## Courses

*(This list of courses may not be up to date. Please see the latest General Catalog for a complete list of current courses.)*

**MATH 033. Elements of Calculus (4)** Polynomial, rational, exponential and logarithmic functions. Differentiation. Integration. Maxima/minima of functions of several variables. Elementary differential equations. Applications to natural sciences, social sciences and other fields. Credit will not be given for this course if a student has received credit for MATH 051 or AP credit in Calculus. Prerequisites: two years of high school algebra and an appropriate score on either the Intermediate Algebra placement test or the Pre-Calculus placement test; or MATH 005 or 041.

**MATH 035. Elementary Statistical Inference (4)** Emphasis is on the applications and limitations of statistical methods of inference, especially in the social and behavioral sciences. Topics include: estimation and test of hypothesis concerning a single group, One-way Analysis of Variance and analysis of categorical data. Use of statistical computer programs. Credit will not be given for this course if a student has received credit for MATH 037 or has AP credit in Statistics. Prerequisite: MATH 003, 005, or 041, or an appropriate score on either the Elementary Algebra placement test, the Intermediate Algebra Placement test, or the Pre-calculus placement test or permission of the instructor.

**MATH 037. Introduction to Statistics and Probability (4)** Elements of descriptive statistics: graphs, tables, measures of central tendency and dispersion. Probability models including binomial and normal. Introduction to estimation, hypothesis testing and analysis of variance. Linear and multiple regression and correlation. Use of statistical computer programs. The course is not recommended for first semester freshmen. Credit will not be given for this course if a student has received credit for MATH 035 or has AP credit in Statistics. Prerequisite: MATH 033, 041, 045, 051, 053 or appropriate score on the calculus placement test.

**MATH 039. Probability with Applications to Statistics (4)** Probability concepts in discrete and continuous spaces will be explored in some depth as well as important probability models (e.g., binomial, Poisson, exponential, normal, etc.), mathematical expectation and generating functions. Applications to statistical inference including maximum likelihood, moment and least squares estimation, confidence intervals and hypothesis testing will be covered. Credit will not be given for both MATH 039 and MATH 131. Prerequisite: MATH 053.

**MATH 041. Pre-calculus (4)** The algebraic and trigonometric concepts which are necessary preparation for Calculus I. Topics include the real number system, algebraic, trigonometric, exponential and logarithmic functions. Emphasis is on the function concept; graphing functions; solving equations, inequalities and linear systems; and applied problems. Credit for this course will not be given if a student has AP Calculus credit. Prerequisites: MATH 005 or an appropriate score on either the Intermediate Algebra placement test, the Pre-calculus placement test or the calculus placement test.

**MATH 045. Introduction to Finite Mathematics and Calculus (4)** Systems of equations. Elements of matrix algebra. Elementary linear programming. Introduction to calculus. Applications to problems in economics, management and other fields. Prerequisites: two years of high school algebra and an appropriate score on either the Intermediate Algebra placement test, the Pre-calculus placement test, or the calculus placement test; or MATH 005 or 041.

**MATH 049. Introduction to Abstract Mathematics (4)** An introduction to the spirit and rigor of mathematics. Course content may vary with instructor, but the objective is to develop the skills required to read and write mathematics and prove theorems. Concepts: elementary logic, sets and functions, cardinality, direct and indirect proofs, mathematical induction. Prerequisite: MATH 053 or permission of the instructor.

**MATH 051. Calculus I (4)** Differential calculus of algebraic and elementary transcendental functions. Anti-derivatives, introductory definite integrals, and the Fundamental Theory of Calculus. Applications, including the first and second derivative tests and optimization. Students earning AP A/B Calculus credit will not receive credit for MATH 051. Prerequisites: MATH 007 or 041 or four years of high school mathematics including Trigonometry and an appropriate score on the placement test for calculus.

**MATH 053. Calculus II (4) **Techniques and applications of integration. Sequences and series. Convergence of series. Taylor Polynomials. Students earning AP B/C Calculus credit will not receive credit for MATH 053. Prerequisite: MATH 051 or an appropriate score on the calculus placement test.

**MATH 055. Calculus III (4)** An introduction to multivariable calculus. Topics covered include vector geometry of the plane and Euclidean 3-space; differential calculus of realvalued functions of several variables, including partial derivatives, gradient, max-min theory, quadric surfaces, multiple integrals. Prerequisite: MATH 053 or AP B/C credit.

**MATH 057. Applied Differential Equations I: ODES (4)** Ordinary differential equations, first-order equations, separable and linear equations. Direction fields. Second order linear equations with constant coefficients. Method of undetermined coefficients. Laplace Transforms. Unit impulse response and convolutions. Homogeneous systems of first order linear equations. Matrix algebra determinants, eigenvalues, eigenvectors. Existence and uniqueness theorems. Use of calculators or computers to display solutions. Applications. Prerequisite: MATH 055 or permission of the instructor.

**MATH 072. Operations Research Models (4)** Operations Research (OR) is concerned with scientific design and operation of systems which involve the allocation of scarce resources. This course will survey some of the quantitative techniques used in OR. Linear Programs will be solved using graphical techniques and the simplex algorithm. Among the other models studied will be the transportation, assignment, matching, and knapsack problems. Prerequisite: MATH 033 or 045 or 051 or the appropriate score on the calculus placement test.

**MATH 074. Discrete and Combinatorial Mathematics (4)** The fundamental principles of discrete and combinatorial mathematics. Topics include the fundamental principles of counting, the Binomial Theorem, generating functions, recurrence relations and introductory graph theory, including trees and connectivity. Prerequisite: MATH 033 or 045 or 051, or an appropriate score on the calculus placement test.

**MATH 075. Introduction to Linear Algebra (4)** Linear algebra is the generalized study of solutions to systems of linear equations. The study of such systems dates back over 2000 years and now is foundational in the design of computational algorithms for many modern applications. This course will serve as an introduction to basic computational tools in linear algebra including the algebra and geometry of vectors, solutions to systems of linear equations, matrix algebra, linear transformations, determinants, eigenvalue-eigenvector problems, and orthogonal bases. Prerequisite: C- or higher in MATH 051.

**MATH 089a, 189a. Statistical Consulting Practicum (2)** While working under close faculty supervision, students will gain valuable practical experience in applying statistical methods to problems presented by University researchers, business and industry. Students enrolled in MATH 189a will ordinarily participate in more sophisticated projects and take a more responsible role than students in MATH 089a. Pass/No credit. Prerequisites: for MATH 089a, MATH 130 or permission of the instructor; for MATH 189a, 089a and permission of the instructor.

**MATH 110. Numerical Analysis (4)** Numerical analysis deals with approximation of solutions to problems arising from the use of mathematics. The course begins with a necessary but brief discussion of floating point arithmetic, and then proceeds to discuss the computer solution of linear algebraic systems by elimination and iterative methods, the algebraic eigenvalue problem, interpolation, numerical integration, including a discussion of adaptive quadrature, the computation of roots of nonlinear equations and the numerical solution of initial value problems in ordinary differential equations. Prerequisite: MATH 055.

**MATH 130. Topics in Applied Statistics (3)** This course covers topics in applied statistics not normally covered in an introductory course, including multiple regression and correlation, analysis of variance of one- and two-way designs; other topics selected from nonparametric methods, time series analysis, discriminant analysis, factor analysis, depending upon student interest. Extensive use of packaged computer programs. Prerequisite: MATH 035 or 037.

**MATH 131. Probability and Mathematical Statistics I (4)** Counting techniques; discrete and continuous random variables; distribution functions; special probability densities such as Binomial, Hpergeometric, Geometric, Negative Binomial, Poisson, Uniform, Gamma, Exponential, Weibull, and Normal; joint distributions; marginal and conditional distributions; mathematical expectations, moment generating functions; functions of random variables; sampling distribution of the mean; Central Limit Theorem. Credit will not be given for both MATH 039 and MATH 131. Prerequisite: MATH 053.

**MATH 132. Probability and Mathematical Statistics II (4)** Sampling distributions such as Chi-square, t and F; estimation methods such as methods of moments, maximum likelihood, least squares; properties of estimators such as unbiasedness, consistency, sufficiency; tests of hypothesis concerning means, difference between means, variances, proportions; one and two-way analysis of variance. Prerequisite: MATH 131.

**MATH 141. Linear Algebra (4)** Fundamental linear algebra concepts from an abstract viewpoint, with the objective of learning the theory and writing proofs. Concepts include: vector spaces, bases, linear transformations, matrices, invertibility, eigenvalues, eigenvectors, invariant subspaces, inner product spaces, orthogonality, and the spectral theorem. * *Prerequisites: MATH 049 and MATH 075.

**MATH 143. Abstract Algebra I (4)** An introduction to groups, rings and fields, with an emphasis on number theory and group theory: including, finite groups, permutation groups, cyclic groups, factor groups, homomorphisms, and the isomorphic theorem. The course concludes with an introduction to polynomial rings. Prerequisite: MATH 049 or permission of instructor.

**MATH 144. Abstract Algebra II (4)** This course is a continuation of MATH 143; it emphasizes field theory and the application of groups to geometry and field extensions. Algebraic and separable field extensions, dimension, splitting fields, Galois theory, solvability by radicals, geometric constructions. Prerequisite: MATH 143 or permission of instructor.

**MATH 145. Applied Linear Algebra (4)** This is a second semester course in linear algebra with an emphasis on the theory and application of matrix decompositions. Topics include methods for solving systems of equations, QR factorization, the method of least squares, diagonalization of symmetric matrices, singular value decomposition, and applications. Prerequisites: C- or better in Math 53 and Math 75.

**MATH 148. Cryptography (3)** A survey of cryptography and cryptanalysis from historical cryptosystems through the modern use of cryptology in computing. Topics include public and symmetric key cryptosystems, digital signatures, modular arithmetic and other topics in number theory and algebra. Possible additional topics include error correcting codes, digital cash, and secret sharing techniques. Prerequisites: MATH 053 or permission of the instructor.

**MATH 152. Vector Analysis (4)** Vector analysis and related topics for students of applied mathematics, physics and engineering. Vector fields, Gradient, divergence and curl. Parametric surfaces. Line integrals; surface integrals; integral theorems. Formulations of vector analysis in cylindrical and spherical coordinates. Prerequisite: MATH 055.

**MATH 154. Topology (4)** An introduction to general topology and its relation to manifold theory. Topics include metric spaces, general spaces, continuous functions, homeomorphisms, the separation axioms, connectedness, compactness, and product spaces. Prerequisite: MATH 049.

**MATH 155. Real Analysis I (4)** Properties of the real numbers. Sequences and series of real numbers. Limits, continuity and differentiability of real functions. Prerequisites: MATH 049 and 055.

**MATH 156. Real Analysis II (4)** Integration, series of real numbers, sequences and series of functions, and other topics in analysis. Prerequisite: MATH 155.

**MATH 157. Applied Differential Equations II: PDES (4)** Partial differential equations. Derivation and solutions of the Wave, Heat and Potential equations in two and three dimensions. Fourier series methods, Bessel functions and Legendre polynomials. Orthogonal functions. Additional topics may include Fourier integral transform methods, the Fast Fourier Transform and Sturm-Liouville theory. Computer exercises using MATLAB. Prerequisite: MATH 057.

**MATH 161. Elementary Concepts of Mathematics I (4)** Concepts of arithmetic and geometry underlying elementary school programs in mathematics. Laboratory materials will be used to reinforce understanding of concepts. Prerequisite: MATH 003 or 005 or 035 or 041 or 051 or 053, or appropriate score on the algebra placement tests. Not open to freshman. This course does not count as an elective for a B.S. degree.

**MATH 162. Elementary Concepts of Mathematics II (4)** Development of arithmetic and geometric concepts within a classroom setting. The course includes related topics such as diagnostic/prescriptive techniques, the use of calculators and computers, approaches to a K-8 MATH curriculum and current trends within mathematics education. The course will include field experiences, seminar discussions and laboratory workshops. Prerequisite: MATH 161, or permission of the instructor.

**MATH 164. Topics in the History of Mathematics (3)** Topics in mathematics will be studied from a historical perspective. Topics will be chosen from: numeration systems; mathematics of the ancient world, especially Greece; Chinese, Hindu and Arabic mathematics; the development of analytic geometry and calculus; and modern axiomatic mathematics. Students will solve problems using historical and modern methods. Students will read and report on the biography of a mathematician. Prerequisites: MATH 053 and junior standing or permission of the instructor.

**MATH 166. Mathematical Concepts for Secondary Education (3)** Secondary school mathematics from an advanced viewpoint and pedagogical perspective. Content is aligned with the mathematics subject matter requirements from the California Commision on Teacher Credentialing. Prerequisites: MATH 053.

**MATH 168. Modern Geometries (4)** Selected topics from Euclidean, non-Euclidean and transformational geometry. Both analytic and synthetic methods. History of the development of geometries and axiomatic systems. Laboratory materials and computer packages used to reinforce understanding of the concepts. Required for high school teacher candidates. Prerequisite: MATH 049 or permission of the instructor.

**MATH 174. Graph Theory (4)** An in-depth consideration of discrete structures and their applications. Topics include connectivity, Eulerian and Hamiltonian paths, circuits, trees, Ramsey theory, digraphs and tournaments, planarity, graph coloring, and matching and covering problems. Applications of graph theory to fields such as computer science, engineering, mathematics, operations research, social sciences, and biology are considered. Prerequisites: MATH 051 or 074 or COMP 047 or an appropriate score on the calculus placement test.

**MATH 093. Special Topics (3 or 4)**

**MATH 191. Independent Study (2-4)** Student-initiated projects covering topics not available in regularly scheduled courses. A written proposal outlining the project and norms for evaluation must be approved by the department chairperson.

**MATH 193. Special Topics (3-4)**

**MATH 197. Undergraduate Research in Mathematics (2-4)**