MATH 303 (3) Themes for Society Descriptive overviews of selected areas of mathematics which play a visible role in the modern world. Topics include management science and operations research, political science, statistics, computer science, biology, and some late 20th Century advancements in pure mathematics. Credit may not be counted toward the mathematics major. Prerequisite: Completion of the lower division General Education requirement in Mathematics/Quantitative Reasoning.
MATH 304 (3) Women and Mathematics Examination of the social phenomena that have led to the small number of women in the mathematical profession. Exploration of the controversy concerning research on the comparative mathematical ability of boys and girls. Study of the lives, times, and works of women mathematicians. Prerequisite: Completion of the lower-division General Education requirement in Mathematics/Quantitative Reasoning.
MATH 308 (3) Non-Statistical Mathematics in the Social Sciences Themes involving applications of mathematics in the social sciences such as: proportional representation, voting rules and aggregation of individual preferences, spatial models of election competition, power in weighted voting systems, power indices in politics, balance theory and social inequalities, measurement theory, game theory, static models of animal dominance, rumor and information networks. May not be taken for credit by students who have received credit for MATH 404. Prerequisite: Completion of the lower-division General Education requirement in Mathematics/ Quantitative Reasoning (B4).
MATH 311 (3) Mathematics for K-8 Teachers, III: Algebra, Probability, Statistics, and Data Analysis Designed to reinforce mathematical concepts for those teaching grades K-8. Emphasis on linear and quadratic equations and inequalities; collection, organization, and representation of data; inferences, predictions, and arguments based on data; basic notions of chance and probability; appropriate use of technology; historical/ cultural perspectives. Credit may not be counted toward the mathematics major. Prerequisite: Math 212 with a grade of C (2.0) or better.
MATH 311B (3) Mathematics for K-8 Teachers III: Algebra, Probability, Statistics, and Data Analysis Designed to reinforce mathematical concepts for those teaching grades K-8. Emphasis on linear and quadratic equations and inequalities; collection, organization, and representation of data; inferences, predictions, and arguments based on data; basic notions of chance and probability; appropriate use of technology; historical perspectives. Credit may not be counted toward the mathematics major. May not be taken for credit by students who have received credit for MATH 311. Corequisite: EDMS 512B, EDMS 522B, EDMS 543B. Prerequisites: MATH 212 with a grade of C or better and participation in the Integrated Credential Program.
MATH 314 (1) Workshop for Future Mathematics Educators Provides a discussion forum for students pursuing the Mathematics Single-Subject CSET Waiver Program, while co-enrolled in EDUC 350, Foundations of Teaching as a Profession. Discussions focus on various mathematical subject matters typically presented in secondary-level classrooms which students visit and observe in EDUC 350. Students link their observations from the field experience to their own study of relevant mathematical skills and knowledge. Credit may not be counted towards the mathematics major. Prerequisite: MATH 162 with a grade of C or better. Corequisite: EDUC 350.
MATH 315 (3) Finite Mathematics Sets, permutations, combinations, probability, linear equations and inequalities, matrices, linear programming, finance. Credit may not be counted toward the mathematics major. May not be taken for credit by students who have received credit for MATH 130. Prerequisite: Completion of the B4 Lower-Division General Education requirement.
MATH 330 (3) Introduction to the History of Mathematics Major currents in the evolution of mathematical thought from early civilization to modern times. Prerequisite: MATH 160.
MATH 350 (3) Foundations for Theoretical Mathematics A bridge course between computation-driven mathematics and theoretical mathematics. Designed to familiarize the students with the language and process of rigorous mathematical thought, speech, and writing through the introduction of typical and important examples from algebra, analysis, combinatorics, as well as careful development of the natural, rational, real, and complex numbers. In the process, this course will cover: elementary logic, methods of proof, mathematical induction, sets, relations, functions, binary operations, equivalence classes, modular arithmetic, groups, matrices, and limits. Prerequisite: MATH 160 with a minimum grade of C.
MATH 362 (3) Differential Equations Analysis and application of ordinary differential equations: linear and nonlinear equations, existence and uniqueness theorems, analytic methods, qualitative analysis of solutions, numerical methods. Combines theoretical ideas along with hands-on experience using appropriate computer software. Prerequisite: MATH 162 with a grade of C (2.0) or better.
MATH 346 (3) Mathematical Methods for Physics Survey of mathematical methods applicable to physics. Includes series, complex analysis, ordinary and partial differential equations, and special functions and transforms. Recommended: MATH 260. Prerequisite: MATH 162.
MATH 370 (3) Discrete Mathematics The terminology, concepts, and techniques of some areas of discrete mathematics applicable in computer science. Logic, proof techniques, recursion, set theory and counting, relations and functions, groups and codes, graphs. Prerequisite: MATH 160 with a grade of C (2.0) or better.
MATH 374 (3) Linear Algebra Systems of linear equations, vector spaces, independence, bases, dimension, orthogonality, least squares, determinants, eigenvalues and eigenvectors, positive definiteness, computation, linear programming. Combines theoretical ideas with hands-on experience using appropriate computer software packages. Prerequisite: MATH 160 with a grade of C (2.0) or better.
MATH 378 (3) Number Systems Numbers: natural, rational, real, complex. Algebraic laws: commutative, associative, distributive. Brief introduction to groups, rings and fields. Divisibility and unique factorization for integers and polynomials. Integers modulo n as finite rings and fields. The rational numbers as a non-complete countable ordered field. The real numbers as a complete uncountable ordered field. Sequences and limits including Cauchy sequences, lim inf and lim sup. Complex numbers including De Moivre's theorem and related trigonometric identities. Factoring polynomials over the various number systems. The Fundamental Theorem of Algebra. Prerequisites: MATH 350 or MATH 370 with a grade of C (2.0) or better.
MATH 390 (1) Mathematics Colloquium Guest lecturers present seminars on mathematical topics, e.g., recent advances in mathematics research, interesting applications of mathematics, or fun and challenging math problems. Students must attend each seminar, prepare a journal summarizing the content of each presentation, and write a follow up paper on one of the topics that they found particularly interesting. May be repeated for credit for a total of three (3) units. Graded Credit/No Credit. MATH 162 with a grade of C (2.0) or better.
MATH 401 (3) Number concepts for Teachers Designed to reinforce mathematical concepts for those teaching in middle school. Properties, relations, and extensions of the natural numbers, integers, rational, irrational, real, and complex numbers. Subjects include number sequences, patterns, functional relationships, some number theory, meaning of infinity, applications, historical/cultural perspectives. Will use appropriate technology and physical materials. Credit may not be counted toward the mathematics major. Prerequisite: MATH 210 and 212 with a grade of C (2.0) or better or consent of instructor.
MATH 403 (3) Geometry for Teachers Designed to reinforce mathematical concepts for those teaching in middle school. Geometry and measurement. Properties and relationships of shape, size, and symmetry in two- and three-dimensional space: points, lines, planes, curves, triangles, convex figures, parallelism, congruence, similarity, symmetry, rotations, reflections, translations, perimeter, area, volume. Historical development of Euclidean and non-Euclidean geometries. Will use appropriate technology and physical materials. Combines theoretical ideas with hands-on experience using appropriate computer software packages. Credit may not be counted toward the mathematics major. May not be taken for credit by students who have received credit for EDUC E596S. Prerequisite: MATH 210 and 212 with a grade of C (2.0) or better, or consent of instructor.
MATH 405 (3) Statistics and Probability for Teachers Designed to reinforce mathematical concepts for those teaching in middle school. Data collection, random experiments, data organization and interpretation, formulation of convincing arguments; inferences and informed decisions based on statistical methods; experimental probabilities; counting techniques; analysis of correct and incorrect uses of statistics. Combines theoretical ideas with hands-on experience using appropriate computer software packages. Credit may not be counted toward the mathematics sciences major. Prerequisite: MATH 210 and 212 with a grade of C or better, or consent of instructor.
MATH 407 (3) Problem Solving for Teachers Designed to reinforce mathematical concepts for those teaching in middle school. Problem strategies and approaches, in the context of problems from various fields in mathematics. Four step method; noticing patterns; reformulating the problem; decomposing and recombining; examine related problems; logic, valid arguments, and proof techniques; induction. Historical/cultural perspectives. Credit may not be counted toward the mathematics sciences major. Prerequisite: MATH 210 and 212 with a grade of C or better or consent of instructor.
MATH (1-3) 409 Special Topics in Mathematics for Teachers Designed to reinforce mathematical concepts for those teaching in elementary, middle, or high school. May be repeated for credit as topics change for a total of six (6) units. Credit may not be counted toward the mathematics sciences major. Prerequisite: MATH 210 and 212 with a grade of C or better or consent of instructor.
MATH 410 (3) Modern Geometry Critical review of the foundations and basic structure of plane and solid Euclidean geometry, non-Euclidean geometries, incidence and affine geometries; convexity and applications. Prerequisite: MATH 350 or 370 with a grade of C (2.0) or better, or consent of instructor.
MATH 422 (3) Introduction to Number Theory Divisibility, Euclidean algorithm, unique factorization, congruences, and quadratic reciprocity. May also cover some of the following: included primitive roots and indices, continued fractions, sum of squares, introduction to Diophantine equations, prime numbers, pseudo-primes, the prime number theorem, and factorization and primality-testing algorithms. May not be taken for credit by students who have received credit for MATH 372. Prerequisites: MATH 378 with a grade of C (2.0) or better, or consent of instructor.
MATH 430 (3) Foundations of Analysis A classical treatment of the basic concepts of calculus of one variable: the real number system, limits, continuity, differentiability, the Riemann integral, sequences and series of numbers and functions. May not be taken for credit by students who have received credit for MATH 360. Prerequisites: MATH 378 with a grade of C (2.0) or better, or consent of instructor.
MATH 440 (3) Mathematical Statistics Basic concepts of probability: axiomatic formulation, combinatorics, conditional probability, independence, standard discrete and continuous random variables, expectation, variance, joint distributions, limit theorems. Statistical inference: tests of significance, point estimation methods, confidence intervals, simple linear regression. Combines theoretical ideas with hands-on experience using appropriate computer software packages. Prerequisite: MATH 260 with a grade of C (2.0) or better.
MATH 441 (3) Introduction to Probability Discrete and continuous probability spaces, axiomatic formulation, combinatorics, conditional probability and independence, standard discrete and continuous probability distributions (including uniform, Bernoulli, binomial, Poisson, geometric, normal, and exponential), random variables, expectation and variance, joint distributions, limit theorems. Emphasis on modeling. Simple proofs required. Additional topics may include random walks, branching processes, and generating functions. Prerequisite: MATH 162 with a grade of C (2.0) or better. Prerequisite or Corequisite: MATH 260.
MATH 442 (3) Introduction to Mathematical Statistics Data analysis and inferential statistics: random samples, estimation, sufficient statistics, confidence intervals, hypothesis tests, curve fitting, linear regression, least squares, goodness of fit. Covers both theory and applications, with emphasis on applications. Simple proofs required. Prerequisite: MATH 441 with a grade of C (2.0) or better.
MATH 464 (3) Numerical Analysis and Computing Computer arithmetic, solution of a single algebraic equation, solution of systems of equations interpolating polynomials, numerical integration, numerical solution of ordinary differential equations; error analysis and computational effort of numerical algorithms. Combines theoretical ideas with hands-on laboratory experience. Also offered as CS 464. Students may not receive credit for both. Prerequisites: CS 111 or equivalent and MATH 162.
MATH 470 (3) Introduction to Abstract Algebra An introduction to the theory of groups, rings, and fields with abstract ideas reinforced by concrete and important examples, such as permutation groups, polynomial rings, and finite fields. The power of the axiomatics systems introduced will be illustrated via several applications to concrete and classical problems. Prerequisites: MATH 378 with a grade of C (2.0) or better, or consent of instructor.
MATH 472 (3) Introduction to Graph Theory Fundamental concepts of undirected and directed graphs, trees, connectivity and traversability, planarity, colorability, networks, matchings; emphasis on modern applications. Prerequisites: MATH 350 or 370 with a grade of C (2.0) or better, or consent of instructor.
MATH 474 (3) Introduction to Combinatorics Introduction of the basic tools of combinatorics and their applications. Permutations, combinations, occupancy problems, generating functions, recurrences, inclusion/exclusion, graph theory, pigeonhole principle, experimental design, coding theory. Prerequisite: MATH 350 or 370 with a grade of C (2.0) or better, or consent of instructor.
MATH 480 (3) Introduction to Optimization, I Modern study of linear programming with an emphasis on model formulation, solution, and interpretation of software output. Applications in work scheduling, diet, capital budgeting, blending, production process, transportation, assignment, transshipment, and flow problems. Programming methods include the simplex method and its specialized variations, Big M Method, goal programming, and integer programming. Theoretical aspects include optimality conditions, sensitivity analysis, and duality. Requires using industry-standard software to strengthen the ideas and concepts. Also offered as CS 480. Students may not receive credit for both. Prerequisite: MATH 374 or consent of instructor.
MATH 490 (3) Senior Seminar Presentation and discussion of selected topics in mathematical sciences in order to supplement available offerings. Sample areas include differential forms, complex variables, partial differential equations, a second course in analysis, abstract algebra, or discrete math. May be repeated twice as course content changes, with consent of the program, for a maximum of nine (9) units of credit from MATH 490 491. Prerequisites: Twelve (12) units of upper-division mathematics. Other prerequisites to be determined by instructor.
MATH 491 (3) Senior Seminar with Lab Presentation and discussion of selected topics in mathematical sciences in order to supplement available offerings. Sample areas include mathematical modeling and a second course in numerical optimization or statistics. This course meets for four hours per week. May be repeated for a maximum of nine (9) units of credit for MATH 490 and 491. Prerequisites: Twelve (12) units of upper-division mathematics. Other prerequisites to be determined by instructor.
MATH 495 (1-3) Internship in Mathematics Faculty-sponsored academic internship in business, industrial, government, research firm, or university labs and centers. Prerequisite: Consent of instructor.
MATH 498A (1) 498B (2) 498C (3) Individual Study in Mathematics Individually directed reading and study in mathematical sciences literature. May be repeated for a maximum of three (3) units. Prerequisites: Twelve (12) units of upperdivision in Mathematics and consent of instructor.
MATH 499A (1) 499B (2) 499C (3) Independent Research in Mathematics Designed for students capable of independent and original research. May be repeated for a maximum of three (3) units. Prerequisites: Twelve (12) units of upper division mathematics and consent of instructor.
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