## Program: M.S., Mathematics

## Program Description

### Switching Between Specialization I and II

Students may request in writing to switch between Specialization I and II. Such requests will be considered by the graduate committee.

## Program Requirements

### A. For Admission to Graduate Status

Admission as a classified graduate student requires: (1) Academic preparation essentially equivalent to a B.A. or a B.S. degree in Mathematics at CSUN with a GPA of at least 3.0 in all undergraduate work; and (2) A grade of “B” or better in each of the common five upper division core courses in the Mathematics major. Students with less than a “B” average may be eligible for conditionally classified status. Applicants with undergraduate degrees in fields outside the mathematical sciences also may be considered for conditionally classified status, provided that they have successfully taken a significant number of both lower and upper division mathematics courses. Their eligibility and admission status will be determined by the graduate committee on an individual basis. Conditionally classified students are required to attain classified status by passing the Mathematics Screening Exam and satisfying all University requirements within two semesters of being admitted as a conditionally classified graduate student.

### B. The Mathematics Screening Examination

This exam will be given three times every year, in the week just before the start of each semester and in the week just after the end of the Spring semester. It will cover topics from the core undergraduate upper division mathematics curriculum, with emphasis on analysis and linear algebra.

### C. Residency Requirement

To maintain good standing, graduate students must complete at least one approved course during each semester. Students who fail to do so will be placed on probation. Students who fail to fulfill this requirement twice will be disqualified.

### D. Comprehensive Exam or Master’s Thesis

Students must successfully complete one of the following:

- Comprehensive Examination: This two-part examination will be based on the students’ required courses. Students in Specialization I must take Algebra and either Analysis I or Analysis II. Students in Specialization II must take Analysis I and one other exam excluding algebra.

Comprehensive exams are given in the following areas:

Algebra (material from MATH 462, MATH 460 and MATH 560)

Analysis I (material from MATH 501 and MATH 552)

Analysis II (material from MATH 550 and MATH 655)

Numerical Analysis (material from MATH 581 and MATH 582)

Applied Functional Analysis (material from MATH 680A/B)

Probability/Statistics (material from MATH 540 and MATH 542) - Master’s Thesis: In order to write a master’s thesis, students must maintain a GPA of 3.4 in their required courses. Each student also must defend his or her thesis in an oral examination by his or her thesis committee.

The University requires that students take at least 1 unit of MATH 697 (if they take a comprehensive exam) or 1 unit of MATH 698 (if they write a thesis). Units for MATH 697 or 698 count toward the 32 units required for the degree.

### Courses of Study

### Specialization I. Mathematics

#### 1. Required Courses (16 units)

##### Basic Coursework (15 units)

MATH 501 Topology (3)

MATH 550 Calculus on Manifolds (3)

MATH 552 Real Analysis (3)

MATH 560 Abstract Algebra III (3)

MATH 655 Complex Analysis (3)

##### Participating Seminar (1 unit)

MATH 589 Seminar in Mathematics (1)

#### 2. Electives (15 units)

Select approved courses. At least 6 of these 15 units must be at 500- or 600-level. Up to 6 units may be taken in departments outside of mathematics with prior approval of the graduate committee.

This specialization is primarily designed to prepare students for community college teaching, entry-level positions in industry or future graduate work in mathematics. The core of this program consists of an in-depth study of the mainstream of modern mathematics—algebra, analysis and topology.

### Specialization II. Applied Mathematics

#### 1. Required Courses (16 units)

##### Basic Preparation (6 units)

MATH 501 Topology (3)

MATH 552 Real Analysis (3)

##### Participating Seminar (4 units)

MATH 542A-D Topics in Probability/Statistics (3)

or MATH 581 Numerical Methods for Linear Systems (3)

##### Choose two courses from the following (6 units):

MATH 540 Regression Analysis (3)

MATH 542A-D Topics in Probability/Statistics (3)

MATH 581 Numerical Methods for Linear Systems (3)

MATH 582A-D Topics in Numerical Analysis (3)

MATH 592A-D Topics in Applied Mathematics (3)

MATH 625 Advanced Mathematical Modeling (3)

MATH 655 Complex Analysis (3)

MATH 680A/B Applied Functional Analysis I/II (3)

#### 2. Electives (15 units)

Select approved courses. At least 6 of these 15 units must be at 500- or 600-level. Up to 9 units may be taken in departments outside of mathematics with prior approval of the graduate committee.

#### Total Units Required for the M.S. Degree: 32

## Contact

Department of Mathematics

Chair: Rabia Djellouli

Live Oak Hall (LO) 1300

(818) 677-2721

## Student Learning Outcomes

#### Specialization I: Mathematics

- Demonstrate proficiency in abstract algebra, including group theory and Galois theory.
- Demonstrate proficiency in real and complex analysis, including measure theory.
- Demonstrate proficiency in general topology, including metric spaces.
- Communicate abstract mathematical ideas clearly and cogently.
- Solve mathematical problems at the graduate level.

#### Specialization II: Applied Mathematics

- Demonstrate proficiency in real analysis, including measure theory.
- Demonstrate proficiency in general topology, including metric spaces.
- Demonstrate proficiency in numerical methods or statistics.
- Communicate abstract mathematical ideas clearly and cogently.
- Solve mathematical problems at the graduate level.