May 21, 2024  
2021-2022 Undergraduate and Graduate Catalog 
    
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2021-2022 Undergraduate and Graduate Catalog [ARCHIVED CATALOG]

Mathematics and Statistics (MATH, STAT, MTED, ESM) Courses

Mathematics and Statistics

Courses

Early Start Mathematics

  • ESM 100 - Algebra, Geometry and their Applications

    (1 unit)

    Prerequisites: CSU General Education Mathematics placement.
    Arithmetic, algebra, geometry, and their applications in college and beyond. 
     

    Credit/No Credit grading only. (Seminar 15 hrs) This course will satisfy the Early Start Program requirement for CSULB bound students.

Mathematics and Statistics

  • MATH 92A - Foundations for Essential Algebra A

    (1 unit)

    Corequisite: MATH 112A .
    Topics and skills that support student success in MATH 112A . Students required to enroll in this co-requisite course must remain enrolled in both courses for the semester.  Students will not be permitted to withdraw from one of the courses (either MATH 112A ​ or MATH 92) and not the other.

    Credit/ No-Credit option (Activity 2 hours). May be repeated to a maximum of 2 units in different semesters.

  • MATH 92B - Foundations for Essential Algebra B

    (1 unit)

    Prerequisite: MATH 112A .
    Corequisite: MATH 112B .
    Topics and skills that support student success in MATH 112B . 

    Credit / No Credit only. (Activity 2 hours). May be repeated to a maximum of 2 units in different semesters.

  • MATH 94 - Foundations for Quantitative Reasoning

    (1 unit)

    Corequisite: MATH 104  
    Topics and skills that support student success in MATH 104  . This course is designed as a co-requisite course and should only be taken with MATH 104  . Students required to enroll in this co-requisite course must remain enrolled in both courses for the semester.  Students will not be permitted to withdraw from one of the courses (either MATH 94 or MATH 104  ) and not the other.

    Credit/No Credit. (Activity 2 hours). May be repeated to a maximum of 2 units in different semesters.

  • MATH 95 - Foundations for Business Calculus

    (1 unit)

    Corequisite: MATH 115 .
    Topics and skills that support student success in MATH 115. This course is designed as a co-requisite course and should only be taken with MATH 115. Students required to enroll in this co-requisite course must remain enrolled in both courses for the semester.  Students will not be permitted to withdraw from one of the courses (either MATH 95 or MATH 115) and not the other.

    Credit/ No-Credit option (Activity 2 hours). May be repeated to a maximum of 2 units in different semesters.

  • MATH 103 - Mathematical Ideas

    (3 units)

    Prerequisite: MAPB 7  or MAPB 11 .
    Surveys variety of concepts in undergraduate mathematics. Includes elementary logic, numeration systems, rational and real numbers, modular number systems, elementary combinatorics, probability and statistics, using real world examples.

    Both grading options. (Lecture 3 hrs.) Not open for credit to students with credit in any MATH or MTED course numbered greater than 103, or the equivalent.

  • MATH 104 - The Power of Mathematics

    (3 units)

    Prerequisite/Corequisite: Appropriate CSU Multiple Measures Placement or concurrent enrollment in MATH 94 .

    Topics that demonstrate the power and art of mathematical thinking. Development of quantitative and financial literacy; number sense and computational skills; mathematical habits of mind; communication skills across various mathematical forms; and ability to analyze realistic problems with mathematical tools.

    Letter grade only (A-F). (Lecture 2 hours, activity 2 hours).

  • MATH 109 - Modeling with Algebra

    (3 units)

    Prerequisite: MAPB 7  or MAPB 11 .
    Data, functions, domain, range, representations of functions (verbal, numerical, graphical, algebraic), visualizing functions (increasing, decreasing, maximum, minimum, concave up, concave down). Linear functions, rate of change, slope, modeling data, systems of linear equations, linear inequalities. Exponentials, logs, growth decay, semi log plots for modeling.

    Both grading options. (Lecture 3 hrs.) Not open for credit to students with credit in any MATH or MTED course numbered greater than 103, or the equivalent.

  • MATH 111 - Precalculus Trigonometry

    (3 units)

    Prerequisites: A grade of “C” or better in MATH 112A  or appropriate CSULB Algebra and Calculus Placement.
    Trigonometric functions and applications. Arithmetic and graphical representation of complex numbers, polar form, DeMoivre’s Theorem.

    Both grading options. (Lecture 3 hrs.) Not open for credit to students with credit in MATH 122 .

  • MATH 112A - Essential Algebra A

    (3 units)

    Prerequisite: Appropriate CSU Multiple Measures placement or concurrent enrollment in MATH 92A . MATH 92A  is a co-requisite course for students in need of additional support for MATH 112A.
    Recognize, relate, describe, manipulate and apply functions and equations that are linear, piecewise, quadratic and polynomial. Communicate quantitative ideas both orally and in writing. 

    Letter grade only (A-F). (2 hours lecture; 2 hours activity). Not open for credit for students with credit in MATH 113 , MATH 115 , MATH 119A , or MATH 122 .

  • MATH 112B - Essential Algebra B

    (3 units)

    Prerequisite: A grade of “C” or better in MATH 112A  or equivalent.
    Recognize, relate, describe, manipulate and apply functions and equations that are polynomial, rational, exponential, and logarithmic. Communicate quantitative ideas both orally and in writing. 

    Letter grade only (A-F). (2 hours lecture; 2 hours activity). Not open for credit for students with credit in MATH 113  ,MATH 115  , MATH 119A   , or MATH 122  .

  • MATH 113 - Precalculus Algebra

    (3 units)

    Prerequisites: Appropriate CSULB Algebra and Calculus Placement.
    Equations, inequalities. Functions, their graphs, inverses, transformations. Polynomial, rational functions, theory of equations. Exponential, logarithmic functions, modeling. Systems of equations, matrices, determinants. Sequences, series.

    Both grading options. (Lecture 3 hrs.) Not open for credit to students with credit in MATH 115 , MATH 119A , or MATH 122 .

  • MATH 115 - Calculus for Business

    (3 units)

    Prerequisite(s): Appropriate CSULB Algebra and Calculus Placement or a grade of “C” or better in MATH 112A.
    Functions, derivatives, optimization problems, graphs, partial derivatives. Applications to business and economics. Emphasis on problem-solving techniques.

    Both grading options. (Lecture 2 hrs., Activity 2 hrs) Not open for credit to students with credit in MATH 119A or MATH 122.

  • MATH 115Z - Calculus for Business

    (3 units)

    Prerequisites: MAPB 11  or 12.
    Functions, derivatives, optimization problems, graphs, partial derivatives. Lagrange multipliers, intergration of functions of one variable. Applications to business and economics. Emphasis on problem-solving techniques.

    Both grading options. (Seminar 3 hours.) Only students with contracts through SB 1440 (the STAR Act) may enroll in this class.

  • MATH 119A - Survey of Calculus I

    (3 units)

    Prerequisites: A grade of “C” or better in MATH 112B  or MATH 113 , or appropriate CSULB Algebra and Calculus Placement.
    Functions, limits and continuity, differentiation and integration of functions of one variable including exponential, logarithmic, and trigonometric functions. Graphing, optimization, parametric equations, integration by substitution and by parts, numerical integration. Applications to the life sciences. Emphasis on problem solving.

    Both grading options. (Lecture 3 hrs.) Not open for credit to students with credit in MATH 122 .

  • MATH 119B - Survey of Calculus II

    (3 units)

    Prerequisite: A grade of “C” or better in MATH 119A  or MATH 122 .
    Functions of several variables, partial derivatives, optimization. First order differential equations, second order linear homogeneous differential equations, systems of differential equations. Probability, random variables, difference equations. Introduces matrices, Gaussian elimination, determinants. Life science applications. Emphasis on problem solving.

    Both grading options. (Lecture 3 hrs.) Not open for credit to students with credit in MATH 123  or MATH 224 .

  • MATH 122 - Calculus I

    (4 units)

    Prerequisite: A grade of “C” or better in MATH 111  and either MATH 112B  or MATH 113 , or appropriate CSULB Algebra and Calculus Placement.
    Continuous functions. Derivatives and applications including graphing, related rates, and optimization. Transcendental functions. L’Hospital’s Rule. Antiderivatives. Definite integrals. Area under a curve.

    Both grading options. (Lecture 3 hrs., problem session 2 hrs.)

  • MATH 123 - Calculus II

    (4 units)

    Prerequisite: A grade of “C” or better in MATH 122 .
    Applications of the integral. Techniques of integration. Infinite series including convergence tests and Taylor series. Parametric equations. Polar coordinates. Introduces differential equations.

    Both grading options. (Lecture 3 hrs., problem session 2 hrs.) Not open for credit to students with credit in MATH 222.

  • MATH 224 - Calculus III

    (4 units)

    Prerequisite: A grade of “C” or better in MATH 123  or 222.
    Vectors and three-dimensional analytic geometry. Partial derivatives and Lagrange multipliers. Multiple integrals. Vector calculus, line and surface integrals. Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem.

    Both grading options. (Lecture 3 hrs., problem session 2 hrs.)

  • MATH 233 - Fundamental Concepts for Advanced Mathematics

    (3 units)

    Prerequisite: MATH 123  with a grade of “C” or better.
    Fundamentals of logic and set theory, counting principles, functions and relations, induction and recursion, introduction to probability, elementary number theory, congruences. Introduces writing proofs.

    Both grading options. (Lecture 3 hrs.)

  • MATH 247 - Introduction to Linear Algebra

    (3 units)

    Prerequisite: MATH 123 .
    Matrix algebra, solution of systems of equations, determinants, vector spaces including function spaces, inner product spaces, linear transformations, eigenvalues, eigenvectors, quadratic forms, and applications. Emphasis on computational methods.

    Both grading options. (Lecture 3 hrs.)

  • MATH 249 - Linear Algebra and Differential Equations

    (3 units)

    Prerequisite: MATH 123  with a grade of “C” or better. A course in computer programming is required with a grade of “C” or better.
    Elementary linear algebra and ordinary differential equations (ODEs): first and second order linear differential equations, linear systems of ODEs, phase portraits, graphical and numerical methods for differential equations. Matrix algebra, systems of linear equations, linear independence, determinants, eigenvalues and eigenvectors, Fourier and Laplace transforms. Implementation of algorithms in Matlab.

    Letter grade only (A-F) (Lecture 2 hours, laboratory/problem session 3 hours).

  • MATH 297 - Directed Study

    (1-6 units)

    Prerequisite: Consent of instructor.
    For students who wish to undertake special study, at the lower division level, which is not a part of any regular course, under the direction of a faculty member. Individual investigation, studies or surveys of selected problems.

    Both grading options.

  • MATH 303 - Reflections in Space and Time

    (3 units)

    Prerequisites: GE Foundation requirements, at least one GE Exploration course, upper-division standing.
    An experimentally-driven investigation of the mathematical nature of symmetry and patterns. Considers the pervasive appearance and deep significance of symmetry and patterns in art and science.

    Both grading options. (Lecture 3 hrs.)

  • MATH 304 - The Art of Mathematics

    (3 units)

    Prerequisites: Completion of GE Foundation requirement; at least one GE Explorations course; Completion of 60 units.
    Survey of mathematical ideas across time and cultures. Exploration of the nature of mathematics, mathematical thought, the work of mathematicians, and the relationship between culture and mathematics. Topics may include number, shape, relationships, data, measurement, and change.

    Letter Grade Only (A-F). Not repeatable for credit.

  • MATH 309 - Complexity and Emergence

    (3 units)

    Prerequisites: GE Foundation requirements, at least one GE Exploration course, upper-division standing.
    Introduction to complexity science. Qualitative and computational exploration of emergent properties in dynamical systems, fractals, algorithms, networks, self-organizing behavior and selected topics.

    Letter grade only (A-F)

  • MATH 310 - History of Early Mathematics

    (3 units)

    Prerequisite/Corequisite: At least one of MATH 224  or MATH 233  or MATH 247 .

    History of mathematics through seventeenth century, including arithmetic, geometry, algebra, and beginnings of calculus. Interconnections with other branches of mathematics. Writing component; strongly recommended students enrolling have completed the G.E. A2 requirement.

    Both grading options. (Lecture 3 hrs.)

  • MATH 323 - Introduction to Numerical Analysis

    (4 units)

    Prerequisites: MATH 224 , and a course in computer programming.
    Numerical solution of nonlinear equations, systems of linear equations, and ordinary differential equations. Interpolating polynomials, numerical differentiation, and numerical integration. Computer implementation of these methods.

    Both grading options. (Lecture-discussion 3 hrs., problem session 2 hrs.)

  • MATH 341 - Number Theory

    (3 units)

    Prerequisite: A grade of “C” or better in MATH 233 
    Divisibility, congruences, number theoretic functions, Diophantine equations, primitive roots, continued fractions. Writing proofs.

    Both grading options. (Lecture 3 hrs.)

  • MATH 347 - Linear Algebra

    (3 units)

    Prerequisites: MATH 233  and MATH 247 .
    In-depth study of linear transformations, vector spaces, inner product spaces, quadratic forms, similarity and the rational and Jordan canonical forms. Writing proofs.

    Both grading options. (Lecture 3 hrs.)

  • MATH 349 - Linear Algebra and Differential Equations for Engineers

    (3 units)

    Prerequisites: MATH 123  with a grade of “C” or better, and BME 201  with a grade of “C” or better.
    Matrix algebra, systems of linear equations, linear independence, determinants, eigenvalues and eigenvectors, singular value decompositions. Solution techniques for first and second order linear differential equations, linear systems of ODEs. Graphical and numerical methods for differential equations, Laplace and Fourier transforms. Implementation of algorithms in MATLAB.

    Letter grade only (A-F). (Lecture 3 hours).

  • MATH 355 - College Geometry

    (3 units)

    Prerequisite: A grade of “C” or better in MATH 247 .
    Euclidean geometry, geometric objects, isometry and similarity, transformations and symmetry, algebra and geometry of complex numbers, and topics in non-Euclidean geometry and the axioms of geometry. Writing proofs.

    Both grading options. (Lecture 3 hrs.)

  • MATH 361A - Introduction to Mathematical Analysis I

    (3 units)

    Prerequisites: MATH 224 , and MATH 233  or MATH 247 . Completion of GE Foundation requirements; at least one GE Explorations Course; Completion of 60 units.
    Rigorous study of calculus and its foundations. Structure of the real number system. Sequences and series of numbers. Limits, continuity and differentiability of functions of one real variable. Writing proofs.

    Both grading options. (Lecture 3 hrs.)

  • MATH 361B - Introduction to Mathematical Analysis II

    (3 units)

    Prerequisite: A grade of “C” or better in MATH 361A .
    Riemann integration. Topological properties of the real number line. Sequences of functions. Metric spaces. Introduction to calculus of several variables. Writing proofs.

    Both grading options. (Lecture 3 hrs.)

  • MATH 364A - Ordinary Differential Equations I

    (3 units)

    Prerequisites: MATH 224 .
    Prerequisite/Corequisite: MATH 247 .

    First order differential equations; undetermined coefficients and variation of parameters for second and higher order differential equations, series solution of second order linear differential equations; systems of linear differential equations; applications to science and engineering.

    Both grading options. (Lecture 3 hrs.)

  • MATH 364B - Ordinary Differential Equations II

    (3 units)

    Prerequisite: MATH 364A  or MATH 370A .
    Existence-uniqueness theorems; Laplace transforms; difference equations; nonlinear differential equations; stability, Sturm-Liouville theory; applications to science and engineering.

    Both grading options. (Lecture 3 hrs.)

  • MATH 370A - Applied Mathematics I

    (3 units)

    Prerequisite: A grade of “C” or better in MATH 123 . Excludes freshmen.
    First order ordinary differential equations, linear second order ordinary differential equations, numerical solution of initial value problems, Laplace transforms, matrix algebra, eigenvalues, eigenvectors, systems of differential equations, applications.

    Both grading options. (Lecture 3 hrs.) Not open for credit to mathematics majors.

  • MATH 370B - Applied Mathematics II

    (3 units)

    Prerequisite: MATH 364A  or MATH 370A 
    Arithmetic of complex numbers, functions of a complex variable, contour integration, residues, conformal mapping; Fourier series; separation of variables for partial differential equations. Applications.

    Both grading options. (Lecture 3 hrs.) Not open for credit to mathematics majors.

  • MATH 380 - Probability and Statistics

    (3 units)

    Prerequisite: MATH 224 .
    Frequency interpretation of probability. Axioms of probability theory. Discrete probability and combinatorics. Random variables. Distribution and density functions. Moment generating functions and moments. Sampling theory and limit theorems.

    Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to student with credit in STAT 380.

  • MATH 410 - History of Modern Mathematics

    (3 units)

    Prerequisites: MATH 247 , MATH 310  and at least three of the following: MATH 233 , MATH 341 , MATH 355 , MATH 361A , MATH 380 .
    History of mathematics from seventeenth century onward. Development of calculus, analysis, and geometry during this time period. Other topics discussed may include history of probability and statistics, algebra and number theory, logic, and foundations.

    Both grading options. (Lecture 3 hrs.)

  • MATH 423 - Intermediate Numerical Analysis

    (3 units)

    Prerequisites: MATH 247  and MATH 323 .
    Numerical solutions of systems of equations, calculation of eigenvalues and eigenvectors, approximation of functions, solution of partial differential equations. Computer implementation of these methods.

    Both grading options. (Lecture 3 hrs.)

  • MATH 444 - Introduction to Abstract Algebra

    (3 units)

    Prerequisites: MATH 233  and MATH 247  and a grade of “C” or better in at least one of MATH 341  or MATH 347 .
    Groups, subgroups, cyclic groups, symmetric groups, Lagrange’s theorem, quotient groups. Homomorphisms and isomorphisms of groups. Rings, integral domains, ideals, quotient rings, homomorphisms of rings. Fields. Writing proofs.

     

    Both grading options. (Lecture 3 hrs.) Not open for credit to students with credit in MATH 445.

  • MATH 445 - Abstract Algebra for Secondary Mathematics Teachers

    (3 units)

    Prerequisite(s): MATH 247  and a grade of “C” or better in MATH 341 .
    Algebraic structures including groups, rings, integral domains, fields, and quotient structures. Homomorphisms and isomorphisms. Writing proofs. Connections to the practice of teaching secondary mathematics are made throughout.

    Letter Grade Only (A-F). Lecture 3 hours Not repeatable for credit. Not open for credit to students with credit in MATH 444.

  • MATH 451 - Differential Geometry

    (3 units)

    Prerequisite: MATH 364A  or MATH 370A .
    Structure of curves and surfaces in space, including Frenet formulas of space curves; frame fields and connection forms; geometry of surfaces in Euclidean three space; Geodesics and connections with general theory of relativity.

    Both grading options. (Lecture 3 hrs.)

  • MATH 456 - Dynamics and Geometry of Chaos

    (3 units)

    Prerequisites: MATH 247 , MATH 361A , or consent of instructor.
    An introduction to discrete dynamical systems in one and two dimensions. Theory of iteration: attracting and repelling periodic points, symbolic dynamics, chaos, and bifurcation. May include a computer lab component.

    Both grading options. (Lecture 3 hrs)

  • MATH 461 - Introduction to Complex Analysis

    (3 units)

    Prerequisite: MATH 361A .
    Theory and applications of complex variables. Analytic functions, integrals, power series and applications.

    Both grading options. (Lecture 3 hrs.)

  • MATH 463 - Multivariable Calculus

    (3 units)

    Prerequisites: MATH 224 , MATH 247 , and MATH 361B .
    Topology of Euclidean spaces. Partial derivatives. Derivatives as linear transformations. Inverse and implicit function theorems. Jacobians, vector calculus, Green’s and Stokes’ theorems. Variational problems.

    Both grading options. (Lecture 3 hrs.)

  • MATH 470 - Introduction to Partial Differential Equations

    (3 units)

    Prerequisite: MATH 364A  or MATH 370A .
    First and second order equations, characteristics, Cauchy problems, elliptic, hyperbolic, and parabolic equations. Introduction to boundary and initial value problems and their applications.

    Both grading options. (Lecture 3 hrs.)

  • MATH 472 - Fourier Analysis

    (3 units)

    Prerequisite: MATH 364A  or MATH 370A .
    Theory of Fourier series and Fourier transforms. Physics and engineering applications. Parseval’s and Plancherel’s identities. Convolution. Multi-dimensional transforms and partial differential equations. Introduction to distributions. Discrete and fast Fourier transforms.

    Both grading options. (Lecture 3 hrs.)

  • MATH 473 - Scientific Computing

    (3 units)

    Prerequisites: MATH 323  and MATH 364A  or MATH 370A .
    Introduction to programming languages. Analysis and implementation of numerical algorithms for linear systems, linear and nonlinear regression, differentiation, integration, optimization and fast convolution using FFT. Basic algorithms for differential equations.

    Letter grade only (A-F).

  • MATH 474 - Mathematics of Financial Derivatives

    (3 units)

    Prerequisites: MATH 364A  or MATH 370A , MATH 380 , or consent of instructor.
    Options, futures, and other financial derivatives; arbitrage; riskneutral valuation; binomial trees; the log-normal hypothesis; the Black-Scholes-Merton formula and applications; the Black- Scholes-Merton partial differential equation; American options; exotic options; bond models and interest rate derivatives; credit risk and credit derivatives.

    Both grading options.

  • MATH 479 - Mathematical Modeling

    (3 units)

    Prerequisites: MATH 247 , MATH 323 ; MATH 364A  or MATH 370A ; and consent of instructor.
    Introduction to mathematical modeling in the applied sciences, including validation and practical use of various modeling methodologies. Mathematical models in physics, chemistry, biology, and other natural sciences. Applications of computational mathematics in computer science, engineering, finance, and related disciplines.

    Letter grade only (A-F).

  • MATH 485 - Mathematical Optimization

    (3 units)

    Prerequisites: MATH 247  and at least one of MATH 323 , MATH 347  or MATH 380 .
    Linear and nonlinear programming: simplex methods, duality theory, theory of graphs, Kuhn-Tucker theory, gradient methods and dynamic programming.

    Both grading options. (Lecture 3 hrs.)

  • MATH 491 - Honors Seminar in Problem Solving

    (1 unit)

    Prerequisite: Consent of instructor.
    Challenging problems from many fields of mathematics, taken largely from national and worldwide collegiate and secondary school competitions. Students required to participate in at least one national competition.

    Both grading options. (Lecture-discussion 1 hr.) May be repeated to a maximum of 3 units.

  • MATH 495 - Topics in Modern Mathematics

    (3 units)

    Prerequisite: Consent of instructor.
    Topics of current interest from mathematics literature.

    Both grading options.

  • MATH 496 - Special Problems

    (1-3 units)

    Prerequisite: Consent of instructor.
    Student investigations in mathematics, applied mathematics, mathematics education, or statistics. May include reports and reviews from the current literature, as well as original investigations.

    Letter grade only (A-F). May be repeated to a maximum of 3 units.

  • MATH 497 - Directed Studies

    (1-6 units)

    Prerequisites: Junior or senior standing and consent of instructor.
    Readings in areas of mutual interest to student and instructor which are not a part of any regular course.

    Both grading options. A written report or project may be required. May be repeated to a maximum of 6 units.

  • MATH 498H - Senior Thesis - Honors

    (3 units)

    Prerequisites: Admission to Honors in the Major in Mathematics or to the University Honors Program, and consent of instructor.
    Planning, preparation, completion, and oral presentation of a written thesis in mathematics, applied mathematics, mathematics education, or statistics.

    Letter grade only (A-F). Not available to graduate students.

  • MATH 520 - Finite Element Method

    (3 units)

    Prerequisite: MATH 323 , MATH 361A , MATH 364A . Recommended: MATH 470 .
    Variational forms and weak solutions of partial differential equations, Galerkin method, construction of elements, numerical algorithms for matrix equations and for one-dimensional and two-dimensional problems. Convergence analysis and error estimate. Numerical implementations of algorithms.

    Letter grade only (A-F). (Lecture 3 hrs.)

  • MATH 521 - Matrix Method in Data Analysis and Pattern Recognition

    (3 units)

    Prerequisite: MATH 423  or MATH 576 .
    Vector spaces and linear transformations, optimal orthogonal projections, eigenvalues, eigenvectors, SVD, generalized SVD, Fourier and wavelet transforms, convolution, tangent distance. Implementations include object recognition, handwritten digit classification, digital image processing, feature extraction, image deblurring, text mining.

    Letter grade only (A-F). (Lecture 3 hrs.)

  • MATH 540 - Elements of Abstract Algebra

    (3 units)

    Prerequisite: MATH 444 .
    Group theory including symmetric groups; group actions on sets; Sylow theorems and finitely generated abelian groups; ring theory including polynomial rings, division rings, Euclidean domains, principal ideal domains, and unique factorization domains.

    Letter grade only (A-F). (Lecture 3 hours).

  • MATH 545 - Topics in Abstract Algebra

    (3 units)

    Prerequisite: MATH 540 .
    Selected topics in algebra that build upon the material of MATH 540 . Content will vary by semester.

    Letter grade only (A-F). (Lecture 3 hours). May be taken for credit more than once with the consent of the graduate advisor. Repeatable up to 9 units.

  • MATH 550 - Elements of Topology

    (3 units)

    Prerequisite: MATH 361B .
    Fundamentals of point-set topology: metric spaces and topological spaces; bases and neighborhoods; continuous functions; subspaces, product spaces and quotient spaces; separation properties, countability properties; compactness, compactification; connectedness; convergence of sequences; other topics, such as nets, filters and metrizability, as time permits.

    Letter grade only (A-F). (Lecture 3 hours).

  • MATH 555 - Topics in Topology

    (3 units)

    Prerequisite: MATH 550 .
    Selected topics in topology that build upon the material of MATH 550 . Content will vary by semester.

    Letter grade only (A-F). (Lecture 3 hours). May be taken for credit more than once with the consent of the graduate advisor

  • MATH 560 - Functional Analysis

    (3 units)

    Prerequisites: MATH 247 , MATH 361B .
    Linear spaces, metric and topological spaces, normed linear spaces; four principles of functional analysis: Hahn-Banach, Open Mapping, Uniform Boundedness, and Closed Graph theorems; adjoint spaces; normed space convergence, conjugate spaces, and operator spaces; Banach Fixed Point theorem; Hilbert spaces.

    Letter grade only (A-F). (Lecture 3 hours).

  • MATH 561 - Elements of Real Analysis

    (3 units)

    Prerequisite: MATH 361B .
    Theory of measure and integration, focusing on the Lebesgue integral on Euclidean space, particularly the real line. Modes of convergence. Fatou’s Lemma, the monotone convergence theorem and the dominated convergence theorem. Fubini’s theorem.

    Letter grade only (A-F). (Lecture 3 hours)

  • MATH 562 - Elements of Complex Analysis

    (3 units)

    Prerequisite: MATH 361B .
    Axiomatic development of real and complex numbers; elements of point set theory; differentiation and analytic functions, classical integral theorems; Taylor’s series, singularities, Laurent series, calculus of residues.

    Letter grade only (A-F). (Lecture 3 hours).

  • MATH 563 - Applied Analysis

    (3 units)

    Prerequisites: MATH 361B  and either MATH 364A  or MATH 370A .
    Hilbert Spaces, Lp spaces, Distributions, Fourier Transforms, and applications to differential and integral equations from physics and engineering.

    Letter grade only (A-F). (Lecture 3 hrs.)

  • MATH 564 - Applied Nonlinear Ordinary Differential Equations

    (3 units)

    Prerequisites: MATH 361B ; MATH 364A  or MATH 370A .
    Stability and asymptotic analysis, Perturbation methods, Phase plane analysis, Bifurcation, Chaos, Applications to science and engineering.

    Both grading options. (Lecture 3 hrs.)

  • MATH 565 - Topics in Real Analysis

    (3 units)

    Prerequisite: MATH 561 .
    Selected topics in real analysis that build upon the material of MATH 561 . Content will vary by semester.

    Letter grade only (A-F). (Lecture 3 hours). May be taken for credit more than once with the consent of the graduate advisor

  • MATH 566 - Topics in Complex Analysis

    (3 units)

    Prerequisite: MATH 562 .
    Selected topics in real analysis that build upon the material of MATH 562 . Content will vary by semester.

    Letter grade only (A-F). (Lecture 3 hours). May be taken for credit more than once with the consent of the graduate advisor

  • MATH 570 - Partial Differential Equations

    (3 units)

    Prerequisites: MATH 364A  and MATH 463 .
    Cauchy’s problem; classification of second order equations; methods of solution of hyperbolic, parabolic, and elliptic equations.

    Letter grade only (A-F). (Lecture 3 hrs.)

  • MATH 573 - Advanced Scientific Computing

    (3 units)

    Prerequisites: MATH 323  and MATH 364A  or MATH 370A .
    Analysis and implementation of numerical algorithms for linear systems, linear and nonlinear regression, differentiation, integration, optimization and fast convolution using FFT. Numerical solutions for differential equations.

    Letter grade only (A-F).

  • MATH 574 - Stochastic Calculus and Applications

    (3 units)

    Prerequisites: MATH 361B , MATH 364A  or MATH 370A , MATH 380 .
    Review of probability theory. Markov processes. Wiener processes. Stochastic integrals. Stochastic differential equations. Applications to Finance and Engineering.

    Both grading options. (Lecture 3 hrs.)

  • MATH 575 - Calculus of Variations

    (3 units)

    Prerequisites: MATH 361B  and either MATH 364A  or MATH 370A 
    Solution methods for variational problems. First variation, Euler- Lagrange equation, variational principles, problems with constraints, boundary conditions, applications to physics and geometry. May include multiple integral problems, eigenvalue problems, convexity, and second variation.

    Letter grade only (A-F). (Lecture 3 hrs.)

  • MATH 576 - Numerical Analysis

    (3 units)

    Prerequisites: MATH 323 , MATH 361B , MATH 364A .
    Advanced numerical methods. Introduction to error analysis, convergence, and stability of numerical algorithms. Topics may include solution of ordinary differential equations, partial differential equations, systems of linear and nonlinear equations, and optimization theory.

    Letter grade only (A-F). (Lecture 3 hrs.)

  • MATH 577 - Numerical Solution of Partial Differential Equations

    (3 units)

    Prerequisite: MATH 423  or MATH 576  or consent of instructor.
    Finite difference methods solving hyperbolic, parabolic, elliptic PDE’S; accuracy, convergence, and stability analysis. Selected initial-value boundary-value problems, characteristics, domain of dependence, matrix and von Neumann’s methods of stability analysis. Solutions of large sparse linear systems. Finite element method.

    Both grading options. (Lecture 3 hrs.)

  • MATH 578 - Numerical Linear Algebra

    (3 units)

    Prerequisites: MATH 247  and MATH 323  or consent of instructor.
    Numerical solutions of linear systems, least squares problems, eigenvalue problems. Matrix factorization: LU, QR, SVD, iterative methods. Error analysis. Applications with attention to linear algebra problems arising in numerical solutions of partial differential equations. Numerical implementation of algorithms.

    Letter grade only (A-F). (Lecture 3 hrs.)

  • MATH 579 - Advanced Mathematical Modeling

    (3 units)

    Prerequisites: MATH 247 , MATH 323 ; MATH 364A  or MATH 370A ; one additional graduate level mathematics course, and consent of instructor.
    Application of mathematics to develop models of phenomena in science, engineering, business, and other disciplines. Evaluation of benefits and limitations of mathematical modeling.

    Letter grade only (A-F).

  • MATH 590 - Selected Topics in Mathematics

    (3 units)

    Prerequisite: Consent of Instructor
    Specialized and advanced topics in mathematics.

    Both grading options. (3 hours lecture) May be repeated to a maximum of 9 units in different or same semester.

  • MATH 680 - Topics in Ordinary Differential Equations

    (3 units)

    Prerequisite: MATH 564  and Consent of Instructor.
    Selected topics in Ordinary Differential Equations that build upon the material of MATH 564. Content will vary by semester. Written report and oral presentation required.

    Letter grade only (A-F).

  • MATH 681 - Topics in Partial Differential Equations

    (3 units)

    Prerequisites: MATH 570  and Consent of Instructor.
    Selected topics in Partial Differential Equations that build upon the material of MATH 570. Content will vary by semester. Written report and oral presentation required.

    Letter grade only (A-F).

  • MATH 682 - Topics in Numerical Analysis

    (3 units)

    Prerequisites: MATH 576  and Consent of Instructor.
    Selected topics in Numerical Analysis that build upon the material of MATH 576. Content will vary by semester. Written report and oral presentation required.

    Letter grade only (A-F).

  • MATH 695 - Seminar in Mathematics

    (3 units)

    Prerequisite: Consent of instructor.
    Presentation and discussion of advanced work, including original research by faculty and students. Topics announced in the Schedule of Classes.

    Letter grade only (A-F). May be repeated to a maximum of 6 units.

  • MATH 697 - Directed Studies

    (1-6 units)

    Prerequisite: Consent of instructor.
    Research on a specific area in mathematics. Topics for study to be approved and directed by faculty advisor in the Department of Mathematics and Statistics.

    Letter grade only (A-F).

  • MATH 698 - Thesis or Project

    (1-6 units)

    Prerequisite: Advancement to candidacy.
    Formal report of research or project in mathematics.

    Letter grade only (A-F). May be repeated to a maximum of six units.

Mathematics Education

  • MTED 90 - Foundations for Exploring the Real Number System

    (1 unit)

    Corequisite: MTED 110 .
    Topics and skills that support student success in MTED 110. This course is designed as a co-requisite course and should only be taken with MTED 110. Students required to enroll in this co-requisite course must remain enrolled in both courses for the semester. Students will not be permitted to withdraw from one of the courses (either MTED 90 or MTED 110) and not the other.

    Credit/ No-Credit option (Activity 2 hours). May be repeated to a maximum of 2 units in different semesters.

  • MTED 110 - The Real Number System for Elementary and Middle School Teachers

    (3 units)

    Prerequisite(s)/Corequisite(s): Appropriate CSU Multiple Measures placement or concurrent enrollment in MTED 90 .

    Introduction to problem solving processes and strategies. Development and analysis of structure, properties, and operations of real number system. Concept and process development using appropriate models, manipulatives, and activities.

    Both grading options. (Lecture 2 hrs., activity 2 hrs.) Not open for credit to Mathematics majors.

  • MTED 205 - Activity Based Probability and Statistics for Elementary and Middle School Teachers

    (3 units)

    Prerequisites: MAPB 11  and MTED 110 .
    Activity-based exploration of randomization, data representation, measures of central tendency and dispersion. Analysis of experiments requiring hypothesizing, experimental design and data gathering. Basic laws of probability and set theory, combinations, permutations, and simulations.

    Letter grade only (A-F). (Lecture 2 hrs., activity 2 hrs.) Not open for credit to mathematics (all options) and statistics majors or for students with credit in MTED 105.

  • MTED 211 - Geometry and Measurement for Elementary Teachers

    (3 units)

    Prerequisites: MTED 110  with a grade of “C” or better and one year of high school geometry.
    Problem solving and hands-on modeling of real-world geometry situations focusing on patterning, informal geometry, congruence, similarity, constructions, transformations, tessellations, measurement in 1, 2, and 3 dimensions (English and Metric units). Computer applications are integrated into the course.

    Both grading options. (Lecture 2 hrs., activity 2 hrs.) Not open for credit to Mathematics majors or any student with credit in MTED 312 .

  • MTED 301 - Computer Applications in Mathematics for Teachers

    (3 units)

    Prerequisite(s)/Corequisite(s): MTED 110  or MATH 122  or EDSS 300A-S  (M) or concurrent enrollment in EDSS 300A-S  (M)

    Designed for pre-service or inservice teachers. Software evaluation; teacher tools (spreadsheets, databases, email, collaborative tools, and applications); mathematics using technology; programming; technology use issues in schools. Satisfies California Level I teaching credential computer technology standard.

    Both grading options. (Lecture 2 hrs., activity 2 hrs.) Open for credit to pre-service or in-service teaching credential students only.

  • MTED 305 - Algebraic and Statistical Thinking for Elementary and Middle School Teachers

    (3 units)

    Prerequisite: “C” or better in MTED 110  
    Algebraic, statistical, and probabilistic thinking and content relevant to teaching K-8 mathematics. Topics include conceptual development of equations, inequalities, and functions; data visualization, descriptive statistics, experimental design, simulation, and probability

    Letter grade only (A-F). (Lecture 2 hours, activity 3 hours).

  • MTED 312 - Geometry and Measurement for Mathematics Specialists in Elementary and Middle Schools

    (4 units)

    Prerequisites: “C” or better in MTED 110  
    Exploration, conjecture, justification of geometric relationships, applications relevant to teaching geometry (K-10). Problem solving, informal geometry, proof, non-Euclidean geometry, congruency, similarity, constructions, transformations, tessellations, measurement (English and Metric) in 1, 2 , and 3 dimensions. Computer construction utility used.

    Letter grade only (AF). (Lecture 2 hrs., activity 2 hrs.) Not open for credit to Mathematics majors.

  • MTED 371 - Mathematical Modeling for Secondary Mathematics Teachers

    (3 units)

    Prerequisites: MATH 224 , MATH 233 , MATH 247  
    Introduction to the mathematical modeling cycle and its implementation in the secondary school curriculum. Connections to the practice of teaching single subject mathematics are made throughout.

    Both grading options. (Lecture 2 hrs., activity 2 hrs.).

  • MTED 402 - Problem Solving Applications in Mathematics for Elementary and Middle School Teachers

    (3 units)

    Prerequisite(s):  ”C” or better in MTED 110  , “C” or better in either MTED 205   or MTED 305  , and “C” or better in either MTED 211   or MTED 312  .
    Problem solving processes and strategies; interrelates and applies content from many mathematics areas (real number system, algebra, number theory, geometry, measurement, probability and statistics); develops questioning strategies, fostering understanding of algebra and geometry. Technology integrated throughout.

    Both grading options. (Lecture 2 hrs., activity 2 hrs.) Not open for credit to Mathematics majors.

  • MTED 411 - Topics and Issues in Secondary School Mathematics

    (3 units)

    Prerequisites: MATH 310 , MATH 341 , MATH 355 , MATH 380 , MTED 371 , and EDSS 300A-S  (choose M). 
    Prerequisite or Corequisite: MATH 444  or MATH 445.

    Analysis of topics and issues in secondary school mathematics curriculum. Problem solving, mathematical connections, communication, structures, conjecture, proof, manipulatives, technology, assessment. Observations/interview experiences and portfolio assemblage required. Intended for students preparing to enter Single Subject Credential Program in mathematics.

    Both grading options. (Lecture 2 hrs., laboratory 3 hrs.)

  • MTED 424 - Algebraic Structures for Elementary and Middle School Teachers

    (4 units)

    Prerequisite: MTED 312  with a grade of “C” or better.
    Properties of real and complex numbers, groups, rings, reals and complex fields; polynomial equations and inequalities; polynomial, rational, radical, absolute value, exponential, and logarithmic functions; matrices and vectors.

    Letter grade only (A-F). (Lecture 2 hrs; activity 2 hrs.) Not open for credit to mathematics (all options) or statistics majors or for students with credit in MATH 444  or MTED 324.

  • MTED 425 - Functions, Models and Concepts of Calculus for Elementary and Middle School Teachers

    (4 units)

    Prerequisite: MTED 312  with a grade of “C” or better.
    Numeric, symbolic, graphical, verbal representation of functions; sequences and sums. Intuitive development of concepts of limit, continuity, derivative, integral. Applications, including differential equations. Algebraic methods and technology emphasized in context of learning calculus. Not open for credit to mathematics (all options) or statistics majors or for students with credit in MTED 325.

    Letter grade only (A-F).

  • MTED 495 - Special Topics in Mathematics Education

    (1-3 units)

    Prerequisite: Consent of instructor.
    Topics of interest in Mathematics Education.

    Letter grade only (A-F). May be repeated to a maximum of 9 units with different topics in different semesters.

  • MTED 500 - Advanced Perspectives of Concepts Foundational to Algebra for Teachers

    (3 units)

    Prerequisite: Multiple Subjects Credential, or consent of instructor.
    Analytic investigation of foundational algebra concepts using representations, reasoning and proof, and problem solving. Topics include: number theory, properties of real numbers, proportional reasoning, algebra, discrete mathematics, and functions.

    Letter grade only (A-F). (Lecture 3 hrs). This course will not count toward any M.S. degree options in the Department of Mathematics and Statistics.
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