1. Complete at least 48 hours of coursework. Up to two courses may be taken in another department with the approval of the Graduate Studies Committee. For advanced incoming students, limited (up to 9 hours) transfer credit is possible.

2. Pass the Placement Exam in linear algebra and advanced calculus. All PhD and MS (except 4+1) students must take the placement exam prior to begin with their program. If a student fails to achieve A- in the linear algebra portion, he or she will be required to enroll in Math 3090/6090. If the student fails to achieve A- in the advanced calculus portion, he or she will be required to enroll in Math 4060/6060. Read the **Placement Exam syllabus** for details and previous exams.

3. Pass **qualifying written exams** in Analysis and two others chosen from among:

- Algebra
- Analysis
- Applied Mathematics
- Differential Geometry
- Probability and Statistics
- PDE
- Scientific Computation
- Topology

4. Pass an oral exam on specific topics of research interest to the student.

5. Pass a prospectus.

6. Write a dissertation.

View detailed description of requirements

This program is designed to provide students with the opportunity to broaden and deepen their knowledge of core areas of mathematics. The course work is designed to provide both breadth of knowledge and depth in an area of interest to the student. This experience will prepare the student for further studies leading to a Ph.D. degree in mathematics. Partial tuition waivers may be available to qualified students.

**List of required courses:**

- The sequence Math 7210-7220 Analysis I-II
- Either the sequence Math 7010-7020 (Topology I-II) or the sequence Math 7110-7120 (Algebra I-II)
- Math 7980 Reading and Research (3 credits - for those choosing the non-thesis option) consists of a semester-long project under the supervision of a faculty member from the Department

**List of optional courses:**

- Math 6030 Introduction to Stochastic Processes
- Math 6210 Differential Geometry
- Math 6300 Complex Analysis
- Math 6410 Topology (except for those who have taken Math 7010)
- Math 7240 Mathematical Statistics
- Math 7510-7520 Differential Geometry I-II
- Math 7530-7540 Partial Differential Equations I, II
- Math 7550 Probability
- Math 7710-7790 Special Topics courses

#### Non-thesis option

**1. Ten courses (30 credits) at the 6000/7000 level.**

- All
**five**courses from the required list plus**five**additional courses from the optional list. - Other courses not listed may be substituted with the approval of the Graduate Studies Committee. Up to six credits may be transferred from other departments or institutions with the approval of the Graduate Studies Committee.

**2. A four-hour written examination** to be taken upon completion of the course work, with topics drawn from basic material in algebra, topology and analysis taught in the first-year graduate courses. The student is given two chances to pass this exam. One of the Ph.D. Qualifying examinations may be substituted for the Masters exam.

#### Thesis option

**1. Eight courses (24 credits) at the 6000/7000 level.**

- The first
**four**courses from the required list plus**four**additional courses from the optional list. - Other courses not listed may be substituted with the approval of the Graduate Studies Committee. Up to six credits may be transferred from other departments or institutions with the approval of the Graduate Studies Committee.

**2. A thesis** approved by the thesis committee consisting of a faculty member acting as advisor and two additional faculty. The thesis is typically much more substantial than the Math 7980 project.

This program enables students to obtain a B.S. in mathematics in 4 years, and in one additional year, to obtain an M.S. in mathematics. Students may count up to 4 graduate courses for both the undergraduate and graduate degrees, provided two of the graduate courses are taken above the 120 hours required for the undergraduate degree (SSE rule).

All requirements listed under the MS in mathematics must be satisfied. Students should normally apply in their third year at Tulane, should have a grade-point average of at least 3.0 in major courses, and obtain a positive recommendation from two Mathematics faculty member. The GRE is not required.

This program is designed to provide students with the opportunity to broaden and deepen their knowledge of mathematics with an emphasis on those areas that have been most important in science and engineering. The student will also examine, through seminars and case studies, examples of significant applications of mathematics to other areas. This expanded base of knowledge, together with extensive experience in problem solving should prepare the student for further studies leading to the Ph.D. degree or for immediate employment in many areas of industry and government.

To enter the program the student should have a Bachelor's degree in mathematics, or a related field, and have completed undergraduate courses in Linear Algebra and Differential Equations. Students without these prerequisites may take them without credit toward the M.S. degree. Partial tuition waivers may be available to qualified students.

**List of required courses:**

- One Analysis Course (Math 6050/6060/7210)
- One Statistics Course (Math 6020/6030/6040/7360 and 6370/7370)
- Math 7310-7320 Applied Mathematics I-II
- Math 7570 Scientific Computing II
- Math 7980 Reading and Research (3 credits - for those choosing the non-thesis option)

**List of optional courses:**

- Math 6020 Mathematical Statistics
- Math 6030 Stochastic Processes
- Math 6040 Linear Models
- Math 6050-6060 Real Analysis I-II
- Math 6210 Differential Geometry
- Math 6300 Complex Analysis
- Math 7210-7220 Analysis I-II
- Math 7530-7540 Partial Differential Equations I-II
- Math 7580 Scientific Computing III
- Math 7730 Topics in Applied Mathematics
- Math 7740 Topics in Scientific Computing
- Math 7750 Topics in Partial Differential Equations

Math 798 consists of a semester-long project in differential equations, scientific computation, optimization, analytical methods, engineering or other topics in applied mathematics. The project must be under the supervision of a faculty member from the Mathematics Department.

#### Non-thesis option

**1. Ten courses (30 credits) at the 6000/7000 level.**

- All
**six**courses from the required list plus**four**additional courses from the optional list. - Other courses not listed may be substituted with the approval of the Graduate Studies Committee. Up to six credits may be transferred from other departments or institutions with the approval of the Graduate Studies Committee.

**2. A four-hour written examination** to be taken upon completion of the course work, with topics drawn from differential equations, and scientific computation. The student is given two chances to pass this exam. The Ph.D. Qualifying examination in Applied Mathematics or Scientific Computation can be substituted for the Masters exam.

#### Thesis option

**1. Eight courses (24 credits) at the 6000/7000 level.**

- The first
**five**courses from the required list plus**three**additional courses from the optional list.

**2. A thesis** approved by the thesis committee consisting of a faculty member acting as advisor and two additional faculty. The thesis is typically much more substantial than the Math 798 project.

This program enables students to obtain a B.S. in Mathematics in 4 years, and in one additional year, to obtain an M.S. in Applied Mathematics. Students may count up to 4 graduate courses for both the undergraduate and graduate degrees, provided two of the graduate courses are taken above the 120 hours required for the undergraduate degree (SSE rule).

All requirements listed under the M.S. in Applied Mathematics must be satisfied. Students should normally apply in their third year at Tulane, should have a grade-point average of at least 3.0 in major courses, and obtain a positive recommendation from two Mathematics faculty members. The GRE is not required.

The Master of Science degree in Statistics combines theory and application. Our program emphasizes rigorous coursework in probability and mathematical statistics in addition to training in data analysis and computational methods. Graduates from the M.S. program may either directly enter the workforce as junior level statisticians or continue their studies in pursuit of a more advanced degree.

Course prerequisites include the equivalent of Math 6070 (Introduction to Probability), Math 6080 (Introduction to Statistical Inference) and Math 6090 (Linear Algebra). Enrollment in prerequisites does not provide credit towards the M.S. degree.

**Core Requirements:**

- Probability Theory I
- Math 6020/7240 Mathematical Statistics
- Math 6040/7260 Linear Models

**Optional Courses:**

- Math 6030/7030 Stochastic Processes
- Math 6280 Information Theory
- Math 6370/7370: Time Series Analysis
- Math 7360 Data Analysis
- Math 6350 Optimization Theory
- Math 7550 Probability Theory II
- Math 7570 Scientific Computation II
- Math 7210 Analysis I
- Math 7770 Topics in Statistics
- Biostatistics/Bioinformatics courses at the 7000 level or above (with approval)
- Math 7980 Reading and Research

Math 7980 consists of a semester-long project completed under the supervision of a faculty member from the Mathematics Department, generally completed during the final semester of study.

#### Non-thesis option

**1. Ten courses (30 credits) at the 6000/7000 level.**

- The three courses in the Core Requirements plus seven additional courses from the optional list.
- The student must have an advisor from the Probability and Statistics faculty. Other courses not listed may be substituted with the approval of the student advisor and the Graduate Studies Committee. Credits may be transferred from other departments or institutions with the approval of the student advisor and the Graduate Studies Committee.

**2. A four-hour written examination** to be taken upon completion of the core course work, with topics drawn from probability, linear models, and statistics. The student is given two chances to pass this exam. The Ph.D. Qualifying examination in Statistics can be substituted for the Masters exam.

- If a student receives at most one grade of B- in the courses, the student is eligible to graduate with a MS in Statistics - without taking the Statistics MS qualifying exam -, assuming the student meets all remaining requirements.
- If a student receives two grades of B-, or one grade less than B- in the courses, the student is placed on probation and considered for dismissal from the program, subject to the Quality of Work Requirements in the SSE Graduate Handbook. A student who falls into such a situation may apply to take the Statistics MS qualifying exam. The student should communicate with the Director of Graduate Studies to apply to take the exam.
- If a student passes the exam, the student is once again eligible to graduate with a MS in Statistics, assuming all remaining requirements are met.
- Under exonerating circumstances (serious illnesses, injuries, or critical personal problems) that prevent a student from taking the exam on the designated day, the student must notify the Director of Graduate Studies promptly. The student may re-apply to take the exam upon approval of the Graduate Studies Committee.
- Under normal circumstances, if a student fails the exam, the student is no longer eligible to graduate with a MS in Statistics. However, the student may still get the Certificate in Statistics assuming all remaining requirements (for the Certificate) are met.

#### Thesis option

There is no thesis option for the M.S. in Statistics.

This program enables students to obtain a B.S. in mathematics in 4 years, and in one additional year, to obtain an M.S. in statistics. Students may present up to four of the following core courses for both their B.S. in mathematics and their M.S. in statistics, provided they obtain a grade of B or better in each.

At the discretion of the Statistics Coordinator and the Student's advisor, other similar courses may be substituted for courses on this list. Students should normally apply in their third year at Tulane, should have a grade-point average of at least 3.0 in major courses, and obtain a positive recommendation from two Mathematics faculty. The GRE is not required.

**Math 6020:** Mathematical Statistics

**Math 6030/7030: **Stochastic Processes

**Math 6040:** Linear Models

**Math 6350:** Optimization Theory

**Math 6710 / 7210:** Analysis I

**Math 7150:** Probability Theory I

**Math 7360:** Data Analysis

**Math 7550:** Probability Theory II

**Math 7770:** Topics in Probability and Statistics

**Note:** Any student planning to receive more than one M.S. degree must satisfy all requirements of each degree with no more than two cross-listed courses.

The Certificate in Statistics program provides a flexible option for graduate study in probability theory, statistical methods, and data analysis. This program is appropriate for students who are currently pursuing graduate or professional degrees on the Tulane campus as well as for working professionals who wish to take courses on a part-time basis. The program is offered by the Department of Mathematics within the School of Science and Engineering.

**Enrollment**

In order for courses to award credits towards the Certificate, students must formally enroll in the program prior to course registration. Tuition-paying students registered in the MS in Statistics, MS in Applied Math, or MS in Mathematics program may also receive credits toward the Certificate for completed coursework in the event that they do not complete all requirements for the MS degree.

**Certificate Competencies**

Students who earn the Certificate in Statistics will have a solid foundation in probability theory and statistical inference, will have developed skills in the exploration, management, and analysis of data, and will have experience with one of more areas of application.

**Number of Credits Required for Completion:** 15 (5 courses at the 6000 level or above)

**Prerequisite Courses**

- Math 2210 Calculus III or Math 3050/6050 Real Analysis I (or equivalent)
- Math 3090/6090 Linear Algebra (or equivalent)

**Requirements**

A two-course sequence in mathematical probability and statistical inference: either

- Math 6070 and Math 6080, or
- Math 7150 and Math 6020/7240

Three additional graduate level courses, to be chosen from the following:

- Math 6030/7030 Stochastic Processes
- Math 6040/7260 Linear Models
- Math 6280 Information Theory
- Math 6370/7370: Time Series Analysis
- Math 7360 Data Analysis
- Math 7550 Probability Theory II
- Math 7770 Topics in Statistics
- Selected Biostatistics/Bioinformatics courses at the 7000 level or above (with GSC approval)
- Selected Computer Science courses at the 6000 level or above (with GSC approval)

Tulane’s M.S. in Data Science (MSDS) program is a professional, non-thesis degree that is jointly offered by the Mathematics and Computer Science departments. The burst of data in the modern world has fundamentally changed many fields of human activity, including healthcare, energy, manufacturing and scientific research. It has also generated an ever-increasing demand for a new type of professional: the data scientist. The MSDS program aims at providing the next generation of practitioners with cutting-edge data-driven problem-solving skills. These are based on rigorous mathematical foundations, and include data management, advanced statistical modeling, as well as the practical implementation and use of state-of-the-art algorithms.

**List of required courses:**

The MSDS program requires a total of 33 credit hours. These requirements are composed of 9 credits from Data Science Foundations courses, 12 credits from Data Science Core courses, and 12 credits from Data Science Electives. Students should meet each course’s pre-requisites before taking it.

**Data Science Foundations**

**Math 6070:**Introduction to Probability**Math 6090:**Linear Algebra**CMPS 6100:**Introduction to Computer Science

**Data Science Core**

**Math 6080:**Introduction to Statistical Inference**Math 6040/7260:**Linear Models**CMPS 6160:**Introduction to Data Science**CMPS 6240/6720:**Machine Learning

**List of optional courses:**

The elective requirement consists of 4 full-semester courses chosen from the list below. Additional courses (e.g. independent study) may substitute for elective courses upon approval from the Graduate Studies Committee of the Math and CS Departments.

**Math 7360:**Data Analysis**Math 6030/7030:**Stochastic Processes**Math 6370/7370:**Time Series Analysis**Math 6310:**Scientific Computation I**Math 7570:**Scientific Computation II**Math 7710:**Algebraic Coding Theory**COSC 6000:**C++ Prog for Sci & Engr**COSC 6200:**Large Scale Computation**CMPS 6360:**Data Visualization**CMPS 6260:**Advanced Algorithms**CMPS 6140/6620:**Artificial Intelligence**CMPS 6660:**Deep Learning**CMPS 6610:**Algorithms**CMPS 6660:**Computer Vision**CMPS 6730:**Natural Language Processing**CMPS 6740:**Reinforcement Learning**BIOS 7150:**Categorical Data Analysis**BIOS 7300:**Survival Data Analysis**EBIO 6440:**Introduction to Data Science for Ecologists**BMEN 6800:**Data Science: Medical Imaging/Machine Learning

The Data Science Foundations courses are designed to accommodate students entering the program from diverse backgrounds. Those students who enter with a strong background in math/computer science may substitute foundational courses with additional electives upon approval from the Graduate Studies Committee.

**Suggested Timeline** (* indicates elective courses)

The Tulane 4+1 M.S. in Data Science program targets current Tulane University undergraduate students who obtain a B.S. in Mathematics or Computer Science in 4 years. With the approval of the Graduate Studies Committees of both the Mathematics and Computer Science departments, these students can enroll in the 4+1 program with the goal of obtaining a M.S. in Data Science in one additional year. For the 4+1-degree program, undergraduate students can count 6 credit hours of courses at the 6000-level toward both the undergraduate and graduate degrees. Students must obtain approval to count these courses toward 4+1 credit by completing the SSE Dual Credit Form. In addition to these courses, up to 6 credit hours of graduate coursework (beyond the 120-credit hour requirement for undergraduate degrees) may also be counted toward the 4+1 degree. The GRE is not required for the MSDS program.

Please contact the Director of Graduate Studies if you have additional questions:

Dr. Gustavo Didier

Phone: (504) 862-3466

Office: Gibson 403