested in areas of applied mathematics.

All our professors are active in research, and are devoted to teaching and mentoring of students. Thus, there are many opportunities to be involved in cutting-edge research in pure and applied mathematics. Moreover, the seven other research universities in the Boston area are all within easy reach, providing access to many more classes, seminars and colloquia in diverse areas of mathematical research.

Teaching assistantships are available for incoming PhD students, as well as a limited number of University-wide fellowships. Tufts has on-campus housing for graduate students, but many choose to live off-campus instead.

In addition to the above, PhD students often:

• Mentor undergraduates as teaching assistants and course instructors, and through graduate-student run programs like the Directed Reading Program.
• Meet with advisors and fellow students to share research and collaborate with scholars across disciplines
• Attend professional development workshops and present research at conferences

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• Graduate Students

The Mathematical Association of America (MAA) is the largest mathematical society in the world that focuses on mathematics for students, faculty, professional mathematicians, and all who are interested in the mathematical sciences; that is, mathematics at the undergraduate level. Our members include university, college, and high school teachers; high school, undergraduate and graduate students; and others in academia, government, business, and industry. Our core interests are Education , Research , Professional Development , Public Policy , and Public Appreciation . The student web pages cover topics in academics, careers, research/summer opportunities, meetings for students, and more. If you are not yet a member, we urge you to consider joining and ask you to visit our membership page. As a member, you can help the MAA fulfill our goals to benefit you, the student.

Graduate Newsletter

The Spring 2010 MAA Graduate Newsletter is now available. Featured in this issue:

• Opportunities at MathFest 2010
• MathGradBlog run by Frank Morgan of Williams College
• When Will I Use Math? Website Up and Running
• On the job market? Visit MAA Math Classifieds
• Did you know...?

Graduate Student Blog

AMS Graduate Student Blog is a blog by and for math graduate students, managed by Frank Morgan.

Current Graduate School Students

The MAA offers plenty to graduate students. From our site, you can access pages for meetings, find helpful and innovative teaching ideas, check for summer or travel support, and find information and assistance in your job search. Whether you are getting a Master's or a PhD, whether you wish to stay in academics or go into industry, we can help you.

Teaching assistantships are an integral part of many a graduate student's education. It's an important job and there are many web resources to help you do your best. This link will take you to the Handbook for Mathematics Teaching Assistants by Tom Rishel of Cornell University. Bonnie Gold, from Monmouth University is the editor of the Innovative Teaching Exchange , containing a collection of novel teaching experiences. The Mathematics Digital Library is a vast resource of articles for teachers and students. After graduation, interested young professors should apply for the MAA's wildly successful Project NExT and join the Young Mathematicians Network .

Meetings have always been a large part of academic life. Now students can get involved early in their undergraduate careers and continue to be active in their post-graduate career. The MAA Sectional Meetings are especially good for PhD students working on their "job search talk". MAA's annual conference, MathFest , provides a number of networking and speaking opportunities for early career mathematicians, including graduate students.

Fellowships and Opportunities

There are a lot of ways to become an active and influential member of the mathematical culture. There are research opportunities while in school, summer programs, and post-graduation activities. Consider these:

• Project NExT
• Preparing Future Faculty
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• Internships from the American Statistical Association
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• AMS-AAAS Mass Media Fellowship
• The Sloan Foundation Fellowships
• Department of Homeland Security Fellowships
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• Naval Research Labs Post-doctoral Fellowships
• Naval Research Enterprise Internship Program
• AWM Education Resources

After graduate school...

Plenty of jobs are out there for people with degrees in mathematics. If you have a PhD and wish to go into academics, the Chronicle of Higher Education and the AMS (using EIMS ) have sites for you. If you want to go into industry (with any degree) then the Math Classifieds is tailored for your needs. This site will let you post your resume and seek employers, while at the same time businesses can hunt through the postings to find you.

Continued Growth

For many academics, teaching and research alone will not earn you the tenure and promotion for which you're looking. The new phrase is "Continued Scholarly Growth" or "Scholarly Engagement". These include items such as development of experimental programs, papers delivered at national and regional meetings of professional societies, offices held in professional organizations, participation in panels at meetings of professional organizations, and editorships of professional journals. The MAA is a place to become involved in so many of these activities. At the Sectional level you can be an officer, helping to organize or even host meetings. On the national level we publish several journals that you can become involved with, we have over a dozen special interest groups (SIGMAAs) you can join, and we rely on well over 100 different committees you can be on to help us run the MAA.

Graduate School Opportunities

If you are not yet in graduate school, but are considering adding to your Bachelor's degree, then the following information is for you:

Master's Degree

Perhaps you've found a favorite subject that you want to investigate more deeply. Maybe you wish to add to your undergraduate degree and make yourself more marketable. Whatever the reason, there are plenty of options for Master's degree programs. At most of them, you'll qualify for a Teaching Assistantship or Research Assistantship which will help pay for the program. It's an investment which can have a big return. According to the Census Bureau, a Master's degree is worth almost $500,000 more over a working lifetime than a Bachelor's alone.

Professional Master's Degree

What is a Professional Master's? It is a degree which is not meant to feed into a PhD program and is capable of standing on its own. Terminal Master's degrees in mathematics can be found with concentration in fields such as Biology, Finance, and Operations Research. For a good list of subjects, and schools with professional Master's in that subject, go to the AMS page .

A PhD in mathematics usually brings to mind a career teaching at a university. While this is true, there are a lot more opportunities available. Operations researcher, statistician, cryptanalyst, and more are available. A good presentation on finding an industry job is here . For advice on both non-academic and academic jobs go to this site run by the AMS.

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• Doing a PhD in Mathematics
• Doing a PhD

What Does a PhD in Maths Involve?

Maths is a vast subject, both in breadth and in depth. As such, there’s a significant number of different areas you can research as a math student. These areas usually fall into one of three categories: pure mathematics, applied mathematics or statistics. Some examples of topics you can research are:

• Number theory
• Numerical analysis
• String theory
• Random matrix theory
• Graph theory
• Quantum mechanics
• Statistical forecasting
• Matroid theory
• Control theory

Besides this, because maths focuses on addressing interdisciplinary real-world problems, you may work and collaborate with other STEM researchers. For example, your research topic may relate to:

• Biomechanics and transport processes
• Evidence-based medicine
• Fluid dynamics
• Financial mathematics
• Machine learning
• Theoretical and Computational Optimisation

What you do day-to-day will largely depend on your specific research topic. However, you’ll likely:

• Continually read literature – This will be to help develop your knowledge and identify current gaps in the overall body of knowledge surrounding your research topic.
• Undertake research specific to your topic – This can include defining ideas, proving theorems and identifying relationships between models.
• Collect and analyse data – This could comprise developing computational models, running simulations and interpreting forecasts etc.
• Liaise with others – This could take many forms. For example, you may work shoulder-to-shoulder with individuals from different disciplines supporting your research, e.g. Computer scientists for machine learning-based projects. Alternatively, you may need frequent input from those who supplied the data for your research, e.g. Financial institutions or biological research colleagues.
• Attend a wide range of lectures, seminars and events.

Browse PhD Opportunities in Mathematics

Application of artificial intelligence to multiphysics problems in materials design, study of the human-vehicle interactions by a high-end dynamic driving simulator, physical layer algorithm design in 6g non-terrestrial communications, machine learning for autonomous robot exploration, detecting subtle but clinically significant cognitive change in an ageing population, how long does it take to get a phd in maths.

The average programme duration for a mathematics PhD in the UK is 3 to 4 years for a full-time studying. Although not all universities offer part-time maths PhD programmes, those that do have a typical programme duration of 5 to 7 years.

Again, although the exact arrangement will depend on the university, most maths doctorates will require you to first register for an MPhil . At the end of your first year, your supervisor will assess your progress to decide whether you should be registered for a PhD.

Additional Learning Modules

Some Mathematics departments will require you to enrol on to taught modules as part of your programme. These are to help improve your knowledge and understanding of broader subjects within your field, for example, Fourier Analysis, Differential Geometry and Riemann Surfaces. Even if taught modules aren’t compulsory in several universities, your supervisor will still encourage you to attend them for your development.

Most UK universities will also have access to specialised mathematical training courses. The most common of these include Pure Mathematics courses hosted by Mathematics Access Grid Conferencing ( MAGIC ) and London Taught Course Centre ( LTCC ) and Statistics courses hosted by Academy for PhD Training in Statistics ( APTS ).

What Are the Typical Entry Requirements for A PhD in Maths?

In the UK, the typical entry requirements for a Maths PhD is an upper second-class (2:1) Master’s degree (or international equivalent) in Mathematics or Statistics [1] .

However, there is some variation on this. From writing, the lowest entry requirement is an upper second-class (2:1) Bachelor’s degree in any math-related subject. The highest entry requirement is a first-class (1st) honours Master’s degree in a Mathematics or Statistics degree only.

It’s worth noting if you’re applying to a position which comes with funding provided directly by the Department, the entry requirements will usually be on the higher side because of their competitiveness.

In terms of English Language requirements, most mathematics departments require at least an overall IELTS (International English Language Testing System) score of 6.5, with no less than 6.0 in each individual subtest.

Tips to Consider when Making Your Application

When applying to any mathematics PhD, you’ll be expected to have a good understanding of both your subject field and the specific research topic you are applying to. To help show this, it’s advisable that you demonstrate recent engagement in your research topic. This could be by describing the significance of a research paper you recently read and outlining which parts interested you the most, and why. Additionally, you can discuss a recent mathematics event you attended and suggest ways in how what you learnt might apply to your research topic.

As with most STEM PhDs, most maths PhD professors prefer you to discuss your application with them directly before putting in a formal application. The benefits of this is two folds. First, you’ll get more information on what their department has to offer. Second, the supervisor can better discover your interest in the project and gauge whether you’d be a suitable candidate. Therefore, we encourage you to contact potential supervisors for positions you’re interested in before making any formal applications.

How Much Does a Maths PhD Typically Cost?

The typical tuition fee for a PhD in Maths in the UK is £4,407 per year for UK/EU students and £20,230 per year for international students. This, alongside the range in tuition fees you can expect, is summarised below:

Note: The above tuition fees are based on 12 UK Universities [1]  for 2020/21 Mathematic PhD positions. The typical fee has been taken as the median value.

In addition to the above, it’s not unheard of for research students to be charged a bench fee. In case you’re unfamiliar with a bench fee, it’s an annual fee additional to your tuition, which covers the cost of specialist equipment or resources associated with your research. This can include the upkeep of supercomputers you may use, training in specialist analysis software, or travelling to conferences. The exact fee will depend on your specific research topic; however, it should be minimal for most mathematic projects.

What Specific Funding Opportunities Are There for A PhD in Mathematics?

Alongside the usual funding opportunities available to all PhD Research students such as doctoral loans, departmental scholarships, there are a few other sources of funding available to math PhD students. Examples of these include:

You can find more information on these funding sources here: DiscoverPhDs funding guide .

What Specific Skills Do You Gain from Doing a PhD in Mathematics?

A doctorate in Mathematics not only demonstrates your commitment to continuous learning, but it also provides you with highly marketable skills. Besides subject-specific skills, you’ll also gain many transferable skills which will prove useful in almost all industries. A sample of these skills is listed below.

• Logical ability to consider and analyse complex issues,
• Commitment and persistence towards reaching research goals,
• Outstanding verbal and written skills,
• Strong attention to detail,
• The ability to liaise with others from unique disciple backgrounds and work as part of a team
• Holistic deduction and reasoning skills,
• Forming and explaining mathematical and logical solutions to a wide range of real-world problems,
• Exceptional numeracy skills.

What Jobs Can You Get with A Maths PhD?

One of the greatest benefits maths PostDocs will have is the ability to pursue a wide range of career paths. This is because all sciences are built on core principles which, to varying extents, are supported by the core principles of mathematics. As a result, it’s not uncommon to ask students what path they intend to follow after completing their degree and receive entirely different answers. Although not extensive by any means, the most common career paths Math PostDocs take are listed below:

• Academia – Many individuals teach undergraduate students at the university they studied at or ones they gained ties to during their research. This path is usually the preferred among students who want to continue focusing on mathematical theories and concepts as part of their career.
• Postdoctoral Researcher – Others continue researching with their University or with an independent organisation. This can be a popular path because of the opportunities it provides in collaborative working, supervising others, undertaking research and attending conferences etc.
• Finance – Because of their deepened analytical skills, it’s no surprise that many PostDocs choose a career in finance. This involves working for some of the most significant players in the financial district in prime locations including London, Frankfurt and Hong Kong. Specific job titles can include Actuarial, Investment Analyst or Risk Modeller.
• Computer Programming – Some students whose research involves computational mathematics launch their career as a computer programmer. Due to their background, they’ll typically work on specialised projects which require high levels of understanding on the problem at hand. For example, they may work with physicists and biomedical engineers to develop a software package that supports their more complex research.
• Data Analyst – Those who enjoy number crunching and developing complex models often go into data analytics. This can involve various niches such as forecasting or optimisation, across various fields such as marketing and weather.

What Are Some of The Typical Employers Who Hire Maths PostDocs?

As mentioned above, there’s a high demand for skilled mathematicians and statisticians across a broad range of sectors. Some typical employers are:

• Education – All UK and international universities
• Governments – STFC and Department for Transport
• Healthcare & Pharmaceuticals – NHS, GSK, Pfizer
• Finance & Banking – e.g. Barclays Capital, PwC and J. P. Morgan
• Computing – IBM, Microsoft and Facebook
• Engineering – Boeing, Shell and Dyson

The above is only a small selection of employers. In reality, mathematic PostDocs can work in almost any industry, assuming the role is numerical-based or data-driven.

How Much Can You Earn with A PhD in Maths?

As a mathematics PhD PostDoc, your earning potential will mostly depend on your chosen career path. Due to the wide range of options, it’s impossible to provide an arbitrary value for the typical salary you can expect.

However, if you pursue one of the below paths or enter their respective industry, you can roughly expect to earn [3] :

Academic Lecturer

• Approximately £30,000 – £35,000 starting salary
• Approximately £40,000 with a few years experience
• Approximately £45,000 – £55,000 with 10 years experience
• Approximately £60,000 and over with significant experience and a leadership role. Certain academic positions can earn over £80,000 depending on the management duties.

Actuary or Finance

• Approximately £35,000 starting salary
• Approximately £45,000 – £55,000 with a few years experience
• Approximately £70,000 and over with 10 years experience
• Approximately £180,000 and above with significant experience and a leadership role.

Aerospace or Mechanical Engineering

• Approximately £28,000 starting salary
• Approximately £35,000 – £40,000 with a few years experience
• Approximately £60,000 and over with 10 years experience

Data Analyst

• Approximately £45,000 – £50,000 with a few years experience
• Approximately £90,000 and above with significant experience and a leadership role.

Again, we stress that the above are indicative values only. Actual salaries will depend on the specific organisation and position and responsibilities of the individual.

Facts and Statistics About Maths PhD Holders

The below chart provides useful insight into the destination of Math PostDocs after completing their PhD. The most popular career paths from other of highest to lowest is education, information and communication, finance and scientific research, manufacturing and government.

Note: The above chart is based on ‘UK Higher Education Leavers’ data [2] between 2012/13 and 2016/17 and contains a data size of 200 PostDocs. The data was obtained from the Higher Education Statistics Agency ( HESA ).

Which Noteworthy People Hold a PhD in Maths?

Alan turing.

Alan Turing was a British Mathematician, WW2 code-breaker and arguably the father of computer science. Alongside his lengthy list of achievements, Turning achieved a PhD in Mathematics at Princeton University, New Jersey. His thesis titled ‘Systems of Logic Based on Ordinals’ focused on the concepts of ordinal logic and relative computing; you can read it online here . To this day, Turning pioneering works continues to play a fundamental role in shaping the development of artificial intelligence (AI).

Ruth Lawrence

Ruth Lawrence is a famous British–Israeli Mathematician well known within the academic community. Lawrence earned her PhD in Mathematics from Oxford University at the young age of 17! Her work focused on algebraic topology and knot theory; you can read her interesting collection of research papers here . Among her many contributions to Maths, her most notable include the representation of the braid groups, more formally known as Lawrence–Krammer representations.

Emmy Noether

Emmy Noether was a German mathematician who received her PhD from the University of Erlangen, Germany. Her research has significantly contributed to both abstract algebra and theoretical physics. Additionally, she proved a groundbreaking theorem important to Albert Einstein’s general theory of relativity. In doing so, her theorem, Noether’s theorem , is regarded as one of the most influential developments in physics.

Other Useful Resources

Institute of Mathematics and its Applications (IMA) – IMA is the UK’s professional body for mathematicians. It contains a wide range of useful information, from the benefits of further education in Maths to details on grants and upcoming events.

Maths Careers – Math Careers is a site associated with IMA that provides a wide range of advice to mathematicians of all ages. It has a section dedicated to undergraduates and graduates and contains a handful of information about progressing into research.

Resources for Graduate Students – Produced by Dr Mak Tomford, this webpage contains an extensive collection of detailed advice for Mathematic PhD students. Although the site uses US terminology in places, don’t let that put you off as this resource will prove incredibly helpful in both applying to and undertaking your PhD.

Student Interviews – Still wondering whether a PhD is for you? If so, our collection of PhD interviews would be a great place to get an insider perspective. We’ve interviewed a wide range of PhD students across the UK to find out what doing a PhD is like, how it’s helped them and what advice they have for other prospective students who may be thinking of applying to one. You can read our insightful collection of interviews here .

[1] Universities used to determine the typical (median) and range of entry requirements and tuition fees for 2020/21 Mathematics PhD positions.

• http://www.lse.ac.uk/study-at-lse/Graduate/Degree-programmes-2020/MPhilPhD-Mathematics
• https://www.ox.ac.uk/admissions/graduate/courses/dphil-mathematics?wssl=1
• https://www.graduate.study.cam.ac.uk/courses/directory/mapmpdpms
• https://www.ucl.ac.uk/prospective-students/graduate/research-degrees/mathematics-mphil-phd
• http://www.bristol.ac.uk/study/postgraduate/2020/sci/phd-mathematics/
• https://www.surrey.ac.uk/postgraduate/mathematics-phd
• https://www.maths.ed.ac.uk/school-of-mathematics/studying-here/pgr/phd-application
• https://www.lancaster.ac.uk/study/postgraduate/postgraduate-courses/mathematics-phd/
• https://www.sussex.ac.uk/study/phd/degrees/mathematics-phd
• https://www.manchester.ac.uk/study/postgraduate-research/programmes/list/05325/phd-pure-mathematics/
• https://warwick.ac.uk/study/postgraduate/research/courses-2020/mathematicsphd/
• https://www.exeter.ac.uk/pg-research/degrees/mathematics/

[2] Higher Education Leavers Statistics: UK, 2016/17 – Outcomes by subject studied – https://www.hesa.ac.uk/news/28-06-2018/sfr250-higher-education-leaver-statistics-subjects

[3] Typical salaries have been extracted from a combination of the below resources. It should be noted that although every effort has been made to keep the reported salaries as relevant to Math PostDocs as possible (i.e. filtering for positions which specify a PhD qualification as one of their requirements/preferences), small inaccuracies may exist due to data availability.

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Ph.D. Program

Degree requirements.

In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements.

• Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics
• Pass the six-hour written Preliminary Examination covering calculus, real analysis, complex analysis, linear algebra, and abstract algebra; students must pass the prelim before the start of their second year in the program (within three semesters of starting the program)
• Pass a three-hour, oral Qualifying Examination emphasizing, but not exclusively restricted to, the area of specialization. The Qualifying Examination must be attempted within two years of entering the program
• Complete a seminar, giving a talk of at least one-hour duration
• Write a dissertation embodying the results of original research and acceptable to a properly constituted dissertation committee
• Meet the University residence requirement of two years or four semesters

Detailed Regulations

The detailed regulations of the Ph.D. program are the following:

Course Requirements

During the first year of the Ph.D. program, the student must enroll in at least 4 courses. At least 2 of these must be graduate courses offered by the Department of Mathematics. Exceptions can be granted by the Vice-Chair for Graduate Studies.

Preliminary Examination

The Preliminary Examination consists of 6 hours (total) of written work given over a two-day period (3 hours/day). Exam questions are given in calculus, real analysis, complex analysis, linear algebra, and abstract algebra. The Preliminary Examination is offered twice a year during the first week of the fall and spring semesters.

Qualifying Examination

To arrange the Qualifying Examination, a student must first settle on an area of concentration, and a prospective Dissertation Advisor (Dissertation Chair), someone who agrees to supervise the dissertation if the examination is passed. With the aid of the prospective advisor, the student forms an examination committee of 4 members.  All committee members can be faculty in the Mathematics Department and the chair must be in the Mathematics Department. The QE chair and Dissertation Chair cannot be the same person; therefore, t he Math member least likely to serve as the dissertation advisor should be selected as chair of the qualifying exam committee . The syllabus of the examination is to be worked out jointly by the committee and the student, but before final approval, it is to be circulated to all faculty members of the appropriate research sections. The Qualifying Examination must cover material falling in at least 3 subject areas and these must be listed on the application to take the examination. Moreover, the material covered must fall within more than one section of the department. Sample syllabi can be reviewed online or in 910 Evans Hall. The student must attempt the Qualifying Examination within twenty-five months of entering the PhD program. If a student does not pass on the first attempt, then, on the recommendation of the student's examining committee, and subject to the approval of the Graduate Division, the student may repeat the examination once. The examining committee must be the same, and the re-examination must be held within thirty months of the student's entrance into the PhD program. For a student to pass the Qualifying Examination, at least one identified member of the subject area group must be willing to accept the candidate as a dissertation student.

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Ph.D. Program in Mathematics

Degree requirements.

A candidate for the Ph.D. degree in mathematics must fulfill a number of different departmental requirements .

NYU Shanghai Ph.D. Track

The Ph.D. program also offers students the opportunity to pursue their study and research with Mathematics faculty based at NYU Shanghai. With this opportunity, students generally complete their coursework in New York City before moving full-time to Shanghai for their dissertation research. For more information, please visit the  NYU Shanghai Ph.D. page .

Sample course schedules (Years 1 and 2) for students with a primary interest in:

Applied Math (Math Biology, Scientific Computing, Physical Applied Math, etc.)

Additional information for students interested in studying applied math is available here .

Probability

PDE/Analysis

The Written Comprehensive Examination

The examination tests the basic knowledge required for any serious mathematical study. It consists of the three following sections: Advanced Calculus, Complex Variables, and Linear Algebra. The examination is given on three consecutive days, twice a year, in early September and early January. Each section is allotted three hours and is written at the level of a good undergraduate course. Samples of previous examinations are available in the departmental office. Cooperative preparation is encouraged, as it is for all examinations. In the fall term, the Department offers a workshop, taught by an advanced Teaching Assistant, to help students prepare for the written examinations.

Entering students with a solid preparation are encouraged to consider taking the examination in their first year of full-time study. All students must take the examinations in order to be allowed to register for coursework beyond 36 points of credit; it is recommended that students attempt to take the examinations well before this deadline. Graduate Assistants are required to take the examinations during their first year of study.

For further details, consult the page on the written comprehensive exams .

The Oral Preliminary Examination

This examination is usually (but not invariably) taken after two years of full-time study. The purpose of the examination is to determine if the candidate has acquired sufficient mathematical knowledge and maturity to commence a dissertation. The phrase "mathematical knowledge" is intended to convey rather broad acquaintance with the basic facts of mathematical life, with emphasis on a good understanding of the simplest interesting examples. In particular, highly technical or abstract material is inappropriate, as is the rote reproduction of information. What the examiners look for is something a little different and less easy to quantify. It is conveyed in part by the word "maturity." This means some idea of how mathematics hangs together; the ability to think a little on one's feet; some appreciation of what is natural and important, and what is artificial. The point is that the ability to do successful research depends on more than formal learning, and it is part of the examiners' task to assess these less tangible aspects of the candidate's preparation.

The orals are comprised of a general section and a special section, each lasting one hour, and are conducted by two different panels of three faculty members. The examination takes place three times a year: fall, mid-winter and late spring. Cooperative preparation of often helpful and is encouraged. The general section consists of five topics, one of which may be chosen freely. The other four topics are determined by field of interest, but often turn out to be standard: complex variables, real variables, ordinary differential equations, and partial differential equations. Here, the level of knowledge that is expected is equivalent to that of a one or two term course of the kind Courant normally presents. A brochure containing the most common questions on the general oral examination, edited by Courant students, is available at the Department Office.

The special section is usually devoted to a single topic at a more advanced level and extent of knowledge. The precise content is negotiated with the candidate's faculty advisor. Normally, the chosen topic will have a direct bearing on the candidate's Ph.D. dissertation.

All students must take the oral examinations in order to be allowed to register for coursework beyond 60 points of credit. It is recommended that students attempt the examinations well before this deadline.

The Dissertation Defense

The oral defense is the final examination on the student's dissertation. The defense is conducted by a panel of five faculty members (including the student's advisor) and generally lasts one to two hours. The candidate presents his/her work to a mixed audience, some expert in the student's topic, some not. Often, this presentation is followed by a question-and-answer period and mutual discussion of related material and directions for future work.

Summer Internships and Employment

The Department encourages Ph.D. students at any stage of their studies, including the very early stage, to seek summer employment opportunities at various government and industry facilities. In the past few years, Courant students have taken summer internships at the National Institute of Health, Los Alamos National Laboratory, Woods Hole Oceanographic Institution, Lawrence Livermore National Laboratory and NASA, as well as Wall Street firms. Such opportunities can greatly expand students' understanding of the mathematical sciences, offer them possible areas of interest for thesis research, and enhance their career options. The Director of Graduate Studies and members of the faculty (and in particular the students' academic advisors) can assist students in finding appropriate summer employment.

Mentoring and Grievance Policy

For detailed information, consult the page on the Mentoring and Grievance Policy .

Visiting Doctoral Students

Information about spending a term at the Courant Institute's Department of Mathematics as a visiting doctoral student is available on the Visitor Programs  page.

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In most cases an applicant to the PhD program should have completed work in mathematics equivalent to that required for a Bachelor's Degree at Kansas State University.

Details on the application process can be found on the graduate program admission site . Admission is granted upon approval by the Graduate Program Advisory Committee (GPAC), the Department Head, and the Graduate School. Students pursuing graduate studies are enrolled in the Graduate School and are subject to the policies as outlined in the Graduate School Handbook , as well as the regulations of the Department of Mathematics. Though the GRE Subject test in mathematics is not a requirement for admission, providing a score for that test may help your application.

Overview of the Program

The goal of the doctoral program in mathematics at Kansas State University is to prepare each student for a successful career in academia or industry. Candidates must demonstrate to the faculty that they have met criteria for both breadth and depth in their studies. A two-part qualifying exam system first examines students on their breadth, which is gained through coursework in the first year, and then examines students on depth in the area of specialty---which is achieved through further coursework and independent study. Together these exams (QE I and QE II) comprise the Graduate School's Preliminary Exam.

COURSE LOAD: The student is required to complete a minimum of 90 hours of graduate credit (courses numbered at the 700 level or above), with at least 60% of the credit hours in courses numbered 800 or higher. Students entering with a Master's Degree from an accredited program may transfer up to 30 hours of that degree toward the PhD coursework requirement. The above-mentioned 90 credit hours must contain a minimum of 30 credit hours of MATH 999 (PhD research), and at least 24 credit hours of coursework (exclusive of MATH 999 courses) in the Department of Mathematics. Eligibility to enroll in MATH 999 is restricted to students having passed the Specialty Exam (see below). This coursework must be completed according to the Graduate School's policy regarding grades and minimum GPA; see paragraph 3, below.

Qualifying Examination QE I

The first part of the qualifying exam, QE I, consists of subject exams, currently offered in four areas.

Algebra (based on MATH 730-731) Analysis (based on MATH 721-722-Complex) Applied Math (based on Math 715-716) Geometry/Topology (based on MATH 770-771)

Students are asked to attempt at least three of these exams upon arrival at Kansas State. The results are used to help determined appropriate placement in graduate courses and teaching assignments. Students must pass exams in three subjects. Two are to be passed by the June following the student's first year of study; a third must be passed by the following August. Exams are offered every June and every August.

Supervisory Committee and the Program of Study

Within two years of passing QE I (or one year of passing the old-system Qualifying Exam) the PhD student is expected to select a major professor, form a supervisory committee, and to file a Program of Study with the Graduate School. The Supervisory Committee will advise the student throughout the remaining period of the study, as well as administer the QE II and the final oral defense. The Program of Study primarily serves to notify the Graduate School of the student's supervisory committee as well as to list the relevant coursework. The Graduate School requires that the Program of Study be filed at least one semester prior to taking the QE II. See more information for Doctoral Candidates .

The Program of Study must be approved by the student's Supervisory Committee, the Department Head, and the Dean of the Graduate School. The Program of Study must list a minimum of 90 credit hours of graduate credit (courses numbered at the 700 level or above that have been taken or will be taken), with at least 60% of the credit hours in courses numbered 800 or higher. Students entering with a Master's Degree from an accredited program may transfer up to 30 hours of that degree toward the Ph.D. Furthermore, the student's program of study must contain a minimum of 30 credit hours of MATH 999 (PhD research) and at least 24 credit hours of coursework (exclusive of MATH 999) in the Mathematics Department. The student must maintain at least a 3.0 GPA in the courses listed on the Program of Study. Furthermore, the student must earn a grade of A or B in three-fourths of these courses, with no worse than a C grade in the remaining courses.

Qualifying Exam QE II

The second part of the Qualifying Exam system consists of written or oral exams in two subjects, a major subject and a minor subject. The student, along with his or her dissertation committee, designs a syllabus based on material from 800-level courses or more advanced topics. The major subject portion of the syllabus must cover at least two semesters at this level; the minor portion at least one semester. The student's advisor and dissertation committee must approve the format (oral, written, or combined) of the exams, which may be taken on separate occasions. The syllabus and proposed method of examination must be submitted to GPAC at least eight weeks before the examination date.

Once the syllabus is approved by GPAC, the candidate submits a Request for Preliminary Examination Ballot form (among forms for grad students to the graduate school. Shortly before the examination date, the Graduate School will issue a ballot for the Preliminary Examination to the Major Professor on which the results of both QE I and QE II are to be recorded. Failure of the QE II is tantamount to failing the Preliminary Exam, and will be grounds for termination of financial support by the Department of Mathematics (if applicable), and failure of the second attempt will be grounds for dismissal from the Ph.D. program by the Graduate School. Upon satisfactory completion of QE II, the doctoral student is automatically advanced to candidacy for the PhD degree.

The PhD Dissertation

After successful completion of the QE II, students will continue their research under the supervision of their doctoral advisors. In order to receive the PhD degree, the student will be required to write a PhD thesis containing non-trivial, new results of publishable quality, and successfully defend this thesis in a final oral examination administered by the Supervisory Committee. All K-State PhD students are required to submit an electronic version of their dissertation (the Graduate School does not accept paper copies). More information, including templates, at K-State Electronic Theses, Dissertations, and Reports .

MATH 999 - PhD Research Coursework

It is the intention of the Department that a PhD student enrolled in MATH 999 (PhD research) is actively doing research directly relevant to the writing of the doctoral dissertation. Since a student not having passed the Specialty Exam has not yet demonstrated sufficient depth to embark on PhD level research, enrolling in MATH 999 coursework is restricted to only those students having passed the Specialty Exam. Students enrolling in MATH 999 for the first time (only) will need to complete the Request for Permission to take Math 999, PhD Research . The student's program of study must contain a minimum of 30 credit hours of MATH 999.

Final Defense of Dissertation

After the student's dissertation has been deemed acceptable by the doctoral advisor, a final oral examination will be scheduled through the Graduate School and held in accordance with Graduate School requirements. When the student is admitted to candidacy, the Dean of the Graduate School appoints an examining committee. This committee consists of the supervisory committee and a member of the graduate faculty not on the supervisory committee. The additional member serves as chairperson for the final oral examination. For further information on the responsibilities of the doctoral advisor and the chairperson during the final examination, read Section L in Chapter 3 of the Graduate School Handbook .

Time Allowed

Students are expected to complete this program within six years and should not anticipate receiving financial support (such as Teaching Assistantships) from the department for more than six years. Students are also responsible for being aware of and following the Graduate School time requirements. (See the Graduate Handbook and the Graduate Catalogue for these requirements.)

In any case, the date that the student was originally admitted to the graduate program in the Department of Mathematics will be considered the beginning date for the purpose of deciding time guidelines/deadlines in reference to the QE I and QE II (major and minor), as well as maximum length of time to complete a degree and for possible financial support.

Consult the Checklist for Doctoral Students prepared by the Graduate School. Any questions concerning the above requirements can be directed to the Director of Graduate Studies.

Ph.D. degrees awarded in Mathematics at KSU.

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Ph.D. in Applied Mathematics

See the catalog copy of the description of the Ph.D. in Applied Mathematics program.

1. Overview

A student in the Ph.D. in Applied Mathematics degree program must maintain satisfactory academic progress towards completion of the degree. Student satisfactory academic progress is primarily assessed by: (a) satisfactory coursework performance, (b) the Qualifying Examination, (c) the Dissertation Topic Approval Defense, and (d) the Dissertation Defense. Courses and the Qualifying Examination are used to ensure that the student has the breadth as well as the depth of knowledge needed for research success. The Dissertation Topic Approval Defense is used to ensure that the scope of dissertation research is important, that the plan is well thought out, and that the student has sufficient skills and thoughtfulness needed for success. The Dissertation Defense is used to assess the outcomes of the dissertation research, and whether or not the plan agreed upon by the Dissertation Committee has been appropriately followed.

The key requirements and milestones for the Ph.D. in Applied Mathematics degree are provided below. Failure to satisfy the requirements can result in suspension or dismissal from the program.

• Minimum Hours
• Interdisciplinary Minor
• Core Courses
• Additional “Core” Courses
• Qualifying Examination
• Dissertation Committee
• Dissertation Topic Approval Defense
• Dissertation Defense

2. Minimum Hours

To earn a Ph.D. in Applied Mathematics degree, a student must complete at least 56 approved post baccalaureate credit hours. This includes 2 hours of Responsible Conduct of Research (GRAD 8302), at least 18 hours of dissertation research and reading (MATH 8994), and the hours for the interdisciplinary minor. Graduation requirements mandate that students must achieve a minimum grade point average of 3.0 to graduate. Receiving more than two grades of C or a single grade of U in any graduate course will result in a suspension from the program.

A limited amount of transfer credit is allowed. In accordance with rules of the UNC Charlotte Graduate School, students are allowed to transfer up to 30 semester hours of graduate credit earned at UNC Charlotte or other recognized graduate programs. Only courses with grades A or B may be accepted for transfer credit. To receive transfer credit, students must file an online request (and submit all necessary documents including copies of transcripts and course syllabi if requesting to transfer non-UNC Charlotte courses).

File an online request to transfer post-Baccalaureate credits at http://gpetition.uncc.edu .

3. Interdisciplinary Minor

The interdisciplinary minor may be satisfied by 9 hours of graduate work outside the mathematics department, by 6 credit hours for a directed project in an area of application (MATH 8691/8692), or by a combination of external coursework and a directed project in an area of application totaling 9 credit hours.

It is expected that interdisciplinary minor courses shall in general be in STEM disciplines, but if there are applications in the student’s dissertation work towards the social sciences, courses in those fields are allowed too. The following is a non-exhaustive list of interdisciplinary minor courses allowed for several fields.

Physics: PHYS 5222, 5232, 5242, 5271, 6101 through 6201, 6203 through 6211, 6221 through 6271. A common example is PHYS 6210, but 5242 and 5271 would also be along the same lines.

Optics: OPTI 8101, 8102, 8104, 8105, 8211 with 8102, 8104, and 8211 being particularly relevant.

Molecular Biophysics: PHYS 6108/OPTI 8000, PHYS 6204, PHYS 6610 ( https://mbp.charlotte.edu/ )

Mechanical Engineering: MEGR 6116, 7113, 7164 for students who have specialized in math of fluids, while 6141, 6125, 7102, 7142, and 7143 for those specializing in continuum mechanics and elasticity.

Computer Science: ITCS 6111, 6114, 6150, 6153, 6155, 6165, 6170, 6171, 6220, 6226 with 6114 commonly taken.

Finance and Economics: Any of FINN or ECON courses listed under the MS Mathematical Finance program. Common examples include FINN 6203, 6210, 6211, and ECON 6206, 6113, 6219.

Mathematics Education: Any graduate level MAED courses such as MAED 6122, 6123, 6124.

4. Core Courses

All students in the Ph.D. in Applied Mathematics degree program must take the following courses, regardless of their intended area of study:

• GRAD 8302 Responsible Conduct of Research (2 hours, usually required to take within the first year in the program)
• MATH 8143 Real Analysis I (3 hours)
• MATH 8144 Real Analysis II (3 hours)
• MATH 8994 Doctoral Research and Reading (at least 18 hours)

Students whose intended area of study is statistics or mathematical finance are also required to take

• MATH 8120 Theory of Probability I (3 hours)

5. Additional “Core” Courses

The following courses, though not explicitly required, are strongly recommended for each area of study.

Statistics: STAT 5123, 5124, 5126, 5127, 6115, 8127, 8133, 8135, 8137, 8139, 8122, 8123, 8027 (at least once)

Computational Math: MATH 5165, 5171, 5172, 5173, 5174, 5176, 8172, 8176

PDE and Mathematical Physics: MATH 5173, 5174, 8172

Probability: MATH 5128, 5129, 8120, 8125

Dynamical Systems: MATH 5173, 5174, 7275, 7276, 7277

Topology: MATH 5181, 8171, 8172 and independent study

Algebra: MATH 5163, 5164, 8163, 8164, and 8065 and/or independent study

Mathematical Finance: MATH 6202, 6203, 6204, 6205, 6206

6. Qualifying Examination

After being admitted to the Ph.D. program, a student is expected to take the qualifying examination within three semesters. This time limit may be extended up to two additional semesters in certain cases, depending on the background of the student and with program approval. The qualifying examination consists of two parts: the first part is a written examination based on Real Analysis I and II (MATH 8143/8144) or Theory of Probability I and Real Analysis I (MATH 8120/8143), the latter intended for a student with intended area of study in statistics or mathematical finance . The second part is a written examination based on two other courses chosen by the student to be specifically related to the student’s intended area of study and approved by the Graduate Coordinator. Typical choices for Part II are STAT 5126/5127, MATH 5173/5174, MATH 5172/5176, MATH 5163/5164, MATH 6205/6206, etc. The student may be allowed to retake a portion of the qualifying examination a second time if the student does not pass that portion on the first attempt within the guidelines of the Graduate School regulations pertaining to the qualifying examination and as overseen by the department Graduate Committee. A student who does not complete the qualifying examination as per the regulations of the Graduate School will be terminated from the Ph.D. program.

Complete and submit the following form after taking the Qualifying Examination. (Qualifying Exam Report Form) -> Graduate School form.

7. Dissertation Committee

After passing the Qualifying Examination, the student must set up a Dissertation Committee of at least four graduate faculty members, which must include at least three graduate faculty members from the Department of Mathematics and Statistics and one member appointed by the Graduate School. The committee is chaired by the student’s dissertation advisor. If the dissertation advisor is a graduate faculty member from an outside department or institution, a graduate faculty member from the Department of Mathematics and Statistics must be a co-chair of the committee. The Dissertation Committee must be approved by the Graduate Coordinator. After identifying and obtaining the signatures of the Dissertation Committee faculty, the Appointment of Doctoral Dissertation Committee Form must be sent to the Graduate School for the appointment of the Graduate Faculty Representative.

The Dissertation Committee should be appointed as soon as it is feasible, usually within a year after passing the Qualifying Examination.

Complete and submit the following form within a year of passing the Qualifying Examination. (Appointment of Doctoral Dissertation Committee Form) -> Graduate School form.

8. Dissertation Topic Approval Defense

Each student must present and orally defend a Ph.D. dissertation proposal after passing the Qualifying Examination and within ten semesters of entering the Program. The Dissertation Topic Approval Defense will be conducted by the student’s Dissertation Committee, and will be open to faculty and students. The dissertation proposal must address a significant, original and substantive piece of research. The proposal must include sufficient preliminary data and a timeline such that the Dissertation Committee can assess its feasibility.

The student should provide copies of the written dissertation proposal to the Dissertation Committee at least two weeks prior to the oral defense. At the discretion of the Dissertation Committee, the defense may include questions that cover the student’s program of study and background knowledge and techniques in the research area. The Dissertation Committee will unanimously grade the Dissertation Topic Approval Defense as pass/fail according to the corresponding rubrics. A student may retake the Dissertation Topic Approval Defense if he/she fails the first time. The second failed attempt will result in the termination of the student’s enrollment in the Ph.D. program. It is expected that the student first take the proposal defense by the ninth semester after enrollment to provide time for a second try should the first one fail. A doctoral student advances to Ph.D. candidacy after the dissertation proposal has been successfully defended. Candidacy must be achieved at least six months before the degree is conferred (so if you plan to graduate in a spring semester with the commencement on May 14, then you would need to successfully defend your dissertation topic by November 13 the prior year.)

The student must follow the following procedure in order to defend the dissertation proposal.

• Communicate with the Dissertation Committee to set up a date/time for the oral defense, and reserve a defense room for at least two hours .
• Send an electronic or written copy of the dissertation proposal to each member of the Dissertation Committee at least two weeks prior to the oral defense.
• Inform the Graduate Coordinator the schedule at least one week prior to the oral defense.

Complete and submit the following form only after successfully passing the Dissertation Topic Approval Defense. (Petition for Topic Approval Form) -> Graduate School Form.

9. Dissertation

Each student must complete and defend a dissertation based on a research program approved by the student’s dissertation advisor which results in a high quality, original and substantial piece of research. The student must orally present and successfully defend the dissertation before the student’s doctoral dissertation committee in a defense that is open to the public. The Dissertation will be unanimously graded as pass/fail based on the corresponding rubrics by the Dissertation Committee and must be approved by the Dean of the Graduate School. Two attempts of the Dissertation Defense are permitted. The second failed attempt will result in the termination of the student’s enrollment in the Ph.D. program.

The student must follow the following procedure in order to defend the dissertation.

• Communicate with the Dissertation Committee to set up a date/time for the public defense, and reserve a defense room for at least two hours with the help of the Graduate Coordinator.
• Send an electronic or written copy of the dissertation to each member of the Dissertation Committee at least three weeks prior to the public defense.
• Send an electronic copy of the dissertation in PDF as well as an abstract in a separate word file to the Graduate Coordinator at least two weeks prior to the public defense. The abstract is limited to 200 words, and does not have to be the same as the abstract included in the dissertation.
• Prepare a presentation that should be at least 45 minutes long.

Complete and submit the following forms after defending your Dissertation. (Dissertation Report for Doctoral Candidates Form) -> Graduate School Form.

Also, submit the Dissertation Title Page with Original Committee Signatures.

In addition, submit ETD Signature Form with original committee and student signatures to the Graduate School within 24 hours after defense.

10. Graduation

Detailed information about graduation including the dissertation manual can be found on the Graduate School’s Graduation website . The Graduation process consists of the following steps and all three are required to complete the graduation process.

• Complete the online graduation application – directions below – deadlines in the academic calendar.
• Submit an approved candidacy application to the Graduate School – directions below – deadlines in the academic calendar.
• Register for the term of graduation – deadlines in the academic calendar.

How to Apply for Graduation: Log into My UNCC. Select Banner Self Service, Student Services, Student Records and Online Graduation Application. Read the directions. Click “Continue” if this is the first time you have applied for graduation or “Create a New Application” if you have applied previously. After you complete all sections, remember to click the “Submit” button.

How to Access the Electronic Candidacy Application: Log into My UNCC. Select Banner Self Service, Student Services, Student Records and Apply for Candidacy for Graduate Students. Carefully read and follow all directions for each section. The total number of credit hours selected must be at least the minimum required for your degree or certificate. After you complete all sections, click the “Print” button. Do not change the page layout or formatting in any way. Take the printed document to your department for the Graduate Coordinator’s approval signature and then submit it to the Graduate School. Electronically submitted forms are not accepted.

Pay attention to the various deadlines in the official UNC Charlotte academic calendar , in particular, the following deadlines if you are planning to graduate.

• Deadline for graduate students to file candidacy form
• Deadline for graduate students to apply for graduation
• Doctoral dissertation pre-defense formatting consultation deadline
• Doctoral dissertation defense deadline
• Doctoral dissertation post-defense formatting consultation deadline
• Last day to submit doctoral dissertations to Graduate School

In addition, complete and submit the following forms to the graduate school.

• Complete Survey of Earned Doctorates at https://sed.norc.org/doctorate . Print the Certificate of Completion and submit to the Graduate School within 24 hours after defense.
• Contact Information Form
• Copyright and Open Access Publishing Payment Form (optional)

Finally, a sample graduation checklist for doctotal graduates can be found here . Make sure

• All courses with In Progress grades have been assigned grades; check with your advisor to ensure this happens. This must be completed 10 days prior to the commencement.
• All courses in the current term have been assigned grades; check with your advisor or instructor to ensure this happens. This must be completed 10 days prior to the commencement.

Apply Online

Online Graduate Applications for Fall quarter admission will be available the beginning of September at:

Apply Now! — https://connect.grad.ucsd.edu/apply/

Applying to the Graduate Program

Applications are accepted for the Fall quarter only. The application deadlines for admission are:

Fall 2024 Admission

The Department of Mathematics application process is paperless. All application materials must be uploaded to your online application. Please do not send any application materials to us in the mail.

We appreciate your interest in our graduate program here in the Department of Mathematics at UC San Diego!

For doctorate degrees, we offer a Ph.D. in Mathematics allowing study in any area of mathematics (encompassing Pure Mathematics and Applied Mathematics), a Ph.D. in Mathematics with a  Specialization in Computational Science , and a Ph.D. in Mathematics with a  Specialization in Statistics .

For master degrees, we offer a M.A in Pure Mathematics, a M.A. in Applied Mathematics, and a M.S. in Statistics. Admission decisions for all degree programs are made separately.

For new prospective UC San Diego graduate students, admission to the graduate program is managed through the Department of Mathematics and the Graduate Division. We accept applications for the Fall quarter only.

For any current UC San Diego graduate student who wants to earn a master's degree from the Department of Mathematics, send email from your UC San Diego email account to  [email protected]  to inquire about the application procedure; this must be done before taking any courses or comprehensive/qualifying examinations to be counted toward a degree.

Departmental support offered to Ph.D. students typically includes a Teaching Assistantship in each academic quarter as well as full tuition and fee remission. This is guaranteed for five years as long as a student is in good academic standing and fulfills all teaching responsibilities satisfactorily. There will be no changes to this policy as long as funds remain available.

Application Requirements

For admission to the graduate programs, a Bachelor's degree in Mathematics is recommended or a strong background in mathematics with a minimum GPA of 3.0 required. A year's sequence in both upper-division algebra and real analysis is strongly encouraged.

The following GRE Tests are strongly recommend (but not required) for all applicants:

You are not required to submit a GRE General test score. If you are unable to provide the GRE Mathematics Subject test score, it is strongly recommended that you submit a GRE General test score.

It is strongly recommended that you submit a GRE Mathematics Subject test score. Applicants who do not submit such a score will still be considered, and may be accepted if there is solid evidence of the skills that are included in the GRE Mathematics Subject test. In case you are unable to submit the GRE Mathematics Subject test results, please include a short explanation in your application.

There is no required minimum score for the GRE General Test.

We recommend that the GRE General or Subject Test be taken no later than October in order for scores to be reviewed by the Admissions Committee.   

English Proficiency Requirements

The university's policy regarding English language proficiency can be found at  https://grad.ucsd.edu/admissions/requirements/international-students/english-proficiency.html

Test Scores Reporting Requirements

The school code to send GRE and TOEFL scores is  4836 .

Fees Requirements

The application fee is:

• $135.00 for U.S. Citizens and Permanent Residents Applicants
• $155.00 for International Applicants

Document Requirements

The following documents are required for a complete application:

• Statement of Purpose
• Unofficial transcripts (official transcripts are only required if admitted into the program)
• List of mathematics courses taken/projected as well as textbooks used
• Exactly 3 letters of recommendation
• TOEFL or IELTS or PTE Academic test scores (for international applicants from non-English speaking countries)

Candidates applying to the Ph.D. in Mathematics with a Specialization in Statistics, should select "Statistics" in the "Current Area of Interest" section of their online application (this means the person is applying to the Specialization in Statistics degree).

Candidates applying to the Ph.D. in Mathematics with a Specialization in Computational Science (CSME), should select "Computational Science" in the "Current Area of Interest" section of their online application (this means the person is applying to the Specialization in Computational Science degree).

Application Questions?

For answers to your questions, please read the answers to  Admissions FAQs (Graduate)  before submitting inquiries to [email protected].

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(858) 534-3590

Master of Science in Mathematics and Applied Statistics

At California State University Long Beach

The Department of Mathematics & Statistics at CSULB offers four Master of Science programs .

Teaching & Graduate Assistantships provide students with funding and with college teaching experience.

Graduates have found employment in both technical and academic workplaces. Many have obtained tenure-track community college professorships. Others have gone on to PhD programs.

MS in Mathematics, General Option

Study and explore concepts in areas including analysis, algebra, topology, and geometry, as well as the   deep connections between and among these subjects.

MS in Mathematics, Option in Applied Mathematics

Study applied math methods with an emphasis on computational skills.

MS in Mathematics, Option in Mathematics Education for Secondary School Teachers

A flexible program that includes coursework in mathematics and in mathematics education research & theory.

MS in Applied Statistics

Using conceptual foundations and statistical software packages ( SAS , R , and Python ), students are trained to analyze real world data appropriately and communicate their findings effectively. The tools learnt here will open the door for careers in data science and analytics, or prepare you for a PhD in a variety of related fields.

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Is a Doctorate Degree Worth It?

Know before you read At SNHU, we want to make sure you have the information you need to make decisions about your education and your future—no matter where you choose to go to school. That's why our informational articles may reference careers for which we do not offer academic programs, along with salary data for those careers. Cited projections do not guarantee actual salary or job growth.

Earning a doctorate takes time, money and discipline. Like many things worth doing, the process is challenging but also rewarding. Becoming an expert in your subject area and immersing yourself in your chosen area of study makes the process of earning a doctorate important to many people. Certain professions require or value a doctorate for promotion potential.

In fact, career advancement, love of the subject matter and personal satisfaction are three of the top reasons why Dr. Bridgitte Kiprop '23 , Dr. Jennifer Barry ’23 and Dr. Torialyn Draper Crook earned their doctorates.

• For Kiprop '23, part of her motivation for earning a doctorate in International Business was setting an example for her six children.
• For Barry, ’23, who earned a doctor of education degree in educational leadership, part of her motivation was to prepare for success in meeting her long-term career goal to become a university president.
• And for Crook, earning her doctorate in education was a commitment that she undertook to honor her family’s legacy of valuing education.

How Difficult is Earning a Doctorate?

For Kiprop, time management was her key to success. With six children, she had to make the most of any time in the day that she could find. “If I had … five minutes, I would use the five minutes,” she said. “Other times, I was luckier (and had) two hours.”

Despite the time-management  challenges of earning an advanced degree while raising her family, Kiprop feels that the process of earning that degree was a way to inspire her children to work hard to meet their own goals.

“I really hope that my children will ... know that whatever it is they feel called to do, whatever their ambitions, their goals are achievable,” she said.

To manage the challenge of advanced studies, having the right people around you as you work on your degree is essential, according to Crook. “Surround yourself with family, friends, colleagues and mentors who can provide encouragement during challenging times,” she said.

Crook stresses that everyone’s journey to earning their doctorate is unique. She recommends being prepared for the unexpected, and remaining flexible in adjusting your path as you work toward completing your degree.

How Long Does a Doctorate Take?

Students may have family commitments, health challenges or need to work full or part-time while attending school . Many students face all of these circumstances. Crook managed to complete her doctorate in 5 years, though it wasn't easy for her. She faced a significant personal health challenge and was raising two children while also attending school.

For Barry, earning her doctoral degree is part of an educational path that started with her bachelor’s degree at SNHU (formerly New Hampshire College) in 2000. She then continued her education to earn a master's degree throughout several jobs and geographic moves.

Barry views her entire educational journey as part of the process that led to meeting her ultimate goal of earning a doctorate.

What Skills Are Needed to Earn a Doctorate?

While every academic program is different, Crook finds certain skills and competencies necessary for success, regardless of field. These skills include:

• Building relationships
• Organizational skills
• Self-motivation
• Writing skills

Crook finds building relationships particularly important. While working on her degree, the strong relationship that she developed with her dissertation chairperson proved essential. She also built positive relationships with other doctoral students, which led to a strong peer support network throughout her program.

Kiprop echoes the importance of building relationships in her field as well. For her, building new relationships is a way to open your mind to new experiences and opportunities.

Find Your Program

What types of jobs can you get with a doctorate.

While a doctorate is helpful for working in leadership roles at colleges and universities, there are many opportunities for doctoral degree holders to work at the highest levels in their profession outside of higher education as well.

Some of the top professions that require a doctoral or professional degree and have a faster-than-average predicted growth rate, according to the BLS, are:

• Astronomers* (SNHU does not currently offer graduate degrees in astronomy or physics)
• Biochemists and biophysicists* (SNHU does not currently offer graduate degrees in biochemistry or biophysics)
• Clinical and counseling psychologists* (SNHU does not currently offer doctorates in psychology, but you could start with a bachelor's in psychology , followed by a master's in psychology )
• Higher education teachers and professors — particularly business, computer science and engineering teachers*

Two more examples of areas where a doctorate can help prepare you for advancement in your career are educational leadership and international business.

A doctorate in educational leadership can be a Doctor of Philosophy degree, known as a PhD, or a Doctor of Education degree, known as an EdD. The PhD in Education Leadership  typically leads to higher education roles in teaching and research. The EdD in Educational Leadership , which Barry earned, typically leads to leadership and strategy roles in an education setting that may be at the higher education or secondary school level.

A PhD in International Business  may include addressing a gap in an existing body of knowledge by conducting research. Kiprop, who earned her doctorate at SNHU, plans to use her degree to research entrepreneurship in small business finance.

Motivated by being from a developing country — Kenya — she has a personal interest in helping grow small businesses in similar developing areas. “I can also use that same knowledge at the New Hampshire level because the issues there perhaps are different but still … relevant,” she said.

Regardless of your program field, the process of earning a doctorate can help you explore ways of applying your newfound and existing knowledge that you may not have considered prior to starting your program.

Is it Better to Have a Master’s or Doctorate?

Both a master’s degree  and a doctorate offer opportunities for career advancement. Choosing which to earn, or whether to earn both, is a highly personal decision based on your personal and professional goals and aspirations, according to Crook.

Before deciding which degree is right for you, consider your goals. Speaking with a career counselor  or graduate admissions counselor to learn about career options and pathways toward earning the degree can be a helpful step toward making this decision.

In many fields, a master’s degree is enough  to move forward in your career. But, earning a doctorate is an opportunity to take your career a step further, according to Crook. That step “gives one the opportunity to direct their career trajectory specifically through research and other specialized skills and knowledge,” she said.

How Valuable is a Doctorate?

A doctorate isn’t for everyone, but it can be right for you depending on your chosen field and career path.

For many people, earning a doctorate is just as important as a personal accomplishment as it is a professional one. “I (always) understood the significance of progressing in my career and staying connected to my field of higher education,” Crook said. “My doctoral journey was worthwhile as it aligned with my career goals  and personal aspirations,” she said.

For Barry, the doctorate was worth it because she believes strongly in the power of education . “You see how (education) transforms people’s lives and … gives people opportunities that they didn’t see before,” she said.

She has seen many people earn degrees only for their family members to then continue in their footsteps. “I just think that generationally, (education) is creating pathways for people,” she said.

Deciding whether to pursue a doctorate is ultimately a very personal decision, but one that can lead you to build new relationships and a new knowledge base while helping you reach or exceed your career goals.

A degree can change your life. Find the SNHU doctorate degree  that can best help you meet your goals.

*Cited job growth projections may not reflect local and/or short-term economic or job conditions and do not guarantee actual job growth. Actual salaries and/or earning potential may be the result of a combination of factors including, but not limited to: years of experience, industry of employment, geographic location, and worker skill. 

A former higher education administrator, Dr. Marie Morganelli  is a career educator and writer. She has taught and tutored composition, literature, and writing at all levels from middle school through graduate school. With two graduate degrees in English language and literature, her focus — whether teaching or writing — is in helping to raise the voices of others through the power of storytelling. Connect with her on LinkedIn .

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How to Get a Master's Degree

Is a Bachelor's Degree Worth It?

Is a Master’s Degree Worth It?

About southern new hampshire university.

SNHU is a nonprofit, accredited university with a mission to make high-quality education more accessible and affordable for everyone.

Founded in 1932, and online since 1995, we’ve helped countless students reach their goals with flexible, career-focused programs . Our 300-acre campus in Manchester, NH is home to over 3,000 students, and we serve over 135,000 students online. Visit our about SNHU  page to learn more about our mission, accreditations, leadership team, national recognitions and awards.

A Mathematician in Foundation Year

April 11, 2024

Spotlight: Fareed Hawwa, PhD, Assistant Teaching Professor

Fareed Hawwa, Assistant Teaching Professor, enriches his students’ learning experience with his extensive real-world financial expertise. A significant career in the finance sector preceded his time at Northeastern University in Foundation Year, one of a variety of pathway programs offered by the College of Professional Studies (CPS).

Hawwa began his career as an equities trader in New York City. He also occupied other roles such as analyst, partner, and head of trading at a financial firm in Chicago, before transitioning to his current position at CPS. In these various professional capacities, he had to hone his knowledge of mathematics and apply it to his management of both technical analysis and risk management methodologies, utilizing logic and quantitative analysis. He led trading operations and strategic initiatives for funds valued at $250 million in assets under management during this time. The experience of managing a high-net-worth portfolio helped him acutely understand the mechanics of money. He now shares this knowledge in the classroom.

Hawwa’s upbringing took place in Rhode Island. During his high school years, he participated in wrestling and garnered attention from a coach at New York University (NYU). Enrolling at NYU, he devoted himself to the sport, recognizing its rigorous demands. Hawwa frequently undertook the arduous task of cutting weight by up to ten pounds in just a few days to meet the requirements of specific weight classes, demonstrating extraordinary discipline of both body and mind while maintaining his academic performance.

During his time at NYU, he made the decision to major in mathematics. Expressing his sincere affinity for the subject, he said,

“While some find math boring or difficult, for me, it brings joy.” Fareed Hawwa

Approaching the completion of his bachelor’s degree at NYU, Hawwa knew that he wanted to obtain a doctoral degree in mathematics.

He decided to attend Louisiana State University (LSU) for his master’s and PhD degrees. Halfway through his studies there, Hawwa was awarded a National Science Foundation GK-12 fellowship, contingent upon his commitment to teach each semester while pursuing his doctoral studies.

“There were six times I looked for flights home because I was going to quit; it took a lot of discipline to stay the course.”, he said. But Hawwa realized that he had to want to put in the work to get the result. “This realization really shaped me as both a jock and an academic” , he said.

In the initial year of his graduate studies, he taught mathematics at a local alternative high school, an institution for students facing suspension within the public school system.

“The students had different challenges, and I witnessed some unfortunate situations, such as students being summoned to court during class time. I always assumed that all students desired to attend school, but that isn’t always the reality.” Fareed Hawwa – Reflecting on his Experience

In addition to teaching, Hawwa also resumed wrestling. His unwavering commitment to the sport propelled him to a coaching role for the NCWA LSU wrestling team.

During the next two years in his doctoral program, he continued to coach wrestling, and he also transitioned to teaching undergraduate courses on campus.

He expressed satisfaction with this shift, stating, “I had the opportunity to engage with students who possessed a genuine interest in mathematics and were able to be fully vested in their academic journey.”

In the course of his time at LSU, Hawwa was a three-time recipient of the Mathematics Department Teaching Excellence Award for his work with students.

In 2010, after successfully defending his PhD dissertation, Hawwa moved back to New York and bartended before landing a job at a trading firm. Shortly after this, he got an offer to join a hedge fund in Chicago as an analyst, later becoming partner and head of trading.

Hawwa describes his time at the hedge fund as exciting. While the role was challenging, the substantial salary served as an attempt to rationalize the extensive hours and the inevitable sacrifice of work-life balance inherent to such demanding positions. Despite the financial compensation, he came to realize that mere pursuit of monetary gain was not his primary motivator.

In March 2018, Hawwa left the firm and took a year off work. He took time to look inward and got certified in transcendental meditation. “These pursuits helped me to identify my true passion of teaching” , he said.

Foundation Year

In 2019, now back in Rhode Island, Hawwa applied for jobs and seized an opportunity to teach within Northeastern University’s Foundation Year, a program that serves students in the city of Boston in transitioning from high school to college. Administered by the College of Professional Studies, it offers rigorous academic coursework within a supportive cohort environment during students’ initial college year. Completion of the Foundation Year enables students to progress into a degree program at Northeastern University. The program’s design aims to maximize student potential, offering small classes and individualized advising. Additionally, the cohort model fosters a strong sense of community, supplemented by provisions such as textbooks, technology access, and a dining plan providing meals on campus throughout the year. The program boasts a 92% average matriculation rate for students who successfully complete the program and meet progression standards and continue at Northeastern. Many of these students successfully graduate with a bachelor’s degree.

Hawwa was hired by Foundation Year to teach a variety of math classes. The very first class he taught, Foundations of Math, started a few weeks after he was hired. He has since taught other classes, including: College Algebra, PreCalculus, Calculus 1, Calculus 2 recitation, and most recently, Personal Finance.

As a pragmatic and empathetic educator, Hawwa places a high value on fairness and respect in his interactions with students. He maintains accountability among students while being mindful not to place undue pressure on them.

He emphasized, “Especially during the COVID-19 pandemic, if a student didn’t have their camera on, I didn’t press the issue. I like to employ a deeper concentration on the subject matter itself and what support they require from me.”

As Hawwa taught his math classes that first year, his colleagues at CPS got to know him better. They learned that he used to work in finance and he started to attract financial questions from them, like how to change allocation in a 403b retirement plan to maximize return, how to open a Roth IRA account, or whether they should purchase cryptocurrency.

Seeing that Hawwa was becoming known for his professional expertise, Director of the Program, Martha Loftus, suggested that Hawwa teach a course around financial literacy.

“Fareed’s exuberance for helping others better understand their personal finance was clear when he started at CPS. The fact that he did so with industry experience was an added benefit. We’re always looking to add new courses to the Foundation Year curriculum, so it made sense to add Personal Finance and draw upon his energy, knowledge and commitment to the subject. Financial literacy is an important skill for everyone. The Foundation Year holistic model of student success prompts us to always be thinking of ways we can help students thrive in and out of the classroom” – Martha Loftus

In his Personal Finance course, Hawwa shows students skills like how to read a stock chart, and he explains the dangers and benefits of compound interest. For many of his students, the discussion he has with them about the importance of a healthy FICO score is the first time they are introduced to the concept.

Hawwa says that teaching is ‘the highest honor of [his] life. It’s taught [him] a lot about humility and empathy.’ He said, “some students have told me that the way they viewed personal finance before they took my class was stressful, but now that they understand the basics, they are able to rise above it and pursue financial success.”

“Math is like life. In math, you need humility, or it’ll eat you up.” Fareed Hawwa

Fareed’s Money Management Top Tips

• On investing: “Time and compounding are what will really make people money, as opposed to buying stocks they heard about on the train.”
• Understanding ‘ compound interest’ is key to financial success.
• If you allow money to control your life, you risk missing out on other things that bring you joy.
• Some people are so poor, all they have is money.
• Develop a personal financial practice.

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Quantifying content-specific language use and classroom dynamics in elementary math education.

Jiner Zheng

Understanding academic language specific to subjects like mathematics is crucial for students to grasp domain knowledge. The ability to use mathematically accurate language is a key indicator of math mastery, yet research quantifying this relationship remains scarce. Traditional classroom observations, the main method for evaluating pedagogical practices, suffer from limitations in time efficiency and reliability. To address these challenges, this study applies Natural Language Processing (NLP) to analyze elementary math class transcripts from the National Center for Teacher Effectiveness (NCTE). It focuses on quantifying mathematical language use and its impact on classroom dynamics, revealing a significant link between mathematical language usage and classroom interactions, such as student engagement and teachers’ conversational uptakes.

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MS in GeoInformatics

Program Overview

The MS in GeoInformatics program provides training for the next generation of analysts and leaders in geospatial and informational technologies, and includes environmental modeling and programming, remote sensing, visualization, databases, spatial ontologies and statistics, and applied research.

Master of Science (MS) in GeoInformatics

Students must obtain 35 credits to complete the Master of Science in GeoInformatics.

The MS GeoInformatics program is designed to prepare students for management- and advanced research-level employment positions and/or acceptance into PhD programs in GIS-related fields. Classes vary in their structure from lecture to computer laboratory classes to seminars. Most classes provide hands-on computer experience.

Students must choose one of two program options: the Thesis Option or Internship Option. The Thesis Option is recommended for students who will subsequently pursue a Ph.D. For other students, either option is acceptable.

Students will be required to take courses from the following groups:

• GeoInformatics and GIS core courses (19 credits);
• Elective courses in GeoInformatics and GIS or allied fields such as Geography, Computer Science, Urban Planning, Geology, Economics, etc. (12 credits);
• One three-credit course in the Thesis Option (3 credits) OR one to three elective courses in the Internship Option (3 credits in total).

In addition to traditional courses, students will have the opportunity to participate in an active technology and research seminar series, field trips to local private and public sector GIS groups and research sites, as well as contribute to real-world GIS projects through internal and external mentorship programs.

You must meet the following minimum requirements in order to be considered for admission.  Meeting these minimum requirements does not guarantee acceptance to the program.

• A bachelor’s degree from a regionally accredited institution comparable in standard and content to a bachelor’s degree from Hunter College-  College & University Transcripts
• Minimum undergraduate grade point average of 3.0.
• An introductory statistics course and an introductory computer science/programming course are required.
• Official score report of the  Graduate Record Examination (GRE) General Test . *GREs are waived for the incoming Spring and Fall 2024 class.
• Two letters of recommendation from appropriate academic or professional references.
• A statement of purpose of approximately 500 words describing your objectives in undertaking graduate study. In reviewing applications, considerable importance is placed on the applicant’s interest in and commitment to advanced study and professional developmen

Providing an exceptional value is what we do best. See how Hunter's annual tuition compares against in-state tuition at other top graduate programs.

Career Paths

While specific career paths and salaries can vary based on factors such as experience, location, and industry demand, here are ten potential career paths for individuals with an MS in GeoInformatics in New York City, along with approximate average salaries:

Cartographers utilize GeoInformatics tools to create maps, integrating geographical data into visual representations.

Average Salary: $55,000 - $75,000

Geospatial data analysts interpret and analyze geographic data using GeoInformatics tools for insights and decision-making.

Average Salary: $60,000 - $80,000

GIS specialists utilize GeoInformatics technologies to manage, analyze, and visualize spatial data for various applications.

Average Salary : $65,000 - $90,000

These professionals manage databases containing geographical data, ensuring accuracy, security, and accessibility.

Average Salary: $60,000 - $85,000

Remote sensing analysts use GeoInformatics tools to interpret remote sensing data for environmental analysis, urban planning, etc.

Average Salary: $65,000 - $85,000

Spatial data scientists use GeoInformatics techniques to analyze spatial data and develop models for predictive analysis.

Average Salary: $70,000 - $95,000

Surveying technicians use GeoInformatics tools for precise measurement and mapping of land areas.

Average Salary: $50,000 - $70,000

Urban planners with a geospatial focus utilize GeoInformatics for urban development plans, infrastructure, and zoning.

Geospatial visualization specialists create visual representations of geographical data for analysis and presentation.

Web GIS developers create and maintain web-based geographic information systems, allowing data access and visualization.

Average Salary: $70,000 - $90,000

Application Deadlines

Applicants are encouraged to apply as early as possible. Hunter College may consider late applications on a rolling basis pending space is still available in the program.

Some programs may extend their application deadlines beyond those listed above. Please contact Graduate Admissions for specific information. For information on how to apply, click the link below.

Students Educated Outside the US

Applicants whose native language is not English and who have taken all or part of their undergraduate education in a country where English is not the native language are required to submit scores on the  Test of English as Foreign Language (TOEFL ) or the  International English Language Testing System (IELTS ). The following minimum scores must be obtained:

• TOEFL iBT: 80/ Paper Based Test: 550/ Computer Based Test: 213
• IELTS: 6.5 Overall Band Score

Ready to Apply?

Get started on your application now or visit the academic department's website to learn more about this graduate program.

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