# Mathematics, M.S.

COLLEGE OF SCIENCE AND TECHNOLOGY

Learn more about the Master of Science in Mathematics.

## About the Program

The Department of Mathematics offers graduate work leading to the Master of Science degree. The aim of the M.S. program is to provide students with a foundation sufficient to pursue careers in mathematics in industry, government, or education. The program offers opportunities to conduct original research under the supervision of a faculty member.

**Time Limit for Degree Completion:** 3 years

**Campus Location:** Main

**Full-Time/Part-Time Status:** Students complete the degree program through classes offered before 4:30 p.m. The degree program can be completed on a full- or part-time basis.

**Interdisciplinary Study:** The program encourages interdisciplinary coursework, research, and interactions among faculty and students with interest in computer and information sciences, physical and life sciences, statistics, and engineering.

**Affiliation(s):** The Mathematics program at Temple University is affiliated with the American Mathematical Society and the Mathematical Association of America.

**Study Abroad:** Department faculty are active internationally and sometimes travel overseas for conferences and extended research visits. In some cases, students may participate in these activities.

**Accreditation:** This program adheres to accepted professional standards of mathematics education and research.

**Areas of Specialization: **The department has approximately 25 faculty members actively involved in research and graduate education. With a graduate student body of less than 40, we are a program of moderate size with a high faculty/student ratio. Thus, we provide students with unique opportunities for flexible program design and ample interaction with faculty. Classes are small and are held in an informal atmosphere enabling students and faculty to work closely together.

The department offers a great variety of choices for areas of specialization. A strong research presence exists in the following areas: algebra, computational mathematics, differential geometry and topology, geometric group theory, global geometry, harmonic analysis, invariant theory, mathematical biology, mathematical physics, mathematics of materials, numerical analysis, partial differential equations, probability, representation theory, and several complex variables. Both prospective and matriculated students are encouraged to browse faculty web pages and contact faculty directly for more detailed information regarding areas of specialization and opportunities for further research.

**Job Prospects:** Graduates either continue advanced educational programs or pursue employment in industry, education, or government laboratories and agencies.

**Non-Matriculated Student Policy:** Non-matriculated students must coordinate coursework with the Graduate Chair.

**Financing Opportunities**: Teaching Assistants teach basic undergraduate mathematics courses, ranging from remedial courses through calculus. The standard teaching load is 20 hours per term. In determining the load, credit is given for more difficult and challenging teaching assignments. Research Assistantships are sometimes available, typically through special projects and grants. Support generally includes a stipend and tuition of up to 9 credits per term.

## Admission Requirements and Deadlines

**Application Deadline:**

*Fall:* February 15

Applications are processed on a semi-rolling basis.

*APPLY ONLINE to this graduate program**.*

**Letters of Reference:**

*Number Required:* 3

*From Whom:* Letters of recommendation should be obtained from individuals who are well acquainted with the applicant's abilities and achievements in mathematics and related areas, particularly former instructors in mathematics courses and projects. Letters from instructors in related areas such as computation or the physical and life sciences are also appropriate. In certain cases, letters from employment supervisors or project leaders may be appropriate as well.

**Coursework Required for Admission Consideration:** Applicants must have completed fundamental undergraduate mathematics courses.

**Bachelor's Degree in Discipline/Related Discipline:** All applicants must hold a baccalaureate degree from an accredited college or university.

**Statement of Goals:** Describe your strengths and motivation, the purpose for applying to a graduate program in mathematics, and why you are interested in the intended degree. This forum should be used to make your strongest case for admission and, thus, should be well written.

**Standardized Test Scores:**

GRE: No rigid minimum score criteria. The department considers an applicant's overall record. Students who wish to discuss their scores are encouraged to contact the department directly.

TOEFL score: 79 iBT or 550 PBT minimum

**Resume:** Current resume required.

**Transfer Credit:** Students who have taken graduate courses at other institutions, or at Temple University prior to matriculation, may apply for transfer credit. Applications for transfer credit are not considered until the student has completed at least one term of full-time graduate study or the equivalent, if the student is part-time. All applications for transfer credit are reviewed by the Mathematics Graduate Committee and may be denied if the committee decides that the courses involved are substantially inferior to similar courses offered by the department. No course completed more than five years before the date of application will be awarded credit. Credit for courses substantially similar to courses taken since matriculation will not be awarded. If a course was taken before the bachelor's degree was earned, it cannot be awarded transfer credit. Transfer credit is only available for graduate-level courses in mathematical content. The maximum number of credits a student may transfer is 9.

**Test Waivers:** An applicant who wishes to have certain admission requirements waived must contact the department directly. Requests are considered by the department on a case-by-case basis. In some cases, an additional appeal to the Graduate School may be required. In such a case, the department makes a preliminary determination for the applicant and, if positive, issues a supporting letter to the Graduate School on the applicant's behalf.

## Program Requirements

**General Program Requirements:**

*Number of Credit Hours Required Beyond the Baccalaureate:* 30

*Required Courses:*

The Master of Science degree requires 10 graduate courses at the 5000 level or above. The program of study must be designed in coordination with a Mathematics faculty advisor and approved by the departmental Graduate Committee. With the approval of the faculty advisor and Graduate Committee, relevant courses from departments other than Mathematics may be included.

The M.S. degree is offered with an optional concentration in Applied and Computational Mathematics. The concentration is designed for students interested in incorporating advanced study in mathematical and computational methods into the Master of Science program. Students pursuing this concentration complete at least 15 credits of coursework in applied and computational mathematics within their 30-credit degree program.

**Culminating Events:**

After satisfying the 30-credit course requirement, students may choose between the following three options as the culminating event of the M.S. degree:

- Master's Thesis
- Master's Comprehensive Examination
- Master's Pass on the Ph.D. Comprehensive Examination

*Master's Thesis:*

Students who choose to submit a master's thesis must select a faculty advisor and a thesis advisory committee. These arrangements are subject to the approval of the Mathematics Graduate Committee. The date, time, and location of a thesis defense are set by the Graduate Chair in consultation with the student's advisory committee.

*Master's Comprehensive Examination:*

For students selecting this option, a written Master's Comprehensive Examination will be composed by at least two departmental Graduate Faculty. The topics covered should correspond to the student's program of study as approved by the Graduate Committee. The exam is graded by at least two Mathematics faculty members, with grades of either Pass or Fail. Students interested in taking the Master's Comprehensive Examination are required to make a written request to the Graduate Chair at least four weeks in advance. If the examination is failed, it may be taken again once, or the student may attempt a master's pass on the Ph.D. Comprehensive Examination.

*Master's Pass on the Ph.D. Comprehensive Examination:*

Students choosing this option must take three of the separate 25-point sections of the written Ph.D. Comprehensive Examination. A student who achieves a total score of at least 40 on the three sections of the examination, with no individual section below 8, obtains a master's pass on the exam and has fulfilled the examination requirement for the M.S. degree. If one of the individual exam scores falls below 8 points, that exam may be repeated once, or the exam in a different topic may be attempted once, or the student may take the Master's Comprehensive Examination described above. Such arrangements are subject to approval by the Graduate Committee. The case of a student failing the comprehensive exam by a small margin is discussed by the department's Graduate Committee, which takes the student's whole academic record into account in its decision.

### Courses

**MATH 5000. Special Topics in Math. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 5001. Linear Algebra. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 5041. Concepts of Analysis I. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 5042. Concepts of Analysis II. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 5041|Minimum Grade of B-|May not be taken concurrently.

**MATH 5043. Introduction to Numerical Analysis. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 5044. Introduction to Numerical Analysis II. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 5045. Ordinary Differential Equations. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 5061. Fundamentals of Computer Programming for Scientists and Engineers. 4 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 5063. Introduction to High-Performance Computing Technology for Scientists. 4 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 5061|Minimum Grade of B-|May be taken concurrently.

**MATH 8001. Candidates Seminar. 1 to 3 Credit Hour.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 8002. Candidates Seminar. 1 to 3 Credit Hour.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 8003. Number Theory. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 8004. Number Theory. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 8007. Introduction to Methods in Applied Mathematics I. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 8008. Introduction to Methods in Applied Mathematics II. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 8011. Abstract Algebra I. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 8012. Abstract Algebra II. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 8011|Minimum Grade of B-|May not be taken concurrently.

**MATH 8013. Numerical Linear Algebra I. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 8014. Numerical Linear Algebra II. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 8013|Minimum Grade of B-|May not be taken concurrently.

**MATH 8023. Numerical Differential Equations I. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 8024. Numerical Differential Equations II. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 8023|Minimum Grade of B-|May not be taken concurrently.

**MATH 8031. Probability Theory. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 8032. Stochastic Processes. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 8031|Minimum Grade of B-|May not be taken concurrently.

**MATH 8041. Real Analysis I. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 8042. Real Analysis II. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 8041|Minimum Grade of B-|May not be taken concurrently.

**MATH 8051. Functions of a Complex Variable I. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 8052. Functions of a Complex Variable II. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 8051|Minimum Grade of B-|May not be taken concurrently.

**MATH 8061. Differential Geometry and Topology I. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 8062. Differential Geometry and Topology II. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 8061|Minimum Grade of B-|May not be taken concurrently.

**MATH 8107. Mathematical Modeling for Science, Engineering, and Industry. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics, Engineering: Engineering.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

(MATH 8007|Minimum Grade of B-|May not be taken concurrently)

AND (MATH 8008|Minimum Grade of B-|May not be taken concurrently)

**MATH 8141. Partial Differential Equations I. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 8142. Partial Differential Equations II. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 8141|Minimum Grade of B-|May not be taken concurrently.

**MATH 8161. Topology. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 5041|Minimum Grade of B-|May not be taken concurrently.

**MATH 8200. Topics in Applied Mathematics. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 8210. Topics in Applied Mathematics II. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 8700. Topics Computer Program. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 8710. Topics Computer Program. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 8985. Teaching in Higher Education. 1 to 3 Credit Hour.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for a total of 3 credit.

**MATH 9000. Topics in Number Theory I. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9003. Modular Functions. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 9004. Modular Functions. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 9005. Combinatorial Mathematics. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 9010. Topics in Number Theory II. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9011. Homological Algebra. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

(MATH 8011|Minimum Grade of B-|May not be taken concurrently)

AND (MATH 8012|Minimum Grade of B-|May not be taken concurrently)

**MATH 9012. Representation Theory I. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

(MATH 8011|Minimum Grade of B-|May not be taken concurrently)

AND (MATH 8012|Minimum Grade of B-|May not be taken concurrently)

**MATH 9013. Representation Theory II. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 9012|Minimum Grade of B-|May not be taken concurrently.

**MATH 9014. Commutative Algebra and Algebraic Geometry I. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

(MATH 8011|Minimum Grade of B-|May not be taken concurrently)

AND (MATH 8012|Minimum Grade of B-|May not be taken concurrently)

**MATH 9015. Commutative Algebra and Algebraic Geometry II. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 9014|Minimum Grade of B-|May not be taken concurrently.

**MATH 9021. Riemannian Geometry. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

(MATH 8061|Minimum Grade of B-|May not be taken concurrently)

AND (MATH 8062|Minimum Grade of B-|May be taken concurrently)

**MATH 9023. Knot Theory and Low-Dimensional Topology I. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

(MATH 8061|Minimum Grade of B-|May not be taken concurrently)

AND (MATH 8062|Minimum Grade of B-|May not be taken concurrently)

**MATH 9024. Knot Theory and Low-Dimensional Topology II. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 9023|Minimum Grade of B-|May not be taken concurrently.

**MATH 9031. Advanced Probability Theory. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 9041. Functional Analysis I. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

(MATH 8041|Minimum Grade of B-|May not be taken concurrently)

AND (MATH 8042|Minimum Grade of B-|May not be taken concurrently)

AND (MATH 8161|Minimum Grade of B-|May not be taken concurrently)

**MATH 9042. Functional Analysis II. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 9041|Minimum Grade of B-|May not be taken concurrently.

**MATH 9043. Calculus of Variations. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 9044. Harmonic Analysis. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 9051. Several Complex Variables I. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

(MATH 8051|Minimum Grade of B-|May not be taken concurrently)

AND (MATH 8052|Minimum Grade of B-|May not be taken concurrently)

**MATH 9052. Several Complex Variables II. 3 Credit Hours.**

**Department Restrictions:** Must be enrolled in one of the following Departments: CST:Mathematics.

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

MATH 9051|Minimum Grade of B-|May not be taken concurrently.

**MATH 9053. Harmonic Analysis. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 9061. Lie Groups. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 9062. Lie Groups. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 9063. Riemann Surfaces. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 9064. Riemann Surfaces. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 9071. Differential Topology. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 9072. Differential Topology. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**MATH 9073. Geometric Group Theory. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may not be repeated for additional credits.

**Pre-requisites:**

(MATH 8061|Minimum Grade of B-|May not be taken concurrently)

AND (MATH 8062|Minimum Grade of B-|May not be taken concurrently)

**MATH 9082. Independent Study. 1 to 3 Credit Hour.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9083. Independent Study. 1 to 3 Credit Hour.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9100. Topics in Algebra. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9110. Topics in Algebra. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9120. Seminar in Algebra. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9200. Topics in Numerical Analysis. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9210. Topics in Numerical Analysis. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9300. Seminar in Probability. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9310. Seminar in Probability. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9400. Topics in Analysis. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9410. Topics in Functional Analysis. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9420. Topics in Differential Equations II. 3 Credit Hours.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9991. Master's Research Projects. 1 to 6 Credit Hour.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Degree Restrictions:** Must be enrolled in one of the following Degrees: Master of Arts, Master of Science, Prof Science Masters.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9994. Preliminary Examination Preparation. 1 to 6 Credit Hour.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9995. Capstone Project. 1 to 6 Credit Hour.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Degree Restrictions:** Must be enrolled in one of the following Degrees: Master of Arts, Master of Science, Prof Science Masters.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9996. Master's Thesis Research. 1 to 6 Credit Hour.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9998. Pre-Dissertation Research / Elevation to Candidacy. 1 to 6 Credit Hour.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Repeatability:** This course may be repeated for additional credit.

**MATH 9999. Dissertation Research. 1 to 6 Credit Hour.**

**Level Registration Restrictions:** Must be enrolled in one of the following Levels: Graduate.

**Student Attribute Restrictions:** Must be enrolled in one of the following Student Attributes: Dissertation Writing Student.

**Repeatability:** This course may be repeated for additional credit.

## Contacts

### Program Web Address:

### Department Information:

Dept. of Mathematics

638 Wachman Hall

1805 N. Broad Street

Philadelphia, PA 19122-6094

215-204-7842