Last Updated on February 7, 2023 by Fola Shade

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The Ph.D degree in mathematics at the University of South Carolina serves to prepare students for professional careers in academic research, college and university teaching, industry, and national laboratories.

## Columbia Math PhD Overview

A PhD usually involves students engaged independently in original and significant research in a specific field or subject prior to the production of a publication-worthy thesis. By undertaking a PhD, you will become an expert, possibly an international expert, in your chosen field. A doctorate is the highest academic degree that can be awarded by a university. In Germany, studying for a doctorate means working intensively on a specific subject or research project over a long period of time. The duration of the doctorate also varies. Three to five years is typical. If you decide to take a doctorate, you can choose between different forms of study.

Math

Program and Specialty rankings

**#7**in**Mathematics (tie)****#8**in**Algebra / Number Theory / Algebraic Geometry (tie)****#13**in**Analysis****#15**in**Applied Math****#7**in**Geometry****#9**in**Topology**

## What Is a PhD in Mathematics?

A PhD in Mathematics is a doctoral degree obtained by a graduate student in mathematics. This kind of mathematics graduate program allows students to develop their research capabilities in mathematics and its potential applications.

PhD in Mathematics can be a Doctor of Philosophy, Doctor of Science, or Doctor of Applied Mathematics degree. Students need to submit their PhD thesis in order to complete the math degree program they are pursuing. Math doctorate programs can take between three and six years to complete, depending on how much time is dedicated to the thesis and its required research.

## How Long Does It Take to Get a PhD in Mathematics?

It takes about five years to get a PhD in Mathematics. Depending on the academic institution and the specifications of the program, it can take between three and six years. Some students prefer to have a master’s degree before entering a doctoral program in mathematics, but most programs do not require students to have more than a bachelor’s degree.

Some doctoral mathematics academic programs offer two degrees called dual degree programs. You can begin pursuing a Master’s Degree in Mathematics and begin earning credits for a PhD at the same time.

### Reasons for Getting a PhD in Mathematics

**Specialized skills.**A PhD in Mathematics equips you with highly valuable and marketable skills. Aside from subject-specific abilities, you can obtain several transferable skills that will be beneficial in practically any industry, such as exceptional numeracy, logical ability, holistic deduction, and reasoning skills.**Higher salary.**A PhD is a terminal graduate degree, meaning it is the highest level of academic certification you can achieve in this field. So with a PhD you will gain the highest skills and knowledge in mathematics. High-level skills and knowledge often translate to a high salary.**Career opportunities.**One of the best advantages math PhDs have is the option of following a variety of employment pathways. To some extent, all sciences are built on basic mathematical principles, so there are many career opportunities with a PhD in Mathematics. With this kind of degree, you can work in finance, academia, or IT.**Research opportunities.**Doctoral Degrees in Mathematics cover theoretical mathematics which is one of the best areas for research and research methodology. During your doctoral studies in math, you will study and research with some of the smartest people in the world.

## Columbia Math PhD Program of Study

The Department of Mathematics offers a program leading to the degree of Doctor of Philosophy.

The PhD program is an intensive course of study designed for the full-time student planning a career in research and teaching at the university level or in quantitative research and development in industry or government. Admission is limited and highly selective. Successful applicants have typically pursued an undergraduate major in mathematics.

In the first year of PhD studies, students must pass written examinations in the areas of the basic first-year courses. In the second year an oral examination on two selected topics must be passed. Subsequent years are devoted to seminars, research, and the preparation of a dissertation. Students are required to serve as teaching assistants or instructors for four years beginning with the second year of study. Those contemplating academic careers are strongly encouraged to serve a primary instructor of at least two semesters. En route to the Ph.D., students will earn three degrees: a Master of Arts (after year one), a Master of Philosophy (after year four), and the Doctorate of Philosophy (after a successful thesis defense).

There are also allied doctoral programs in statistics, computer science, and applied mathematics.

## Research Facilities

The Mathematics Department is housed in a comfortable building containing an excellent mathematics library, computing and printing facilities, faculty and graduate student offices, a lounge for tea and conversation, and numerous seminar and lecture rooms.

## Columbia Math PhD Financial Aid

The department has a broad fellowship program designed to help qualified students achieve the PhD degree in the shortest practicable time. Each student admitted to the PhD program is appointed a fellow in the Department of Mathematics for a period of five years, contingent on good progress. A fellow receives a stipend for the nine-month academic year and is exempt from payment of tuition.

A fellow in the Department of Mathematics may hold a fellowship from a source outside Columbia University. When not prohibited by the terms of the outside fellowship, the University supplements the outside stipend to bring it up to the level of the University fellowship. Candidates for admission are urged to apply for fellowships for which they are eligible (e.g., National Science Foundation, Ford and Hertz Foundations).

## Cost of Study

All students admitted to the PhD program become fellows in the Department and are exempt from tuition. Students may be responsible for certain fees: a student activity fee and transcript fee.

## Living and Housing Costs

Students in the PhD program are entitled to affordable University housing near the Department in Morningside Heights. This makes it possible to live comfortably in the University neighborhood on the fellowship stipend.

## Student Group

The PhD program in mathematics has an enrollment of approximately 60 students. Typically, 10-12 students enter each year. While students come from all over the world, they form an intellectually cohesive and socially supportive group.

## Location

New York City is America’s major center of culture. Columbia University’s remarkably pleasant and sheltered campus, near the Hudson River and Riverside Park, is situated within 20-30 minutes of Lincoln Center, Broadway theaters, Greenwich Village, and major museums. Most department members live within a short walk of the University.

## The University

Since receiving its charter from King George II in 1754, Columbia University has played an eminent role in American education. In addition to its various faculties and professional schools (such as Engineering, Law, and Medicine), the University has close ties with nearby museums, schools of music and theology, the United Nations, and the city government.

### Applying

The application deadline is December 12, 2019 for admission the following September. Applicants must submit their undergraduate transcripts, three letters of recommendation, a curriculum vitae and statement of purpose, and scores from the GRE General Test and Mathematics Subject Test. Students whose undergraduate degree was not from an English-speaking country must also submit scores from the TOEFL or IELTS. Applications must be filed online.

### Coursework Requirements

#### I. Credit requirements

- The Graduate School requires Ph.D students to complete a minimum of 60 credits beyond the baccalaureate degree.
- A minimum of 12 of these credits must come from Math 899, Dissertation preparation.
- Students must take 12 credits beyond the courses covering their qualifying exams and comprehensive exams for breadth.

#### II. Typical coursework

Most but not all students will take the following courses as a Ph.D student.

- Four courses on material covered by the qualifying exam: 2 year-long sequences (12 crs.).
- Six courses on material covered by comprehensive exam: 3 year-long sequences (18 crs.).
- Four courses for breadth (12 crs.).
- At most two further elective courses (0 – 6 crs.).
- 12 – 18 credits of Math 899.
- Math 791 (Pedagogy I) and Math 792 (Pedagogy II), 1 credit each. It is necessary for students to pass these courses in order to qualify to be the instructor of record for lower division courses (e.g., Math 111, 115, 122, 170) in the Department.

### Examination Requirements

#### 1. Qualifying Exam

##### A. Structure

The Ph.D. qualifying exam consists of two four-hour written exams. The Department offers these exams two times per year, once in August, and once in January.

##### B. Coverage

Students take exams on two year-long course sequences:

- Analysis: Math 703 and 704.
- either of

a. Algebra: Math 701 and 702.

b. Applied and Computational Math: Math 708 and 709.

##### C. Rules

- Number of attempts. A student gets at most two attempts per exam on two exams. (A student does not get two attempts on each of the three exams.)
- Standard exam schedule.
- A student’s first attempt on both exams should take place on or before August of the start of the second year.
- A student’s second attempt at one or both exams, if necessary, must take place on or before January of the second year.
- A student with exceptional preparation may make a first attempt on one or both exams on entrance (August of the first year) or in January of the first year.
- A student may attempt the qualifying exam without having taken corresponding

preparatory coursework.

- A student must pass both exams within two years of admission to the Ph.D program. Hence, the last opportunity to take exams is January of the second year.
- The exams are uncoupled. If a student chooses to attempt only one exam in a given exam period, the student does not forfeit an attempt on the exam that they did not take.

#### 2. Comprehensive Exam

A student’s comprehensive exam consists of written and oral parts. The student’s Comprehensive Exam Committee oversees all aspects of the student’s exam.

**A. Structure**

- The written part consists of 3 four-hour exams. The exams are offered two times per year, once in August, and once in January.
- The oral part is scheduled for two hours.

**B. Coverage**

- Each of the 3 four-hour written exams is based on a two-course sequence. Therefore, the written part covers material from six courses or three two-course sequences.
- The oral part may cover topics from the written part and from the student’s research area not covered by the written part.

**C. Rules**

- Committee: The Comprehensive Exam Committee must have at least four faculty, exactly one of which must be from an external unit.
- Number of attempts. A student gets at most two attempts to pass the comprehensive exam.
- Standard exam schedule.
- A student’s first attempt must take place no later than January of the third year. Typically, the first attempt takes place in August after the second year.
- A student’s second attempt must occur within one year of the first attempt.

### Dissertation requirement

The doctoral dissertation is the ultimate requirement for a student to earn the Ph.D degree. The dissertation should be original work which contributes significantly to the body of current research and which has the potential for publication in a reputable journal. The Dissertation Committee has the same requirements as the Comprehensive Exam Committee. While these committees do not have to be the same, they frequently are. The final requirement is the student’s defense of the dissertation in an examination before the Dissertation Committee.