Mathematics Courses

Upper Division Courses
(intended for undergraduates)

MATH 302. Transition to Higher Mathematics (3) (Syllabus)
Prerequisite: Mathematics 141 or 150.
Selected topics in mathematics to emphasize proof writing and problem solving. Intended for those planning to teach secondary school mathematics.

MATH 303. History of Mathematics (3) [GE]
Prerequisite: Mathematics 141 or completion of the General Education requirement in Foundations of Learning IIA., Natural Sciences and Quantitative Reasoning for nonmajors.
Major currents in the development of mathematics from ancient Egypt and Babylon to late nineteenth century Europe.

MATH 312. Topics from Elementary Mathematics: Statistics and Probability (3)
Prerequisites: Mathematics 211 and satisfactory performance on Liberal Studies Mathematics Proficiency Assessment.
Topics from statistics and probability. Enrollment limited to future teachers in grades K-8

MATH 313. Topics in Elementary Mathematics: Algebra of Change (3)
Prerequisites: Mathematics 211 and satisfactory performance on Liberal Studies Mathematics Proficiency Assessment. Capstone course for prospective K-8 teachers.
Advanced topics in mathematics selected from algebra, number systems, transformation geometry, and problem solving. Enrollment limited to future teachers in grades K-8.

MATH 320. Abstract Algebra (3) (Syllabus)
Prerequisites: Mathematics 245 and 254 with a grade of C (2.0) or better in each course.
Proof of completion of prerequisites required: Copy of transcript.
Elementary number theory and rings to include ideals, polynomial rings, quotient rings, ring homomorphisms and isomorphisms. Introduction to basic aspects of group theory. (Formerly numbered Mathematics 521A.)

MATH 330. Advanced Calculus I (3) (Syllabus)
Prerequisites: Mathematics 245 and either 254 or 342A with a grade of C (2.0) or better in each course.
Proof of completion of prerequisites required: Copy of transcript.
Completeness of the real numbers and its implications, sequences of real numbers, and continuity and differentiability of functions of one real variable. (Formerly numbered Mathematics 534A.)

MATH 336. Introduction to Mathematical Modeling (3)
Prerequisite: Mathematics 254 with a grade of C (2.0) or better.
Models from the physical, natural, and social sciences including population models and arms race models. Emphasis on classes of models such as equilibrium models and compartment models.

MATH 340. Programming in Mathematics (3)
Prerequisites: Mathematics 151 and 245 with a grade of C (2.0) or better in each course. Proof of completion of prerequisites required: Copy of transcript.
Introduction to programming in mathematics. Modeling, problem solving, visualization. Not open to students with credit in Mathematics 242.

MATH 341. Mathematics Software Workshop (1) (Syllabus)
Prerequisite: Mathematics 150.
Course hours: Two hours of activity. 
Lesson plan design using teacher-based technologies. (Formerly numbered Mathematics 241.)

MATH 342A. Methods of Applied Mathematics I (3)
Prerequisite: Mathematics 252.
Vector analysis, divergence and Stokes’ theorem and related integral theorems. Matrix analysis, eigenvalues and eigenvectors, diagonalization. Introduction to ordinary differential equations. Computer software packages for matrix applications, solving, and graphing differential equations.

MATH 342B. Methods of Applied Mathematics II (3)
Prerequisite: Mathematics 342A with a grade of C (2.0) or better.
Second order ordinary differential equations, power series methods, Bessel functions, Legendre polynomials. Linear partial differential equations, separation of variables, Fourier series, Sturm-Liouville theory, orthogonal expansions, Fourier Transforms. Use of computer software packages for symbolic algebra and solution of differential equations.

MATH 413. Mathematics for the Middle Grades (3) (Syllabus)
Prerequisite: Mathematics 313.
Teacher-level look at mathematics taught in middle grades, to include proportional reasoning, rational and real numbers, probability, and algebra. Intended for those planning to teach mathematics in middle grades; cannot be used as part of major or minor in mathematical sciences with exception of major for single subject teaching credential. Students in the SSTC major must receive instructor permission

MATH 414. Mathematics Curriculum and Instruction (3) (Syllabus)
Prerequisites: Senior standing and 12 upper division units in mathematics.
Historical development of mathematics and mathematics curriculum. Principles and procedures of mathematics instruction in secondary schools. For secondary and postsecondary teachers and teacher candidates. Course cannot be used as part of the major or minor in mathematical sciences with exception of major for the single subject teaching credential.

MATH 496. Experimental Topics (1-4)
Selected topics. May be repeated with new content. See Class Schedule for specific content. Limit of nine units of any combination of 296, 496, 596 courses applicable to a bachelor’s degree.

MATH 499. Special Study (1-3)
Prerequisites: Consent of instructor and at least one 300-level mathematics course with a grade of C (2.0) or better.
Individual study. Maximum credit six units. No more than three units may be applied to the major.

Upper Division Courses
(also acceptable for advanced degrees)

MATH 508. Dynamical Systems and Modeling (3) (Syllabus)
Prerequisite: Mathematics 254 or graduate standing.
Differential equations using analytical, graphical, and numerical representations.

MATH 509. Computers in Teaching Mathematics (3) 
Prerequisite: Mathematics 252 with a grade of C (2.0) or better.
Proof of completion of prerequisite required: Copy of transcript.
Course hours: Two lectures and three hours of laboratory. 
Solving mathematical tasks using an appropriate computer interface, and problem-based curricula. Intended for those interested in mathematics teaching.

MATH 510. Introduction to the Foundations of Geometry (3) (Syllabus)
Prerequisite: Mathematics 151 and 302 with a grade of C (2.0) or better.
Proof of completion of prerequisite required: Copy of transcript.
The foundations of Euclidean and hyperbolic geometries. Highly recommended for all prospective teachers of high school geometry.

MATH 520. Algebraic Structures (3)
Prerequisite: Mathematics 320 with a grade of C (2.0) or better or graduate standing.
Proof of completion of prerequisite required: Copy of transcript.
Continuation of Mathematics 320. Group theory to include finite Abelian groups, group homomorphisms and isomorphisms, normal subgroups, quotient groups, and Sylow theorems. Selected advanced topics to include field extensions or integral domains. (Formerly numbered Mathematics 521B.)

MATH 522. Number Theory (3) (Syllabus)
Prerequisite: Mathematics 245 and 254 with a grade of C (2.0) or better.
Proof of completion of prerequisite required: Copy of transcript.
Theory of numbers to include congruences, Diophantine equations, and a study of prime numbers; cryptography.

MATH 524. Linear Algebra (3) (Syllabus)
Prerequisites: Mathematics 245 and either 254 or 342A with a grade of C (2.0) or better in each course.
Proof of completion of prerequisites required: Copy of transcript.
Vector spaces, linear transformations, orthogonality, eigenvalues and eigenvectors, normal forms for complex matrices, positive definite matrices and congruence.

MATH 525. Algebraic Coding Theory (3) (Syllabus)
Prerequisite: Mathematics 254 with a grade of C (2.0) or better.
Proof of completion of prerequisite required: Copy of transcript.
Linear codes, perfect and related codes, cyclic linear codes, BCH codes, burst error-correcting codes.

MATH 530. Advanced Calculus II (3) (Syllabus)
Prerequisite: Mathematics 330 with a grade of C (2.0) or better or graduate standing.
Proof of completion of prerequisite required: Copy of transcript.
Formal definitions and analysis within the framework of single variable functions. Advanced concepts in analysis. (Formerly numbered Mathematics 534B.)

MATH 531. Partial Differential Equations (3)
Prerequisites: Mathematics 237 and 252 with a grade of C (2.0) or better in each course.
Proof of completion of prerequisites required: Copy of transcript.
Boundary value problems for heat and wave equations: eigenfunction expansions, Sturm-Liouville theory and Fourier series. D’Alembert’s solution to wave equation; characteristics. Laplace’s equation, maximum principles, Bessel functions.

MATH 532. Functions of a Complex Variable (3) (Syllabus)
Prerequisite: Mathematics 252 with a grade of C (2.0) or better.
Proof of completion of prerequisite required: Copy of transcript.
Analytic functions, Cauchy-Riemann equations, theorem of Cauchy, Laurent series, calculus of residues, and applications.

MATH 537. Ordinary Differential Equations (3) (Syllabus)
Prerequisite: Graduate standing or Mathematics 237 or 330 with a grade of C (2.0) or better.
Proof of completion of prerequisite required: Copy of transcript.
Theory of ordinary differential equations: existence and uniqueness, dependence on initial conditions and parameters, linear systems, stability and asymptotic behavior, plane autonomous systems, series solutions at regular singular points.

MATH 538. Discrete Dynamical Systems and Chaos (3) (Syllabus)
Prerequisite: Mathematics 237, 330, 340, or 342B with a grade of C (2.0) or better.
Proof of completion of prerequisite required: Copy of transcript.
One- and two-dimensional iterated maps, equilibria and their stability, sensitive dependence on initial conditions, Lyapunov exponents, horseshoe maps, period doubling, chaotic attractors, Poincare maps, stable/unstable manifolds, bifurcations. Applications in biology, chemistry, physics, engineering, and other sciences.

MATH 542. Introduction to Computational Ordinary Differential Equations (3) (Syllabus)
Prerequisites: Mathematics 340; and either Mathematics 237, 342A, or Aerospace Engineering 280 with a grade of C (2.0) or better in each course.
Proof of completion of prerequisites required: Copy of transcript.
Initial and boundary value problems for ordinary differential equations. Runge-Kutta, linear multi-step, predictor-corrector, adaptive, hybrid, shooting, and general linear methods. System, stiffness, and non-linear problems. Iterative methods.

MATH 543. Numerical Matrix Analysis (3)
Prerequisites: Mathematics 340; and either Mathematics 254, 342A, or Aerospace Engineering 280 with a grade of C (2.0) or better.
Proof of completion of prerequisites required: Copy of transcript.
Singular value decomposition. Projections, QR-factorization, orthogonalization, conditioning and stability, Gaussian Elimination, LU-Factorization, pivoting strategies, Cholesky Factorization. Iterative methods for diagonalization and eigensystem computation. Tridiagonal, Hessenberg, and Household matrices. The QR algorithm.

MATH 579. Combinatorics (3) (Syllabus)
Prerequisite: Mathematics 245 and 254 with a grade of C (2.0) or better.
Proof of completion of prerequisite required: Copy of transcript.
Permutations, combinations, generating functions, recurrence relations, inclusion-exclusion counting. Polya’s theory of counting, other topics and applications.

MATH 595. Mathematical Biology and Biomedicine (3)
Prerequisites: Mathematics 237 and 254, or 342A, or Aerospace Engineering 280.
Mathematical and computational modeling techniques to include difference and differential equations; probabilistic and statistical models.

MATH 596. Advanced Topics in Mathematics (1-4)
Prerequisite: Consent of instructor.
Selected topics in classical and modern mathematical sciences. May be repeated with the approval of the instructor. See Class Schedule for specific content. Limit of nine units of any combination of 296, 496, 596 courses applicable to a bachelor’s degree. Maximum credit of six units of 596 applicable to a bachelor’s degree. Credit for 596 and 696 applicable to a master’s degree with approval of the graduate adviser.

Graduate Courses

MATH 600. Chaos and Fractals (3) (Syllabus)
Prerequisites: Mathematics 320 and 510.
Non-linear dynamics to include Cantor sets, fixed and periodic points, fractal dimensions, fractals, iterative processes, orbit diagrams, orbits, period doubling, and self-similarity.

MATH 601. Topics in Algebra (3) (Syllabus)
Prerequisites: Mathematics 320 and 330.
Unique factorization domains, rings and ideals, groups, algebraic field extensions. A course designed for secondary school teachers.

MATH 602. Topics in Analysis (3) (Syllabus)
Prerequisites: Mathematics 320 and 330.
Topics in analysis, including the real number system, convergence, continuity, differentiation, the Riemann-Stieltjes integral, complex analysis, designed to give the secondary teacher a broad understanding of the fundamental concepts.

MATH 620. Groups, Rings, and Fields (3) (Syllabus)
Prerequisites: Mathematics 320 and either 520 or 522 or 525 with a grade of C (2.0) or better in each course.
Group theory to include finite Abelian groups, isomorphism theorems, matrix groups, and permutation groups. Ring theory to include ideals, principal ideal domains, and unique factorization. Field theory to include field extensions and finite fields.

MATH 621. Advanced Topics in Algebra (3)
Prerequisite: Mathematics 620 with a grade of C (2.0) or better.
Topics in advanced algebra. Typical courses to include algebra-geometry dictionary, commutative algebra, groups, fields, and Galois theory. May be repeated with new content. See Class Schedule for specific content. Maximum credit six units.

MATH 625. Algebraic Coding Theory (3)
Prerequisites: Mathematics 525 and Mathematics 520 or 522 with a grade of C (2.0) or better in each course.
Algebraic theory of error correction codes and decoding algorithms used in modern communications systems. Reed-Solomon codes and algebraic decoding algorithms. Code duality, MacWilliam’s identities and the linear programming bound. Probabilistic decoding of convolutional codes, low-density parity-check codes and turbo codes.

MATH 626. Cryptography (3)
Prerequisites: Mathematics 320 and 522 with a grade of C (2.0) or better in each course.
Design of secure cryptosystems with applications. Classical and public key cryptosystems. Primality testing, factoring, discrete log problem, and knapsack problem.

MATH 630. Applied Real Analysis (3) (Syllabus)
Prerequisite: Mathematics 330 with a grade of B- (2.7) or better. Recommended: Mathematics 530 with a grade of B- (2.7) or better.
Lebesgue measure and integration, metric spaces, Banach spaces, Hilbert spaces. (Formerly numbered Mathematics 630A.)

MATH 633. Advanced Topics in Analysis (3)
Prerequisite: Mathematics 630. Recommended: Mathematics 668.
Specific topics in analysis to include Lebesgue and Sobolev spaces and spectral theory. Investigation of new theoretical tools and their applications.

MATH 635. Pattern Formation (3) (Syllabus)
Prerequisites: Mathematics 237 or 531 and Mathematics 254 or 342A, 342B.
Linear stability, marginal stability curves, classification. One dimensional patterns, bifurcations. Two dimensional patterns, square and hexagonal patterns, spirals, defects. Diffusion driven instability, Turing patterns. Spatio-temporal chaos. Applications in biology, chemistry, and physics.

MATH 636. Mathematical Modeling (3) (Syllabus)
Prerequisites: Mathematics 237 and 254 or Mathematics 342A and 342B or Aerospace Engineering 280 with a grade of C (2.0) or better in each course.
Advanced models from the physical, natural, and social sciences. Emphasis on classes of models and corresponding mathematical structures.

MATH 638. Continuous Dynamical Systems and Chaos (3) (Syllabus)
Prerequisites: Mathematics 237 or 537 and Mathematics 254 or 342A, 342B with a grade of C (2.0) or better in each course.
Nonlinear systems of differential equations, potential fields, periodic solutions, Lyapunov function. Chaos in differential equations, Lyapunov exponents, chaotic attractors, Poincare maps. Lorenz and Rossler attractors, forced oscillators, Chua’s circuit, stable manifolds. Bifurcations. Applications in science and engineering.

MATH 639. Nonlinear Waves (3) (Syllabus)
Prerequisite: Mathematics 531 or 537 with a grade of C (2.0) or better.
Linear waves, dissipation, dispersion. Conservation laws. Water waves. KdV equation, solitary waves, cnoidal waves. Scattering and inverse scattering. Perturbation theory. Nonlinear Schroedinger equation, dark and bright solitons, vortex solutions. Variational techniques, modulational instability, stability.

MATH 667. Mathematical Aspects of Systems Theory (3)
Prerequisites: Mathematics 524 and 537 with a grade of C (2.0) or better in each course.
Linear and nonlinear systems, nonlinear differential equations, equilibrium equations. Linearization, state transition matrix, stability theory, feedback control systems.

MATH 668. Applied Fourier Analysis (3) (Syllabus)
Prerequisites: Mathematics 330, 524; 530 or 532 with a grade of C (2.0) or better in each course.
Discrete and continuous Fourier transform methods with applications to statistics and communication systems.

MATH 693A. Advanced Numerical Methods: Computational Optimization (3)
Prerequisites: Mathematics 340 and 524 with a grade of C (2.0) or better in each course.
Numerical optimization: Newton, Truncated-Newton, and Quasi-Newton methods for unconstrained optimization; with applications to nonlinear least squares, orthogonal distance regression, and nonlinear equations.

MATH 693B. Advanced Numerical Methods: Computational Partial Differential Equations (3)
Prerequisites: Mathematics 340 and 531 with a grade of C (2.0) or better in each course.
Methods for hyperbolic, parabolic, and elliptic partial differential equations: consistency, stability, convergence.

MATH 695. Communication in Interdisciplinary Applied Mathematics (3) (Syllabus)
Prerequisite: Graduate standing.
Analysis of research publications. Communication skills for interdisciplinary mathematics. Development of a grant proposal and outreach item. Maximum credit three units applicable to a master’s or doctoral degree.

MATH 696. Selected Topics in Mathematical Sciences (3)
Prerequisite: Graduate standing.
Intensive study in specific areas of mathematical sciences. May be repeated with new content. See Class Schedule for specific content. Credit for 596 and 696 applicable to a master’s degree with approval of the graduate adviser.

MATH 720. Seminar (1-3)
Prerequisite: Consent of instructor.
An intensive study in advanced mathematics. May be repeated with new content. See Class Schedule for specific content. Maximum credit six units applicable to a master’s degree.

MATH 790. Practicum in Teaching of Mathematics (1) [Cr/NC]
Prerequisite: Award of graduate teaching associateship in mathematics.
Supervision in teaching mathematics. Lecture writing, style of lecture presentation and alternatives, test and syllabus construction, and grading system. Not applicable to an advanced degree. Required for first semester GTA’s.

MATH 797. Research (1-3) [Cr/NC/RP]
Prerequisite: Six units of graduate level mathematics.
Research in one of the fields of mathematics. Maximum credit six units applicable to a master’s degree.

MATH 798. Special Study (1-3) [Cr/NC/RP]
Prerequisite: Consent of staff; to be arranged with department chair and instructor.
Individual study. Maximum credit six units applicable to a master’s degree.

MATH 799A. Thesis or Project (3) [Cr/NC/RP]
Prerequisites: An officially appointed thesis committee and advancement to candidacy.
Preparation of a project or thesis for the master’s degree.

MATH 799B. Thesis or Project Extension (0) [Cr/NC]
Prerequisite: Prior registration in Thesis or Project 799A with an assigned grade symbol of RP.
Registration required in any semester or term following assignment of RP in Course 799A in which the student expects to use the facilities and resources of the university; also student must be registered in the course when the completed thesis or project is granted final approval.

MATH 799C. Comprehensive Examination Extension (0) [Cr/NC]
Prerequisite: Completion or concurrent enrollment in degree program courses.
Registration required of students whose only requirement is completion of the comprehensive examination for the master’s degree Registration in 799C limited to two semesters.