# Mathematics

## MATH 94 INTRODUCTION TO ALGEBRA (5)

Four hours lecture and one hour activity per week

A review of fundamental concepts of arithmetic, geometry and elementary algebra. Students who earn Credit in this course and in MATH 095 satisfy the Entry Level Mathematics (ELM) requirement. This course is offered Credit/No Credit only. Credit will not apply toward the baccalaureate degree but will apply as 5 units of University Credit.

Graded Credit/No Credit

## MATH 95 INTERMEDIATE ALGEBRA (5)

Four hours lecture and one hour activity per week

Prerequisite: MATH 094 or an appropriate Entry Level Mathematics Score

A review of concepts of geometry and intermediate algebra with applications. Students who earn Credit in this course satisfy the Entry Level Mathematics (ELM) requirement. This course is offered Credit/No Credit only. Credit will not apply toward the baccalaureate degree but will apply as 5 units of University Credit.

Graded Credit/No Credit

## MATH 101 COLLEGE ALGEBRA (3) [top]

Three hours lecture per week

Prerequisite: A passing score on the Entry Level Mathematics Examination

Topic include: basic set theory, number systems and their algebraic properties; systems of equations and inequalities; basic analytic geometry, matrix algebra and elementary functions; and problem solving.

## MATH 105 PRE-CALCULUS (4)

Four hours lecture per week

Prerequisite: A passing score on the Entry Level Mathematics Examination

Topics include: number systems and their algebraic properties; systems of equations and inequalities; basic analytic geometry of lines and conic sections; elementary functions including polynomial, rational, exponential, and logarithmic, with emphasis on trigonometric functions, fundamental theorem of algebra and theory of equations; polar equations and curves.

## MATH 108 MATHEMATICAL THINKING (3) [top]

Three hours lecture per week

Prerequisite: A passing score on the Entry Level Mathematics examination or MATH 095

Presents the diversity of mathematics and the spirit, in which it is employed in various situations, including different problem solving strategies, inductive- deductive reasoning, paradoxes, puzzles and mathematical modeling. The contributions of various cultures and influences of other disciplines to mathematical thinking are studied.

GenEd: B3

## MATH 137 STRATEGIES AND GAME DESIGN (3)

Three hours lecture per week

Prerequisites: A passing score on the Entry Level Mathematics Examination

This course introduces mathematics to the analysis of games. The principles of game theory including graphs, logic, algebra, geometry and probability are connected to game design, computer graphics and game strategies in various contexts. Applicable algorithms and techniques are demonstrated through appropriate computer gaming examples.

GenEd: B3

## MATH 140 CALCULUS FOR BUSINESS APPLICATIONS (3) [top]

Three hours lecture per week

Prerequisite: A passing score on the Calculus Placement Examination or MATH 101 or MATH 105

An integrated course in analytic geometry and calculus in the context of business and economics applications. Functions, limits, derivatives, integrals and mathematical modeling are used in problem solving in decision making context.

GenEd: B3

## MATH 150 CALCULUS I (4)

Four hours lecture per week

Prerequisite: Passing scores on the Calculus Placement Examination or MATH 105

A course in analytic geometry and calculus. Topics include: elementary and transcendental functions,their properties, limits, derivatives, integrals and mathematical modeling.

GenEd: B3

## MATH 151 CALCULUS II (4) [top]

Four hours lecture per week

Prerequisite: MATH 150

Topics include: differentiation, integration, sequences, infinite series, and power series.

## MATH 201 ELEMENTARY STATISTICS (3)

Three-hour lecture/laboratory per week

Prerequisite: A passing score on the Entry Level Mathematics Exam (ELM) or Math 105 or Math 101

Critical reasoning using a quantitative and statistical problem-solving approach to solving real-world problems. Topics include: probability and statistics, sample data, probability and empirical data distributions, sampling techniques, estimation and hypothesis testing, ANOVA, and correlation and regression analysis. Students will use standard statistical software to analyze real world and simulated data.

GenEd: B3

## MATH 202 BIOSTATISTICS (3) [top]

Three hours lecture/laboratory per week

Prerequisite: A passing score on the Entry Level Mathematics Exam (ELM) or MATH 105 or equivalent

Critical reasoning using a quantitative and statistical problem-solving approach to solve real-world problems. Uses probability and statistics to describe and analyze biological data collected from laboratory or field experiments. Course will cover descriptions of sample data, probability and empirical data distributions, sampling techniques, estimation and hypothesis testing, ANOVA, and correlation and regression analysis. Students will use standard statistical software to analyze real world and simulated data.

Same as PSY 202

GenEd: B3

## MATH 208 MODERN MATHEMATICS FOR ELEMENTARY TEACHING I-NUMBERS AND PROBLEM SOLVING (3)

Three hours lecture per week

Prerequisite: MATH 101

Current issues of modern math curriculum including abstract thinking and problem solving approaches to teaching. Content covers systems of numeration, nature of numbers and fundamental operations, relations and functions, properties of integers, rational and real numbers, and mathematical modeling. Problem solving strategies and geometric interpretations are stressed. Designed for students intending to teach in K-8. This course is not open to students who have credit for Calculus.

GenEd: B3

## MATH 230 LOGIC & MATHEMATICAL REASONING (3) [top]

Three hours lecture per week

Introduction to modern deductive logic. Critical thinking and abstract approaches to common language. Includes abstract sets and number sets, relations, prepositional logic, common language cases, and theory of quantification.

GenEd: A3,B3

## MATH 240 LINEAR ALGEBRA (3)

Three hours lecture per week

Prerequisite: MATH 151

Topics include: matrices, linear systems of equations, determinants, vectors in 2 and 3 dimensions, eigenvalues, the vector space Rn , linear transformations, introduction to general vector spaces and applications.

## MATH 250 CALCULUS III (3) [top]

Three hours lecture per week

Prerequisite: MATH 151 with a grade of C or better

Topics include: functions of several variables, solid analytic geometry, partial differentiation, multiple integrals with applications; vector analysis, and line and surface integrals.

## MATH 300 DISCRETE MATHEMATICS (3)

Three hours lecture per week

Prerequisite: MATH 151 and MATH 230

Topics include: Sets, algebraic systems, axioms, definitions, propositions and proofs. Combinatorics, graph theory, moduli calculus. Coding, coding errors and Hamming codes. Students are expected to write mathematical proofs, and communicate mathematical ideas clearly in written and oral form.

## MATH 301 DISCRETE MATHEMATICS FOR IT (3) [top]

Three hours lecture per week

Applications of sets, logic, algebraic systems, combinatorics, graph theory, moduli calculus in information technology. Basic coding, coding errors and Hamming codes and applications.

## MATH 308 MODERN MATHEMATICS FOR ELEMENTARY SCHOOL TEACHING II-GEOMETRY, PROBABILITY AND STATISTICS (3)

Three hours lecture per week

Prerequisite: MATH 208 or consent of the instructor

Current issues of modern math curriculum including abstract thinking and problem solving approaches to teaching. Content covers systems of geometry and geometric interpretation of real numbers, geometric constructions, mathematical modeling, basic probability and statistics. Problem solving strategies are stressed. Designed for students intending to become elementary school teachers.

## MATH 318 MATHEMATICS FOR SECONDARY SCHOOL TEACHERS (3) [top]

Three hours lecture in the computer lab per week

Prerequisite: MATH 150

Current issues of modern secondary school math curriculum including abstract thinking, technology use and problem solving approaches to teaching. Content is geometry based, but selected topics from algebra, precalculus, and calculus will be discussed. designed for students intending to teach. service learning project required.

## MATH 329 STATISTICS FOR BUSINESS AND ECONOMICS (3)

Three hours lecture in the lab per week

Introduction to modern statistical methods used in business and economic analysis. Topics include: sampling, probability, various distributions, correlation and regression, statistical inferences, hypothesis testing, problem solving and the consequences to underlying economical systems.

GenEd: B3

## MATH 330 MATHEMATICS AND FINE ARTS (3) [top]

Three hours lecture per week

Prerequisite: A passing score on the Entry Level Mathematics examination, or MATH 095

The course is specially designed for students interested in fine arts, with the emphasis on understanding geometric patterns and concepts by self-explorations. The course creates a vast reservoir of art-related examples and hands-on experiences, and will give an innovative mathematical background for future artistic endeavors of students.

GenEd: B3,Interdisciplinary

## MATH 331 HISTORY OF MATHEMATICS (3)

Three hours lecture per week

Study of breakthrough mathematical ideas and their creators, including historical and scientific context. Important concepts of current mathematics are studied: inception, development, difficulties, significance and various viewpoints will be presented. Lecture-discussion. At least one significant writing assignment is required.

GenEd: B3,D,Interdisciplinary

## MATH 345 DIGITAL IMAGE PROCESSING (3) [top]

Three hours lecture in the lab per week

Prerequisite: Consent of the instructor

An introduction to the basic concepts and techniques for digital image restoration and enhancement, analysis, coding and compression. The emphasis is on processes which analyze primarily two-dimensional discrete images represented at the pixel level, including filtering, noise reduction and segmentation. Fourier analysis techniques will be explored. Programming exercises will be used to implement the various processes, and their performance on synthetic and real images will be studied.

Same as PHYS 345,COMP 345

GenEd: B1,B4,Interdisciplinary

## MATH 350 DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS (3)

Three hours lecture per week

Prerequisite: MATH 250 (may be taken concurrently)

Topics include: ordinary differential equations, existence and uniqueness of solutions. Linear equations. Laplace methods. Flows and diffeomorphisms, limit sets, iterations of maps. Positive entropy systems, chaotic behavior of trajectories.

## MATH 351 REAL ANALYSIS (3) [top]

Three hours lecture per week

Prerequisite: MATH 250

Topics include: real number system, metric spaces, norms, function spaces, continuity, differentiability, integrability of functions, sequences and series.

## MATH 352 PROBABILITY AND STATISTICS (3)

Three hours lecture per week

Prerequisite: MATH 151

Topic include: data gathering, analysis and display. Validity of sampling methods and statistical conclusions. Probability, conditional probability, Bayes' Theorem, discrete and continuous random variables and their distribution (e.g., binomial, Poisson, hypergeometric, negative binomial, normal, exponential, gamma), moments, bivariate distributions, transformations of random variables, central and other limit theorems. Bayesian estimates, tests of hypotheses, nonparametric tests, decision theory. Modern computer software applications in statistics.

## MATH 354 ANALYSIS OF ALGORITHMS (3) [top]

Three hours lecture per week

Prerequisite: MATH 300 and some computer programming experience

Computer-oriented study of seminumerical and non-numerical algorithms. Topics include: sorting, tree searching, generation of combinatorial structures, algorithm proof techniques, best algorithms, programming complexity, and string matching.

## MATH 393 ABSTRACT ALGEBRA I (3)

Three hours lecture per week

Prerequisite: MATH 300

Groups, rings, and fields, the basic algebraic structures in contemporary mathematics.

## MATH 399 MODERN TOOLS IN MATHEMATICS (1) [top]

Three hours laboratory per week

Modern tools and software based problem solving in mathematics.

Graded: Credit/No Credit

## MATH 428 PHILOSOPHY OF MATHEMATICS (3)

Three hours lecture per week

Discuss infinity, paradoxes, Goedel's incompleteness theorem, whether mathematics is discovered or invented, why mathematical knowledge requires proof, whether mathematics is objective truth or social convention, and what kinds of entities mathematical objects are and how we can know about them.

## MATH 429 OPERATIONS RESEARCH (3) [top]

Three hours lecture per week

Prerequisite: MATH 329 or MATH 352 or equivalent

Introduction to applied mathematical methods in management sciences. Topics include: linear programming, managerial optimization methods, duality and equilibrium theorems, the simplex method, development of tools and methods required to make decisions and to solve operational problems in economy, decision and risk analysis, modeling and game theory. Topics of parametric programming, large-scale methods, generalized programming.

## MATH 430 RESEARCH DESIGN AND DATA ANALYSIS (3)

Three hours laboratory per week

Prerequisite: MATH/PSY 202 with a grade of C or better or MATH 352

Discussion of experimental design, sampling methods, data collection, and methods of data analysis related to scientific fields.

GenEd: A3,B3,Interdisciplinary

## MATH 437 MATHEMATICS FOR GAME DEVELOPMENT (3) [top]

Three hours lecture per week

Prequisites: MATH 137 or MATH 300

This course covers the application of basic algebra, Newtonian physics, computational mechanics, linear algebra, probability, and differential equations to game development and computer graphics. Applicable algorithms and techniques are demonstrated through appropriate computer gaming examples.

GenEd: B3,Interdisciplinary

## MATH 445 IMAGE ANALYSIS AND PATTERN RECOGNITION (3)

Three hours lecture in the lab per week

Prerequisite: PHYS/COMP/MATH 345 or consent of the instructor

The course addresses the issue of analyzing the pattern content within an image. Pattern recognition consists of image segmentation, feature extraction and classification. The principles and concepts underpinning pattern recognition, and the evolution, utility and limitations of various techniques (including neural networks) will be studied. Programming exercises will be used to implement examples and applications of pattern recognition processes, and their performance on a variety of diverse synthetic and real images will be studied.

Same as PHYS 445,COMP 445

GenEd: B1,B4,Interdisciplinary

## MATH 448 SCIENTIFIC COMPUTING (3) [top]

Three hours lecture in the lab per week

Prerequisite: MATH 151 and MATH 350 or COMP 151

Topics include: techniques of applied mathematics, solution of equations, finite differences, and wavelets.

GenEd: B3,B4,Interdisciplinary

## MATH 450 PARTIAL DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS (3)

Three hours lecture per week

Prerequisite: MATH 350 or consent of instructor

Topics include: vector field theory and Fourier analysis.

## MATH 451 COMPLEX ANALYSIS (3) [top]

Three hours lecture per week

Prerequisite: MATH 250

Topics include: complex variable, analytic functions, complex integration, power series and conformal mappings.

## MATH 452 COMPUTATIONAL BIOINFORMATICS (4)

Four hours lecture in the lab per week

Prerequisite: Programming experience and Statistics, or consent of the instructor

Basic computational models used in molecular biology will be introduced. Topics include algorithms for string alignments, dynamic programming, structural superposition algorithms, computing with differential information, 3D motifs, Hidden Markov Models, phylogenetic trees, statistical/ information techniques for pattern recognition, genetic algorithms.

Same as COMP 452

## MATH 480 DIFFERENTIAL AND RIEMANNIAN GEOMETRY (3) [top]

Three hours lecture per week

Prerequisite: MATH 351

Topics include: Implicit Function theorem. Differentials, Riemannian manifolds, curvature, local isometries, Gauss-Bonnet Theorem.

## MATH 482 NUMBER THEORY & CRYPTOGRAPHY (3)

Three hours lecture per week

Prerequisite: MATH 300

Topics include: Divisibility, prime numbers, unique factorization theorem, congruences, solutions of linear congruences, solutions of quadratic congruences, Fermat's Little Theorem, Wilson's Theorem, and Euler's phi function, Cryptography.

## MATH 484 ALGEBRAIC GEOMETRY AND CODING THEORY (3) [top]

Three hours lecture per week

Prerequisite: MATH 393

Study of algebraic varieties over algebraically closed fields. Modern application to coding theory.

## MATH 490 TOPICS IN MODERN MATHEMATICS (3)

Three hours lecture per week

Prerequisite: Upper-division standing

New developments in mathematics. Repeatable by topic.

## MATH 492 INTERNSHIP (1-3) [top]

Prerequisite: Upper division standing and Program approval of written proposal

Supervised work and study in educational, industrial or scientific setting involving development of degree related skills. All students are required to present their projects at the Senior Colloquium.

## MATH 493 ABSTRACT ALGEBRA II (3)

Three hours lecture per week

Prerequisites: MATH 393

Field extensions, Galois theory, rings and modules, and further topics on groups, rings, and fields.

## MATH 494 INDEPENDENT RESEARCH (1-3) [top]

Prerequisite: Senior standing and Program approval of written proposal

Supervised project involving theoretical research in the field of mathematics or its applications. All students are required to present their projects at the Senior Colloquium.

## MATH 497 DIRECTED STUDIES (3)

Prerequisite: Program approval of written proposal

Supervised project involving library research in the field of mathematics or its applications. All students are required to present their projects at the Senior Colloquium.

## MATH 499 SENIOR COLLOQUIUM (1) [top]

One hour of seminar per week

Prerequisite: Senior standing

Oral presentations of current advancement in the field, and reports on students' projects. Repeatable.

## MATH 510 PROBABILISTIC METHODS AND MEASURE THEORY (3)

Three hours lecture per week

Prerequisite: Admission to the Computer Science or Mathematics Graduate Program

Introduction to probabilistic methods. Topic include: sigma algebras, measures, integrals, Lebesgue measure, main convergence results and the change of variable results for integrals. Probabilistic methods in computational sciences are studied.

## MATH 511 FUNCTIONAL ANALYSIS (3) [top]

Three hours lecture per week

Prerequisite: Admission to the Computer Science or Mathematics Graduate Program

Topics include: metric spaces, function spaces, normed vector spaces, linear operators. Banach spaces, Hilbert space. Spectral theory, and fundamental theorems in functional analysis. Applications in various fields including computer science, bioinformatics, and statistical analysis.

## MATH 513 ADVANCED ALGEBRA (3)

Three hours lecture per week

Prerequisite: Admission to the Computer Science or Mathematics Graduate Program

Topics include: Techniques of GroupTheory, Rings Fields, Modules, Galois Theory, Algebraic Number Theory, Algebraic Geometry, Techniques of Linear Algebra, Noncommutative Algebra, and Homological Algebra.

## MATH 555 ACTUARIAL SCIENCES (3) [top]

Three hours lecture per week

Prerequisite: Admission to the Computer Science or Mathematics Graduate Program

The course provides a sound grounding in the mathematical, statistical and financial concepts needed for actuarial work, including technical and communication skills. Topics include: probability, statistics, data analysis, mathematical modeling, risk analysis, pension plans, financial economics, and time series.Various software packages are used.

## MATH 565 RESEARCH IN MATHEMATICS EDUCATION (3)

Three hours lecture per week

Prerequisite: Admission to the Computer Science or Mathematics Graduate Program

Mathematical research methods in education. Current issues of college level curriculum including systems of geometry, algebra, precalculus, calculus, probability and statistics, linear algebra, differential equations, and discrete mathematics.

## MATH 581 MATHEMATICAL METHODS IN ARTIFICIAL INTELLIGENCE (3) [top]

Three hours lecture in the lab per week

Prerequisite: Admission to the Computer Science or Mathematics Graduate Program

This course presents several branches of mathematics that provide computational basis for Artificial Intelligence. The course covers Trees and Search, The Concepts of Predicate Logic, The Theory of Resolution, Nonmonotonic Reasoning, Probability Theory, Bayesian Networks, Fuzziness and Belief Theory, Classifier Systems, Math for Neural Networks, Elements of Statistics, Decision Trees and Optimization.

Same as COMP 581

## MATH 582 NUMBER THEORY & CRYPTOGRAPHY (3)

Three hours lecture per week

Prerequisite: Admission to the Computer Science or Mathematics Graduate Program

Topics include: Number theory, finite fields, polynomial rings, elliptic curves, public-key cryptography, zero-knowledge protocols, primality testing, factorization algorithms and applications.

## MATH 584 ALGEBRAIC GEOMETRY AND CODING THEORY (3) [top]

Three hours lecture per week

Prerequisite: Admission to the Computer Science or Mathematics Graduate Program

Topics include: Algebraic varieties over algebraically closed fields and finite fields, Hamming codes, cyclic codes, BCH codes, alternant codes, Goppa codes, and codes on graphs.

## MATH 587 MARKOV CHAINS AND MARKOV PROCESSES (3)

Three hours lecture per week

Prerequisite: Admission to the Computer Science or Mathematics Graduate Program

Topics include: Central Limit Theorem, Law of Large Numbers, Convergence Theorems, Markov Chains and Markov Processes. Applications in other fields, such as bioinformatics and computer science.

## MATH 588 STOCHASTIC ANALYSIS (3) [top]

Three hours lecture per week

Prerequisite: Admission to the Computer Science or Mathematics Graduate Program

Topics include: Brownian motion, stochastic integrals, conditional expectation, Kolmogorv's Theorem, applications of Lebesgue Dominated Convergence Theorem. Introduction to Stochastic Differential Equations will be given.

## MATH 590 GRADUATE TOPICS IN MATHEMATICS (3)

Three hours lecture per week

Prerequisites: Graduate standing/Undergraduate seniors

New developments in mathematics. Repeatable by topic.

## MATH 597 MASTER THESIS (1-9) [top]

Three hours lecture per week

Prerequisite: Admission to the Computer Science or Mathematics Graduate Program

Supervised research in mathematical sciences or applications. Required to present research at Graduate Seminar.

## MATH 598 MASTER PROJECT (1-9)

Three hours lecture per week

Prerequisite: Admission to the Computer Science or Mathematics Graduate Program

Supervised industrial, educational or scientific project involving use of advanced mathematical methods. Required to present projects at the Graduate Seminar.

## MATH 599 GRADUATE SEMINAR (1) [top]

Three hours lecture per week

Prerequisite: Admission to the Computer Science or Mathematics Graduate Program

Oral presentations of current advancements in the field, reports on students' research, master thesis, and projects. Repeatable.