# Mathematics

- Department Information
- Program Description
- Career Opportunities
- Features
- Preparation
- Major Requirements (B.S.)
- Other Degree Requirements
- Minor Requirements
- Minor in Computer Science
- Single Subject Matter Preparation Program
- Certificate in Foundational Mathematics Teaching
- Basic Skills Courses
- Undergraduate Courses

## Department Information

**Department of Mathematics College of Science**

**Office: North Science 335**

**Phone: (510) 885-3414**

**E-mail: mathcs@csueastbay.edu**

Website: http://www20.csueastbay.edu/csci/departments/math-cs/index.html

Student Service Center: North Science 337

Website: http://www20.csueastbay.edu/csci/departments/math-cs/index.html

Student Service Center: North Science 337

**Phone: (510) 885-4011**

*Professor Emeritus*

Stuart Smith, Ph.D. University of California, Berkeley

*Professors*

Kevin E. Callahan, Ph.D. University of California, San Diego

Julie S. Glass, Ph.D. University of California, Santa Cruz

Kathleen Hann, Ph.D. University of California, Davis

Gary E. Lippman, Ph.D. University of California, Riverside

Massoud Malek, Ph.D. University of Houston

Donald L. Wolitzer, Ph.D. Northeastern University

*Associate Professors*

Julia Olkin, Ph.D. Rice University

Chung-Hsing OuYang, Ph.D. University of California, Berkeley

Shirley Yap, Ph.D. University of Pennsylvania

*Assistant Professors*

Ehsan Kamalinejad, Ph.D. University of Toronto (Canada)

## Program Description

Modern technological society has many fields that need specialists in mathematics. The Department of Mathematics and Computer Science offers a variety of courses intended for those who want to pursue a career in mathematics as well as those who wish to develop quantitative and problem-solving skills for use in other fields.

Students choose to major in mathematics for a number of reasons. Some intend to become high school, community college, or university teachers. Others seek careers in business, industry, or government, where mathematically trained people are in demand. An undergraduate major in mathematics is one of the best preparations not only for studying advanced Mathematics, but also for graduate work in Computer Science, Statistics, Operations Research, Actuarial Science, and the Natural Sciences. Most law schools are pleased to accept students with rigorous and logical training in Mathematics.

Many students combine their study of mathematics with the study of computer science. A popular option is to obtain a double major in Mathematics and Computer Science. Or students may earn a major in one of these fields and minor in the other.

The major requires seven lower division courses and eleven upper division mathematics courses. The requirements are flexible enough that a student can choose one of several options according to his/her interest.

Each student is assigned a faculty advisor when (s)he declares a major and should consult this advisor regularly. A booklet containing a number of sample schedules, as well as further information about the mathematics major, is available in the Mathematics/Computer Science Student Service Center (North Science 337) or see the departmental website.

Although it is not a requirement, mathematics majors are urged to take as many courses as possible in an area such as Biology, Chemistry, Economics, Management Sciences, Physics, or Statistics. These are all fields where Mathematics plays a significant role, and it is important for a mathematics major to appreciate the relevance of the subject in applications. Study of one or more foreign languages is also recommended, especially for those students anticipating graduate study.

### Student Learning Outcomes

Students graduating with a B.S. in Mathematics from Cal State East Bay will be able to:

- Apply the definitions, techniques and theorems of undergraduate abstract mathematics.
- Apply the definitions, techniques and theorems of undergraduate applied mathematics.
- Apply mathematical algorithms to solve problems, both individually and in teams.
- Creatively conjecture and rigorously write, analyze and critique proofs.
- Communicate mathematics to others in written and/or oral form with precision, clarity and organization.
- Apply techniques of at least one area of mathematics in depth.

## Career Opportunities

- Actuary
- Computer Analyst
- Cryptologist
- Economist
- Engineer
- Engineering Analyst
- Financial Analyst
- Market Researcher
- Mathematician
- Numerical Analyst
- Operations Research Analyst
- Personnel Representative
- Programmer
- Professor/Teacher
- Publisher Representative
- Statistician
- Stockbroker
- Technical Writer

## Features

Cal State East Bay students can participate in the Mathematics Club, which features lectures by students and faculty and offers a variety of social activities.

Each year the department awards a number of scholarships covering a portion of fees for the subsequent year. Scholarship applications may be obtained from the department student service center office during the Winter quarter.

Qualified upper division and graduate students may be employed as graders for classes.

Students who intend to earn a high school teaching credential after graduation may apply most of their mathematics major courses to meet the standards of California's Single Subject Matter Preparation Program for a Single Subject Credential in Mathematics.

Math majors who continue on to earn a master's degree in mathematics may pursue a career as a community college mathematics teacher.

## Preparation

For Advanced Placement course equivalencies, see Registration chapter.

## Major Requirements (B.S.)

Because requirements are subject to change, consult an advisor in your major department for clarification and interpretation of your major requirements. The major consists of 72 units; the BS degree requires a total of 180 units.

### I. Lower Division Requirements (28 units)

This requirement consists of the following seven courses:

- MATH 1304, 1305, 2304, 2305 The Calculus sequence
- CS 1160 Introduction to Computer Science I
- MATH 2101 Elements of Linear Algebra
- MATH 2150 Discrete Structures

(Mathematics majors may substitute MATH 3151 or MATH 4151 for MATH 2150.)

A student who has recently taken a pre-calculus course in high school should be prepared to begin the calculus sequence. A student with three years of high school mathematics, including two years of algebra and one year of geometry, should be prepared to take MATH 1130, or possibly MATH 1300. Students who are unsure about what mathematics course to begin with should call the department office. Students may not enroll in any baccalaureate level mathematics or computer science courses unless they have met the Entry Level Mathematics (ELM) requirement, or are exempt from it. Contact the Testing Office 885-3661 for more information.

### II. Upper Division Requirements (44 units)

Every Mathematics major is required to complete one of the following options:

#### Option A - Pure Mathematics (44 units)

Required courses:

- MATH 3000 Introduction to Abstract Mathematics and Proofs (4) (Mathematics majors are encouraged to take MATH 3000 as early as possible.)
- MATH 3100 Linear Algebra (4)
- MATH 3331 Differential Equations (4)

The following two sequences:

- MATH 3121-3122 Abstract Algebra I and II (4, 4)
- MATH 3300-3301 Analysis I and II (4, 4)

One sequence from the following five:

- MATH 3151-4151 Combinatorial Mathematics (4, 4)
- MATH 3215-4215 Geometry (4, 4)
- MATH 3361-4361 Differential Equations (4, 4)
- MATH 3750-4750 Numerical Analysis (4, 4)
- MATH 3841-4841 Optimization (4, 4)

Electives: Two upper division courses (8 units), which may include any upper division mathematics courses not already taken for the major or STAT 3401, 3402, 3502, 3503, 3601, 4401, 4515, 4601 or CS 4170, 4245 (but not MATH 4012, 4013, 4014, 4030).

#### Option B - Applied Mathematics (44 units)

Required courses:

- MATH 3000 Introduction to Abstract Mathematics and Proofs (4) (Mathematics majors are encouraged to take MATH 3000 as early as possible.)
- MATH 3100 Linear Algebra (4)
- MATH 3331 Differential Equations (4)

Three out of the four courses from the following two sequences:

- MATH 3121-3122 Abstract Algebra I and II (4, 4)
- MATH 3300-3301 Analysis I and II (4, 4)

Two sequences from the following four:

- MATH 3151-4151 Combinatorial Mathematics (4, 4)
- MATH 3361-4361 Differential Equations (4, 4)
- MATH 3750-4750 Numerical Analysis (4, 4)
- MATH 3841-4841 Optimization (4, 4)

Electives: One upper division course (4 units), which may include any upper division mathematics course not already taken for the major or STAT 3401, 3402, 3502, 3503, 3601, 4401, 4515, 4601 or CS 4170, 4245 (but not MATH 4012, 4013, 4014, 4030).

#### Option C - Mathematics Teaching (44 units)

Required courses:

- MATH 3000 Introduction to Abstract Mathematics and Proofs (4) (Mathematics majors are encouraged to take MATH 3000 as early as possible.)
- MATH 3121 Abstract Algebra I (4)
- MATH 3100 Linear Algebra (4)
- MATH 3215 Geometry I (4)
- MATH 3300 Analysis I (4)
- MATH 3331 Differential Equations (4)
- MATH 3600 Number Theory (4)
- MATH 4040 History of Mathematics (4)
- STAT 3401 Introduction to Probability Theory I (4)

One from the following three courses:

- MATH 3122 Abstract Algebra II (4)
- MATH 3301 Analysis II (4)
- MATH 4215 Topics in Geometry (4)

Electives: One upper division course (4 units), which may include any upper division mathematics courses not already taken for the major or STAT 3401, 3402, 3502, 3503, 3601, 4401, 4515, 4601 or CS 4170, 4245 (but not MATH 4012, 4013, 4014, 4030).

A student who completes Option C can satisfy rather easily the requirements for the State-approved Single Subject Matter Preparation Program in Mathematics, a program of courses designed to prepare the student for entry into the Credential Program in Mathematics, provided that judicious choices of mathematics elective courses and general education courses are made. To accomplish this, the student who completes Option C must:

- Choose MATH 4901 Senior Seminar (4) in the mathematics elective category;
- Complete STAT 3502 Statistical Inference (4); and
- Complete TED 3001 Exploring Education (3) and/or other field experience approved by the Mathematics Subject Matter Preparation Adviser: At least 45 hours of classroom experience in an instructional capacity is required.

## Other Degree Requirements

In addition to major requirements, every student must also complete the University requirements for graduation which are described in the Baccalaureate Degree Requirements chapter in the front of this catalog. These include the General Education-Breadth requirements; the second composition (ENGL 1002) requirement; the cultural groups/women requirement; the performing arts/activities requirement; the U.S. history, U.S. Constitution, and California state and local government requirement; the University Writing Skills Requirement; and the residence, unit, and grade point average requirements.

## Minor Requirements

The minor consists of 28 units.

Required courses:

- MATH 1304 Calculus I (4)
- MATH 1305 Calculus II (4)
- MATH 2101 Elements of Linear Algebra (4)
- MATH 2304 Calculus III (4)
- MATH 3000 Introduction to Abstract Mathematics and Proofs (4)

One course from the following list:

- MATH 3100 Linear Algebra (4)
- MATH 3121 Abstract Algebra I (4)
- MATH 3215 Geometry I (4)
- MATH 3300 Analysis I (4)
- MATH 3331 Differential Equations (4)

One 4-unit course which may include any upper division mathematics courses not already taken for the minor or STAT 3401, 3502 or CS 4170, 4245 (but not MATH 4012, 4013, 4014, 4030).

## Minor in Computer Science

The complete description of this minor may be found in the Computer Science chapter in the undergraduate section of this catalog. It is relatively easy for a Mathematics major to complete a minor in Computer Science. To do this, the student should take the following courses in addition to those required for the mathematics major.

- CS 2360 Introduction to Computer Science II (4)
- CS 2370 Introduction to Computer Science III (4)
- CS 2430 Computer Organization and Assembly Language Programming (4)

*Three upper division courses as follows:*

- Two courses from the following list:
- CS 3120 Programming Language Concepts (4)
- CS 3240 Data Structures and Algorithms (4)
- CS 3430 Computer Architecture (4)
- CS 4560 Operating Systems (4)

- One upper division Computer Science elective. This may be a third course from (A) or any course from category IV of the requirements for the major in Computer Science.

## Single Subject Matter Preparation Program

See the Single Subject Matter Preparation Program chapter in the undergraduate section of this catalog for a description of the Single Subject Matter Preparation Program in Mathematics.

## Certificate in Foundational Mathematics Teaching

The Foundational Mathematics certificate program is designed for students who would like to teach middle school math or would like to become K-8 math specialists. Credentialed teachers who complete this program and pass the Math CSET I and II exams qualify for the Foundational-level Added Authorization in Mathematics.

Candidate for this program should have or plan to obtain their Multiple Subjects teaching credential or a Single Subject teaching credential in a subject other than mathematics. Students who complete this program will be well prepared to teach mathematics at the K-8 level, will have completed the State required Methods Courses in Single Subject Mathematics and will have the content knowledge required to pass the Math CSET I and II exams.

The certificate consists of 21 units.

### Prerequisite:

MATH 2011 Number Systems (4)

### Required Courses (21 units):

- MATH 1130 College Algebra (4)
- MATH 4012 Geometry and Measurement (4)
- MATH 4013 Statistics, Data Analysis, and Probability (4)
- MATH 4030 Advanced Study of School Mathematics (4)
- TED 5390 Instructional Methods for the Single Subject Classroom I (3)
- TED 5391 Instructional Methods for the Single subject Classroom II (2)

*Note: Students who complete the Foundational Mathematics Teaching Certificate program will still need to pass the first two math CSET exams to establish subject matter competency for the credential.*

## Basic Skills Courses

Course Number | Course Information |
---|---|

0800 |
Introduction to Algebra (4)Fractions, signed numbers, percentages, introduction to geometry, simplifying algebraic expressions, solving linear equations, straight lines. Prerequisite: appropriate ELM score (ranges available from the Testing Office or at http://www.csueastbay.edu/ge/remedialinfo/scores.htm). Not for credit toward baccalaureate degree. A/B/C/NC grading only. |

0900 ^{1} |
Elementary Algebra (4)A one quarter course in elementary algebra. On successful completion of this course, students should register for MATH 0950. Prerequisite: Grade of A/B/C in MATH 800 or appropriate ELM score (ranges available from the Testing Office or at http://www.csueastbay.edu/ge/remedialinfo/scores.htm). Not for credit toward baccalaureate degree. A/B/C/NC grading only. |

0911 |
Algebra Lab (2)Supplemental study, discussion, and practice in the theory, problems, and applications of elementary and intermediate algebra. Co-requisite: enrollment in MATH 0900, or 0950. Not for credit toward baccalaureate degree. May be repeated once for credit (non-baccalaureate), with permission of the Math/CS Department, for a maximum of 4 units. A/B/C/NC grading only. |

0950 |
Intermediate Algebra (4)Operations with algebraic expressions, exponents and radicals; linear and quadratic equations; systems of equations and inequalities; linear and quadratic functions and their graphs; elementary conic sections; word problems. Prerequisite: Grade of A/B/C in MATH 0900; or an appropriate ELM score (ranges available from the Testing Office or at http://www.csueastbay.edu/ge/remedialinfo/scores.htm). Not for credit toward baccalaureate degree. A/B/C/NC grading only. |

## Undergraduate Courses

Computer Science courses offered by the Department of Mathematics and Computer Science are fully described in the Computer Science chapter in the undergraduate section of this catalog.

A student who has recently taken a pre-calculus course in high school should be prepared to enter calculus. A student with three years of high school mathematics, including two years of algebra and one year of geometry, should be prepared to take MATH 1130, or possibly MATH 1300. Such students, and others who are unsure about what mathematics course to begin with, should call the Mathematics and Computer Science Department for advice. Also, the Testing Office (885-3661) offers placement tests that can assist students in finding the appropriate starting class.

Course Number | Course Information |
---|---|

1110 ^{2} |
The Nature of Mathematics (4)This course is designed to introduce the student to mathematics as an art and mathematics as a tool, emphasizing the place of mathematics in today's world. Will satisfy the general education requirement for non-majors. Prerequisite: satisfactory completion of Entry-Level Mathematics requirement. Must complete course with a grade of "C-" or better in order to earn General Education, Area B4, credit. |

1130 ^{2} |
College Algebra (4)Functions and graphs: polynomials, rational functions, exponential and logarithmic functions. See note at beginning of course listings. Prerequisite: satisfactory completion of Entry-Level Mathematics requirement. Must complete course with a grade of "C-" or better in order to earn General Education, Area B4, credit. |

1300 |
Trigonometry and Analytic Geometry (4)Definitions, properties and graphs of the trigonometric functions. Applications. Analytic geometry of conic sections. A preparatory course for calculus. See note at beginning of course listings. Prerequisites: MATH 1130 or departmental permission. Must complete course with a grade of "C-" or better in order to earn General Education, Area B4, credit. |

1304 |
Calculus I (4)Differential calculus. Limits and continuity. Exponential and logarithmic functions. Techniques and applications of differentiation. See note at beginning of course listings. Prerequisite: MATH 1300 or departmental permission. Must complete course with a grade of "C-" or better in order to earn General Education, Area B4, credit. |

1305 |
Calculus II (4)Integral calculus. The indefinite integral, area, the Fundamental Theorem and techniques of integration. Applications to volume, arc length, physical and biological problems. Prerequisite: MATH 1304. |

1810 |
Mathematics for Business and Social Sciences (4)Functions and graphs; exponential and logarithmic functions; mathematics of accounting and finance; matrices and systems of equations; geometric approach to linear programming; introduction to differential and integral calculus with applications to business and social sciences. Prerequisite: MATH 1130 or departmental permission. Must complete course with a grade of "C-" or better in order to earn General Education, Area B4, credit. |

2011 ^{3} |
Number Systems (4)Structure of number systems, place value, whole numbers, integers, fractions, decimals, real numbers. Standard and nonstandard algorithms, mental computation. Algebra as generalized arithmetic. Divisibility, prime and composite numbers, GCF, LCM. Ratio, proportion, percents. Prerequisite: satisfactory completion of the Entry Level Mathematics (ELM) requirement. Not open to students with credit for MATH 4021. |

2101 |
Elements of Linear Algebra (4)Vector spaces, linear transformations, matrices, systems of linear equations. Stress on 2 and 3 dimensions, including geometric and other applications. Prerequisite: MATH 1305. |

2150 |
Discrete Structures (4)Topics in discrete mathematics. Elementary logic, set theory, and relations; induction, enumeration techniques, recurrence relations, trees and graphs. Boolean algebra, algorithm analysis. Prerequisite: MATH 1304. |

2304 |
Calculus III (4)Infinite series, convergence of power series. Vectors in space. Partial derivatives, chain rule, directional derivative and gradient. Curves and surfaces. Maxima and minima. Multiple integrals. Prerequisite: MATH 1305. |

2305 |
Calculus IV (4)Definite integrals over plane and solid regions in various coordinate systems. Vector functions and their derivatives and integrals. Motion in space. Line and surface integrals. Green's theorem, Stokes' theorem, divergence theorem. Prerequisite: MATH 2304. |

3000 |
Introduction to Abstract Mathematics and Proofs (4)Introduction to methods and proof techniques in several branches of mathematics, with topics chosen from logic, set theory, abstract algebra, number theory, analysis, and graph theory. Provides a transition from lower division mathematics courses, which concentrate on computation, to upper division proof-oriented mathematics courses. Prerequisite: MATH 2304; co-requisite: MATH 2101. |

3100 |
Linear Algebra (4)Abstract vector spaces, linear transformations, matrices and determinants. Dual spaces and inner product spaces. Eigenvalues and eigenvectors. Prerequisites: MATH 2101 and either 2150 or 3000. (MATH 3000 is strongly encouraged for mathematics majors and may be taken concurrently with MATH 3100.) |

3121 |
Abstract Algebra I (4)Groups and Subgroups, permutation groups and factor groups. Homomorphisms and Isomorphisms. An introduction to Rings, Polynomial Rings, and Factorization. Selected topics as time permits. Prerequisites: MATH 2101 and either 2150 or 3000. (MATH 3000 is strongly encouraged for mathematics majors and may be taken concurrently with MATH 3121.) |

3122 |
Abstract Algebra II (4)Rings and fields: integral domains, ideals, quotient rings, polynomial rings, roots of polynomials, algebraic extensions and finite fields. Selected topics as time permits. Prerequisite: MATH 3121. |

3151 |
Combinatorics (4)Theory of counting, including partitions, Stirling numbers, generating functions. Applications of Burnside's lemma from multiple transitivity to the Polya-Redfield Theorem. Ferrers diagrams, symmetric functions, and majorization. Prerequisites: MATH 2101 and either 2150 or 3000. |

3215 |
Geometry I (4)A rigorous, axiomatic approach to neutral and Euclidean geometry from an advanced standpoint. An introduction to non-Euclidean Geometries. Topics in Euclidean geometry to include congruence, area, parallelism, similarity, properties of circles and triangles, constructions, analytic and transformational geometry. Prerequisite: MATH 2101 and either 2150 or 3000. (MATH 3000 is strongly encouraged for mathematics majors and may be taken concurrently with MATH 3215.) |

3300 |
Analysis I (4)Field properties of the real and complex numbers. Sequences of real numbers, Bolzano-Weierstrass theorem. Topology of R ^{n}, metric spaces, connected and compact sets. Limits, continuity, intermediate and extreme value theorems. Other topics as time permits. Prerequisites: MATH 2101, 2304, and either 2150 or 3000. (MATH 3000 is strongly encouraged for mathematics majors and may be taken concurrently with MATH 3300.) |

3301 |
Analysis II (4)Continuity, uniform continuity. Sequences and series of functions. Differentiation, chain rule, implicit and inverse function theorems. Introduction to Riemann Integration. Prerequisite: MATH 3300. |

3331 |
Differential Equations (4)Methods of solution and applications of first order differential equations. Linear n-th order equations with emphasis on equations of 2nd order. Other topics may include power series solutions, Laplace transforms, linear systems. Prerequisite: MATH 2304. |

3361 |
Ordinary Differential Equations (4)Series solution of linear differential equations with variable coefficients, two point boundary value problems, systems of differential equations, phase plane analysis. Prerequisites: MATH 2101 and 3331. |

3600 |
Number Theory (4)Euclid's algorithm, prime numbers, congruences, theorems of Fermat and Euler, quadratic residues. Prerequisites: MATH 2101 and either 2150 or 3000. (MATH 3000 is strongly encouraged for mathematics majors and may be taken concurrently with MATH 3600.) |

3750 |
Numerical Analysis I (4)Basic numerical methods and analysis; practical solutions of problems from engineering, science, and mathematics. Computer representation of real numbers, errors, root finding, interpolation, numerical integration, ordinary differential equations. Prerequisites: CS 1160, MATH 2101 and 2304. Cross-listed with CS 3750. |

3841 |
Linear Programming (4)Problems of maximizing or minimizing a linear function subject to linear constraints; typical applications involve planning ("programming") the allocation of limited resources to achieve an optimal result. Topics include problem formulation, solution procedures, duality theory, sensitivity analysis, special problems (e.g., transportation and assignment problems). Prerequisite: MATH 2304 and competence in matrix algebra. |

3865 |
Mathematical Modeling (4)Discrete and continuous mathematical models. General introduction to the use of difference and differential equations, probability and statistics, and matrices for solving realistic problems. Computer simulation. Emphasis on effective written reports. Prerequisites: MATH 2101 and 2304. |

3875 |
Mathematical Physics (4)Mathematics theory and methods with applications to physics. In class physics laboratory explorations will utilize mathematical techniques to better understand physics phenomena. Prerequisite: MATH 1305. Co-requisite: MATH 2304. Cross-listed with PHYS 3875. |

3898 |
Cooperative Education (1-4)Supervised work experience in which student completes academic assignments integrated with off-campus paid or volunteer activities. Prerequisites: at least 2.0 GPA; departmental approval of activity; completion of lower division Mathematics major requirements and upper division standing. A maximum of 2 units will be accepted toward the Mathematics major. May be repeated for credit, for a maximum of 8 units. CR/NC grading only. |

4012^{3} |
Geometry and Measurement (4)Properties of 2- and 3-dimensional figures including congruence, similarity, proportional reasoning, area, perimeter, volume, surface area. Informal constructive proofs of properties of angles, polygons, parallel lines and the Pythagorean theorem. Transformational geometry. Measurement systems, estimation, coordinate geometry. Prerequisite: MATH 2011. Not open to students with credit for MATH 4022. |

4013^{3} |
Statistics, Data Analysis, and Probability (4)Displaying and interpreting data via graphs, tables and charts. Descriptive statistics, including mean, median, mode and range. Basic Survey design, including possible sources of biases. Elementary discrete probability. Dependent and independent events. Prerequisites: MATH 2011 and satisfactory completion of the Entry Level Mathematics requirement. Cross-listed with STAT 4013. Not open to students with credit for MATH 4023. |

4014^{3} |
Algebra and Functions (4)Patterns and functional relationships. Linear and quadratic equations and inequalities. Interpretation of graphs, multiple representations of functions. Factoring and completing the square. Proportional reasoning. Systems of linear equations. Prerequisites: MATH 2011 and satisfactory completion of the Entry Level Mathematics requirement. Not open to students with credit for MATH 4024. |

4030^{3} |
Advanced Study of School Mathematics (4)Foundations of school mathematics from an advanced standpoint. An in depth study of middle and high school level algebra, geometry and number theory and its applications, theoretical foundations and extensions. Intended for prospective elementary and middle school teachers. Prerequisites: Math 2011 and Math 1130 or consent of instructor. A-F grading only. |

4040 |
History of Mathematics (4)The historical development of mathematical ideas and techniques. Prerequisite: calculus or consent of instructor. |

4100 |
Mathematical Logic (4)The propositional calculus and its completeness. Boolean algebras. Functional calculi of various orders. Theorems of Godel and Henkin. Prerequisite: Senior standing in mathematics or consent of instructor. |

4121 |
Advanced Algebra (4)Theory of groups, including factor groups, Jordan-Holder Theorem, Sylow theorems. Mappings and homomorphisms. Introduction to rings and fields. Topics continued in MATH 6121. May not be applied towards the Mathematics M.S. degree. Prerequisite: MATH 3122. May not earn credit for MATH 6119. |

4151 |
Graph Theory (4)Introduction to graph theory. Graphic sequences. Planar graphs and the theorems of Euler and Kuratowski. Bipartite graphs. Connectivity and spanning trees. Hamiltonian graphs. Matching, chromatic and characteristic polynomials. Cospectral graphs and the graph isomorphism problem. Algorithms. Prerequisites: MATH 2101 and either 2150 or 3000. |

4215 |
Topics in Geometry (4)Topics in geometry such as algebraic, differential, finite, or projective geometry, convexity, packing and tiling, polytopes, and isoperimetric problems. Prerequisites: MATH 3215 or consent of instructor. May be repeated once for credit with consent of the chair, for a maximum of 8 units. |

4235 |
Introduction to Knot Theory (4)An introduction to the theory of knots and links. Topics covered include Reidemeister moves, knot invariants, including 3-colorings, the linking number, the Alexander polynomial, the Kauffman bracket and Jones polynomial. As time permits, some applications in biology and/or chemistry will be discussed. Prerequisite: MATH 3121. |

4340 |
Introduction to Complex Variables (4)Introduction to theory of functions of complex variables. May not be applied towards the Mathematics M.S. degree. Prerequisite: MATH 3300. |

4350 |
Theory of Functions of a Real Variable (4)Pointwise and uniform convergence, Taylor series, Riemann integration, sets of measure zero, Lebesgue's theorem on the Riemann integral, the metric space of continuous functions, and selected topics. May not be applied towards the Mathematics M.S. degree. Not open to students with credit for MATH 6349. |

4360 |
Introduction to Topology (4)Topological spaces, metric spaces, continuity, connectedness and compactness. May not be applied towards the Mathematics M.S. degree. Not open to students with credit for MATH 6200. Prerequisite: MATH 3300. |

4361 |
Partial Differential Equations (4)Differential equations of physics: the wave equation, the heat equation, Laplace's equation; boundary-value problems. Elementary Sturm-Liouville theory, Fourier series, Fourier and Laplace transforms, Bessel functions, selected topics. Prerequisite: MATH 3331. |

4365 |
Dynamical Systems (4)Introduction to dynamical systems and applications. Variational calculus, Lagrangian dynamics, principle of critical action, Hamiltonian systems and symplectic mechanics, Hamilton-Jacobi equation, chaotic and nonlinear systems, fractals. Prerequisites: MATH 3100, 3300, 3331, or consent of instructor. |

4750 |
Numerical Analysis II (4)Continuation of MATH 3750. Numerical solution of linear systems, matrix norms, approximation of functions, algebraic eigenvalues. Prerequisite: MATH/CS 3750. |

4841 |
Topics in Optimization (4)Sequel to MATH 3841. Topics to be drawn from linear and/or nonlinear programming. Linear programming topics may include integer programming, game theory, network programming; nonlinear programming topics include optimality conditions and solution procedures for unconstrained and constrained optimization problems. Prerequisite: MATH 3841. May be repeated once for credit with consent of the chair, for a maximum of 8 units. |

4842 |
Advanced Topics in Optimization (4)Topics selected from quasi-Newton methods for multi-variable unconstrained optimization; nonlinear least squares; quadratic programming; constrained optimization with nonlinear constraints; convex optimization. Prerequisites: MATH 3750 and 3841 or permission of instructor. May be repeated once for credit, with consent of the Mathematics Graduate Studies Committee, for a maximum of 8 units. |

4845 |
Fuzzy Sets and Fuzzy Logic (4)(See CS 4845 for course description.) |

4900 |
Independent Study (1-5)May be repeated for credit with consent of instructor, for a maximum of 12 units. |

4901 |
Senior Seminar (4)Exploration of topics in mathematics. Topics selected from the literature to illustrate relationships among various areas of mathematics. Oral presentations and paper required. Prerequisite: senior standing in mathematics (completion of 32 units of mathematics courses) or permission of the instructor. |

## Footnotes

- Completion of MATH 0900 does not satisfy the ELM requirement. Students must also pass MATH 0950 before enrolling in a baccalaureate-level mathematics course.
- Upper division mathematics and computer science majors will not receive credit for this course.
- Intended for prospective elementary and junior high school teachers; Mathematics and Computer Science majors will not receive credit for this course.