# High-Performance Computing for Scientific Applications, P.S.M.

COLLEGE OF SCIENCE AND TECHNOLOGY

## About the Program

Computation, in tandem with theory and experiment, is highly regarded in the advance of scientific knowledge and engineering practice. In recognition of a growing need for experts cross-trained in relevant computational sciences, applied mathematics, statistics, and traditional scientific fields such as chemistry and physics, the Professional Science Master's (P.S.M.) program in High-Performance Computing for Scientific Applications is targeted toward STEM graduates seeking to use high-performance computation as their primary research instrument in the physical sciences, life sciences, and engineering. The core curriculum introduces students to the architecture of high-performance computing systems, mathematical techniques employed in high-performance computing, the software tools used in parallel calculations, and computational methods used in the sciences and engineering. A distinguishing feature of the program is its paired emphasis on the algorithms and technology of high-performance computing in applications to problems in science and engineering. Cross-disciplinary techniques are emphasized, and learning through applications and individually designed projects are prioritized over theory.

**Time Limit for Degree Completion:** 2 years

**Campus Location:** Main

**Full-Time/Part-Time Status:** The degree program can be completed on a full- or part-time basis. Most of the classes are offered in the evenings or on weekends to enable full-time working professionals to enroll in the program. International students are required to register as full-time students.

**Interdisciplinary Study: **The program is interdisciplinary by nature.

**Accreditation:** Temple University is fully accredited by the Middle States Commission on Higher Education.

**Job Prospects:** Students in the program are connected to internships in industry and government laboratories by the P.S.M. Scientific Advisory Committee. Graduates are then well prepared to compete for high-quality positions in industry, government laboratories, and academia.

**Non-Matriculated Student Policy:** Non-matriculated students may enroll in a total of three courses (9 credits) with permission of the instructor and the Department of Mathematics.

**Financing Opportunities**: Financial assistance in the form of Research or Teaching Assistantships is not offered.

## Admission Requirements and Deadlines

**Application Deadline:**

*Fall:* March 1; December 15 international

*Spring: *Open only to non-matriculated students who successfully completed P.S.M. coursework in the Fall term

Late applications may be considered for admission.

*APPLY ONLINE to this graduate program**.*

**Letters of Reference:**

*Number Required:* 3

*From Whom:* Letters should be obtained from college/university faculty or faculty who are familiar with the applicant's competency. If the applicant has an established career in the field, the applicant’s immediate supervisor should provide one of the letters.

**Coursework Required for Admission Consideration:** Applicants should have a strong background in one or more STEM fields: Science, Technology, Engineering, and Mathematics.

**Bachelor's Degree in Discipline/Related Discipline:** The P.S.M. program has been designed for recent graduates and professionals who have a bachelor's degree or equivalent in a STEM field.

**Statement of Goals:** Approximately 250 to 500 words include your interest in Temple's program, your research goals, and your academic and research achievements.

**Standardized Test Scores:**

GRE: Required. A combined minimum score of 300 on the quantitative and verbal reasoning sections of the new test is expected.

For applicants whose native language is not English, the TOEFL, IELTS, or PTE Academic exam is required:

TOEFL: 85 iBT or 563 PBT minimum

IELTS: 7.0 minimum

PTE Academic: 53 minimum

**Interview**: An in-person or SKYPE interview with the Program Director or members of the P.S.M. Steering Committee is required.

**Transfer Credit:** Graduate credits from an accredited institution may be transferred into the P.S.M. program. The credits must be equivalent to coursework offered by the Department of Mathematics at Temple University. A grade of "B" or better must have been earned for the credits to transfer. The P.S.M. Steering Committee makes recommendations to the Department Chair for transferring credit on an individual basis. The maximum number of credits a student may transfer is 6.

## Program Requirements

**General Program Requirements:**

*Number of Credits Required Beyond the Baccalaureate:* 30

*Required Courses:*

Code | Title | Credit Hours |
---|---|---|

Core Courses | ||

MATH 5061 | Fundamentals of Computer Programming for Scientists and Engineers | 4 |

MATH 5063 | Introduction to High-Performance Computing Technology for Scientists | 4 |

Two High-Performance Computing Courses | 6 | |

Ethics Course | 2 | |

Professional Development Course | 1 | |

Electives | 9 | |

Select three courses from the following: | ||

Structural Bioinformatics I | ||

Quantum Chemistry | ||

Statistical Thermodynamics | ||

Analysis and Modeling of Social and Information Networks | ||

Neural Computation | ||

Machine Learning | ||

Distributed and Parallel Computer Systems | ||

Numerical Linear Algebra I | ||

Numerical Linear Algebra II | ||

Numerical Differential Equations I | ||

Numerical Differential Equations II | ||

Mathematical Modeling for Science, Engineering, and Industry | ||

Topics Computer Program | ||

Topics Computer Program | ||

Topics in Numerical Analysis | ||

Topics in Numerical Analysis | ||

Introduction to Quantum Computing | ||

Statistical Mechanics | ||

Capstone Course | 4 | |

Total Credit Hours | 30 |

**Additional Requirements: **All graduate-level courses must be passed with a "B-" or better.

**Culminating Events:**

*Capstone Research Project:*

The Capstone Research Project provides students with the opportunity to develop, apply, and demonstrate their skills in a professional high-performance computing environment. The project must be approved in advance by the P.S.M. Steering Committee and requires a supervisor from either the Temple faculty or the P.S.M. Scientific Advisory Committee. Students can undertake their research projects in whole or in part during student internships.

### 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