## Program: M.S., Mathematics

### Pure Mathematics

## Program Description

The Department of Mathematics offers a Master of Science degree with three options: Pure Mathematics (Option I), Applied Mathematics (Option II), and Statistics (Option III). Each of the options prepares a student for further graduate work; for higher mathematical work in industry, business and government; and for teaching at community colleges.

Option I 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.

### Switching among Options I, II, and III

Students may request in writing to switch among Options I, II, and III. 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 Option I must take Algebra and either Analysis I or Analysis II. Students in Option II must take Analysis I and one other exam excluding algebra. Students in Option III must take Probability/Statistics and Analysis I.

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 541) - Master’s Thesis: In order to write a master’s thesis, students must maintain a GPA of 3.4 in their required courses. Students also must each defend their thesis in an oral examination by their thesis committee.

The University requires that students take at least 1 unit of MATH 697A (if they take a comprehensive exam) or 1 unit of MATH 698A (if they write a thesis). Units for MATH 697 or MATH 698 count toward the 31 units required for the degree.

### E. Courses of Study

#### 1. Required Core (15 units)

MATH 501 Topology (3)

MATH 552 Real Analysis (3)

##### Analytic Foundations (3 units)

###### Select one of the following courses:

MATH 541 Theoretical Statistical Inference (3)

MATH 550 Calculus on Manifolds (3)*

MATH 592A Topics in Applied Mathematics (3)

##### Linear/Algebraic Methods (3 units)

###### Select one of the following courses:

MATH 540 Regression Analysis (3)

MATH 560 Abstract Algebra III (3)*

MATH 581 Numerical Methods for Linear Systems (3)

##### Advanced Analytic Methods (3 units)

###### Select one of the following courses:

MATH 543 Multivariate Statistics (3)

MATH 582A Topics in Numerical Analysis (3)

MATH 655 Complex Analysis (3)*

*Students in Option I will normally take MATH 550, MATH 560 and MATH 655.

#### 2. Electives (15 units)

Elective units should support the program of study and be selected in consultation with the graduate coordinator. Up to 9 units may be taken in departments outside of Mathematics with prior approval of the Graduate Committee. A maximum of 9 units of 400-level courses may be applied toward the 31 unit degree.

#### 3. Culminating Experience (1 unit)

MATH 698A Thesis or Graduate Project (1)

or MATH 697A Directed Comprehensive Studies (1)

#### Total Units Required for the M.S. Degree: 31

## Contact

Department of Mathematics

Chair: Rabia Djellouli

Live Oak (LO) 1300

(818) 677-2721

Graduate Coordinator: Alberto Candel

(818) 677-6512

## Student Learning Outcomes

Students shall be able to:

- Communicate abstract mathematical ideas clearly and cogently.
- Solve mathematical problems at the graduate level.
- Demonstrate proficiency in algebraic methods.
- Demonstrate proficiency in mathematical analysis.
- Demonstrate proficiency in general topology, including metric spaces.