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- University Programs

- Undergraduate Degree Roadmaps

Satisfying the Entry-Level Math (ELM) requirement (see “Undergraduate Programs” section of this Catalog) is a prerequisite for all mathematics courses and mathematics education courses. Please contact the ELM Coordinator in the Department of Mathematics and Statistics for details regarding the ELM test score.

Prerequisite: Appropriate ELM score, ELM exemption, or MAPB 7 or 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.

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

Prerequisite: Appropriate ELM score, ELM exemption, or MAPB 7 or 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.

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

Prerequisite: Appropriate ELM score, ELM exemption, or MAPB 11.

Trigonometric functions and applications. Arithmetic and graphical representation of complex numbers, polar form, DeMoivre’s Theorem.

Not open for credit to students with credit in MATH 101, 117 or 122. (Lecture 3 hrs.)

Prerequisite: Appropriate ELM score, ELM exemption, or MAPB 11.

Equations, inequalities. Functions, their graphs, inverses, transformations. Polynomial, rational functions, theory of equations. Exponential, logarithmic functions, modeling. Systems of equations, matrices, determinants. Sequences, series.

Not open for credit to students with credit in MATH 112, 115, 117, 119A, 120, or 122. For students who will continue to MATH 115, 117, 119A, 120, or 122. (Lecture 3 hrs.)

Prerequisite: Appropriate ELM score, ELM exemption, or MAPB 11.

Combinatorial techniques and introduction to probability. Equations of lines and systems of linear equations, matrices, introduction to linear programming.

Not open for credit to students with credit in MATH 233 or 380. (Lecture 3 hrs.)

Prerequisite: Appropriate ELM score, ELM exemption, or MAPB 11.

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. Not open for credit to students with credit in MATH 119A, 120, or 122.

(Lecture 3 hrs, activity 1 hr)

Prerequisite: Appropriate MDPT placement or a grade of “C” or better in MAPB 11.

Polynomial, rational, exponential, logarithmic, and trigonometric functions. Complex numbers, conic sections, graphing techniques.

Not open for credit to students with credit in MATH 122. (Lecture 3 hrs., problem session 2 hrs.)

Prerequisite: Appropriate MDPT placement or a grade of “C” or better in MATH 113.

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.

Not open for credit to students with credit in MATH 115, 120 or 122. (Lecture 3 hrs.)

Prerequisite: MATH 119A or 122.

Functions of several variable, 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.

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

Prerequisite: Appropriate MDPT placement or a grade of “C” or better in MATH 113.

Real and complex numbers and functions; limits and continuity; differentiation and integration of functions of one variable. Introduces calculus of several variables. Science and technology applications.

Not open for credit to students with credit in MATH 122. (Lecture 3 hrs., problem session 2 hrs.)

Prerequisite: Appropriate MDPT placement or a grade of "C" or better in MATH 111 and 113, or a grade of "C" or better in MATH 117.

Continuous functions. Derivatives and applications including graphing, related rates, and optimization. Transcendental functions. L'Hospital's Rule. Antiderivatives. Definite integrals. Area under a curve.

(Lecture 3 hrs., problem session 2 hrs.)

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.

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

Prerequisite: A grade of “C” or better in MATH 122.

Integration by parts and by partial fractions. Numerical integration. Improper integrals. Infinite series including series convergence tests and Taylor series. Vectors. Partial derivatives and directional derivatives. Double integrals. Introduces differential equations.

Enrollment restricted to CECS majors. Not open for credit to students with credit in MATH 123. Letter grade only (A-F). (Lecture 3 hrs., activity 2 hrs.)

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.

(Lecture 3 hrs., problem session 2 hrs.)

Prerequisite: A grade of “C” or better in MATH 123 or 222.

Fundamentals of logic and set theory, counting principles, functions and relations, induction and recursion, introduction to probability, elementary number theory, congruences. Introduces writing proofs.

(Lecture 3 hrs.)

Prerequisite: MATH 123 or 222.

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.

(Lecture 3 hrs.)

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.

Prerequisites: GE foundation, at least one GE Explorations 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.

(Lecture 3 hrs.)

Prerequisite/Corequisite: completion of, or concurrent enrollment in a 200-level mathematics course.

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. A.1 requirement.

(Lecture 3 hrs.)

Prerequisites: MATH 222 or 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.

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

Prerequisites: MATH 123 or 222, and at least one of MATH 233, 247, 310; recommended, MATH 233 or 247.

Divisibility, congruences, number theoretic functions, Diophantine equations, primitive roots, continued fractions. Writing proofs.

(Lecture 3 hrs.)

Prerequisites: MATH 233 and 247.

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

(Lecture 3 hrs.)

Prerequisite: MATH 247.

Transformations, motions, similarities, geometric objects, congruent figures, axioms of geometry and additional topics in Euclidean and non-Euclidean geometry. Writing proofs.

(Lecture 3 hrs.)

Prerequisites: MATH 222 or 224, and MATH 233 or 247.

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.

(Lecture 3 hrs.)

Prerequisite: MATH 361A.

Riemann integration. Topological properties of the real number line. Sequences of functions. Metric spaces. Introduction to calculus of several variables. Writing proofs.

(Lecture 3 hrs.)

Prerequisites: MATH 222 or 224, and prerequisite or 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.

(Lecture 3 hrs.)

Prerequisite: MATH 364A or 370A.

Existence-uniqueness theorems; Laplace transforms; difference equations; nonlinear differential equations; stability, Sturm-Liouville theory; applications to science and engineering.

(Lecture 3 hrs.)

Prerequisite/Corequisite: MATH 224.

First order ordinary differential equations, linear second order ordinary differential equations, numerical solution of initial value problems, Laplace transforms, matrix algebra, eigenvalues, eigenvectors, applications.

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

Prerequisite: MATH 370A.

Arithmetic of complex numbers, functions of a complex variable, contour integration, residues, conformal mapping; Fourier series, Fourier transforms; separation of variables for partial differential equations. Applications.

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

Prerequisite: MATH 222 or 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.) Same course as STAT 380. Not open for credit to student with credit in STAT 380.

Prerequisite: Senior or graduate standing.

The nature and expectations of doctoral programs in Mathematics and related fields. Intensive preparation for GRE mathematics subject exams.

Credit/No Credit grading only. Does not satisfy Mathematics major requirements. (Lecture-discussion 1 hr.)

Prerequisites: MATH 247, 310 and at least three of the following: MATH 233, 341, 355, 361A, 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.

(Lecture 3 hrs.)

Prerequisites: MATH 247 and 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.

(Lecture 3 hrs.)

Prerequisites: MATH 233 and 247 and at least one of MATH 341 or 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.

Not open for credit to students with credit in MATH 444A. (Lecture 3 hrs.)

Prerequisite: MATH 364A or 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.

(Lecture 3 hrs.)

Prerequisites: MATH 247, 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.

(Lecture 3 hrs)

Prerequisite: MATH 361A.

Theory and applications of complex variables. Analytic functions, integrals, power series and applications.

Not open for credit to students with credit in MATH 562A. (Lecture 3 hrs.)

Prerequisites: MATH 224, 247, and 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.

(Lecture 3 hrs.)

Prerequisite: MATH 370A or 364A.

First and second order equations, characteristics, Cauchy problems, elliptic, hyperbolic, and parabolic equations. Introduction to boundary and initial value problems and their applications.

(Lecture 3 hrs.)

Prerequisite: MATH 364A or 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.

(Lecture 3 hrs.)

Prerequisites: MATH 323 and either 364A or 370A. (Undergraduates register in MATH 473; graduates in MATH 573.)

Introduction to programming languages, implementations of numerical alogorithms for solution of linear algebraic equations, interpolation and extrapolation, integration and evaluation of functions, root finding and nonlinear equations, fast Fourier transforms, minimization and maximization of functions, numerical solutions of differential equations.

Not open for credit to students with credit in MATH 573.

Prerequisites: MATH 364A or MATH370A, MATH 380, or consent of instructor.

Options, futures, and other financial derivatives; arbitrage; risk-neutral 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.

Prerequisites: MATH 247, 364A or 370A, 323, and one additional mathematics course, or consent of instructor. (Undergraduates register in MATH 479; graduates in MATH 579.)

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). (Lecture 3 hrs.)

Prerequisites: MATH 247 and at least one of MATH 323, 347 or 380.

Linear and nonlinear programming: simplex methods, duality theory, theory of graphs, Kuhn-Tucker theory, gradient methods and dynamic programming.

(Lecture 3 hrs.)

Prerequisite: Consent of instructor.

Challenging problems form 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.

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

Prerequisite: Consent of instructor.

Topics of current interest from mathematics literature.

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.

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

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. A written report or project may be required.

May be repeated to a maximum of 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.

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

Prerequisite: MATH 323, 361A and 364A. MATH 470 is recommended but not required.

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.)

Prerequisite: MATH 423 or 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.)

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 hrs.)

Prerequisite: MATH 540A.

Modules; Field extensions; Finite fields; Splitting fields, Galois theory. Commutative ring theory including chain conditions and primary ideals. Topics of current interest.

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

Prerequisites: MATH 341, 444, and consent of instructor; MATH 461 and 540A are recommended but not required.

Fermat’s method of descent; finite fields; Weierstrass normal form; integer, rational points on elliptic curves; group structures of rational points; Mordell’s Theorem; computation examples. May include congruent numbers, Certicom’s public cryptography challenges, Lenstra’s factorization method, Birch/Swinnerton-Dyer Conjecture

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

Prerequisite: MATH 540A or consent of instructor.

An introduction to algebraic geometry: Algebraic sets; affine and projective varieties. Additional topics at the discredtion of the instructor may include: Algebraic Curves; Intersection Theory; Invariant Theory; Computational Approaches.

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

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, connectedness; convergence of sequences, nets and filters.

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

Prerequisite: MATH 550A.

Further topics in point-set topology: local compactness, paracompactness, compactifications; metrizability; Baire category theorem; homotopy and the fundamental group. Topics may also include uniform spaces, function spaces, topological groups or topics from algebraic topology.

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

Prerequisites: MATH 247, 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 hrs.)

Prerequisite: MATH 560A or consent of instructor.

Spectral theory of operators on normed spaces; special operators; elementary theory of Banach algebras; selected topics from applied functional analysis.

(Lecture 3 hrs.)

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 hrs.)

Prerequisite: MATH 561A or consent of instructor.

Lp spaces of functions. Holder’s inequality. Minkowski’s inequality. Norm convergence, weak convergence and duality in Lp. Further topics from convergence of Fourier series, measure-theoretic probability, the Radon-Nikodym theorem; other topics depending on time and interest.

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

Prerequisite: MATH 361B. (MATH 461 is recommended.)

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 hrs.)

Prerequisite: MATH 562A.

Multiple-valued functions, Riemann surfaces; analytic continuation; maximum modulus theorem; conformal mapping with applications, integral functions; gamma function, zeta function, special functions.

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

Prerequisites: MATH 361B and either 364A or 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.)

Prerequisites: MATH 361B; 364A or 370A.

Stability and asymptotic analysis, Perturbation methods, Phase plane analysis, Bifurcation, Chaos, Applications to science and engineering.

(Lecture 3 hrs.)

Prerequisites: MATH 364A and 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.)

Prerequisites: MATH 323 and either 364A or 370A. (Undergraduates register in MATH 473; graduates in MATH 573.)

Introduction to programming languages, implementations of numerical algorithms for solution of linear algebraic equations, interpolation and extrapolation, integration and evaluation of functions, root finding and nonlinear equations, fast Fourier transforms, minimization and maximization of functions, numerical solutions of differential equations.

Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 473.

Prerequisites: MATH 361B, 364A or 370A, 380.

Review of probability theory. Markov processes. Wiener processes. Stochastic integrals. Stochastic differential equations. Applications to Finance and Engineering.

(Lecture 3 hrs.)

Prerequisites: MATH 361B and either 364A or 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.)

Prerequisites: MATH 323, 361B, 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.)

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.

(Lecture 3 hrs.)

Prerequisites: MATH 247 and 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.)

Prerequisites: MATH 247, 364A or 370A, 323, and one additional upper-division mathematics course, or consent of instructor. (Undergraduates register in MATH 479; graduates in MATH 579.)

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). (Lecture 3 hrs.)

Prerequisite: Consent of instructor.

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

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

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).

Prerequisite: Advancement to candidacy.

Formal report of research or project in mathematics.

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