# Upper Division Courses

### MATH 320. Foundations of Higher Mathematics (3)

Prerequisite: MATH 150B. The goal of this course is to help students transition from a primarily computational mode of doing mathematics to a more conceptual mode. The emphasis will be on proofs, which are taught in the context of elementary number theory, combinatorics and analysis; the language of sets, relations, order, equivalence classes, functions and cardinality is introduced. Students are expected to write large numbers of proofs and communicate mathematical ideas clearly.

### MATH 326. Discrete Mathematics (3)

Prerequisites: ECE 320 or PHIL 230; MATH 150B. Propositional calculus, predicate calculus, set algebra, relations, functions, mappings, fields and number systems.

### MATH 331. Mathematical Explorations (3)

Prerequisites: Passing Score on the ELM Exam; Completion of the Lower Division writing requirement; Upper Division standing. A course designed to give students an appreciation of the diversity of mathematics and the spirit in which it is employed in various applications. The character and origin of key topics from different branches of mathematics are explored. The contributions of various cultures to the field are studied, along with the use of mathematical models for physical problems. The development is conceptual rather than axiomatic, and includes several supervised reading and writing assignments. One significant writing assignment is required. Strongly recommended for prospective teachers in all fields. (Available for General Education, Basic Skills Mathematics.)

### MATH 340. Introductory Probability (3)

Prerequisite: MATH 150B. Sample spaces, probability rules, independence, conditional probability, BayesÕ Theorem, discrete and continuous random variables and distributions (e.g. binomial, Poisson, geometric, normal, exponential, uniform), expectation, moment generating functions, joint distributions and central limit theorem.

### MATH 341. Applied Statistics I (3)

Prerequisite: MATH 150B. Introduction to the practice of statistics, emphasizing the role of probability. Includes basic probability, discrete and continuous probability distributions, expectation and variance, sample surveys and experiments, displaying and summarizing data, sampling distributions, central limit theorem, inference for proportions, chi-square test and least squares regression. Mathematics majors who are not in the Secondary Teaching Option may not receive credit for both MATH 340 and 341.

### MATH 350. Advanced Calculus I (3)

Prerequisite: MATH 320. Topics include the real number system, continuous functions, differentiation, and Riemann integration of functions of 1 real variable.

### MATH 351. Differential Equations (3)

Prerequisites: MATH 250, 262. Not open to students who have credit for MATH 280. Linear equations, series solutions, singular points, existence and uniqueness of solutions, and systems of equations.

### MATH 360. Abstract Algebra I (3)

Prerequisites: MATH 262, 320. Survey course in abstract algebra. Introduction to groups, rings, fields and vector spaces.

### MATH 366. Combinatorics (3)

Corequisite: MATH 320 or 326. This is a one-semester introduction to combinatorics. Topics include enumerative combinatorics (inclusion-exclusion, generating functions, PolyaÕs Theorem, etc.) and combinatorial structures (graphs, designs, etc.).

### MATH 370. Foundations of Geometry (3)

Prerequisite or Corequisite: MATH 320. One of the goals of this course is to help students write rigorous proofs of results of plane Euclidean geometry. It is also expected that students visualize and develop geometric intuition through the use of dynamic geometry software. The content includes history, axiomatic structure and theorems of plane Euclidean geometry, geometric transformations of the plane, rigid motions, similarities, and inversion, coordinate geometry and an introduction to non-Euclidean geometries.

### MATH 382/L. Introduction to Scientific Computing and Lab (2/1)

Corequisite: MATH 262. This course gives students an introduction to basic numerical techniques and to programming using some of the common software packages used in mathematics. Students apply these techniques in projects from different branches of mathematics.(This course does not replace a rigorous course in numerical analysis.) 2 hours lecture, 2 hours lab.

### MATH 390A-D. Mini-Courses in Mathematics for Pre and in Service Teachers (1)

Prerequisites: MATH 210 with a grade of ÒCÓ or better or instructor consent; Passing score on ELM Exam. This course is intended for Liberal Studies Credential Candidates and in-service elementary- and middle-school teachers. Important concepts of mathematics that have particular application to the elementary-school curriculum, including: AÐHistory of Mathematics; BÐComputational Methods; CÐComputer-Assisted Instruction; and DÐStrategies in Problem Solving. (Credit/No Credit only)

### MATH 391. Field Experience in the Mathematics of the Public Schools (2)

Prerequisites: Multiple Subject CandidatesÑMATH 210 and 310 or corequisite with 310; Passing score on the ELM Exam. Single Subject CandidatesÑMATH 150A, 150B; Junior standing. Field experience course designed to give the prospective teacher an appreciation of a quality mathematics program in public schools. Requirements include 45 hours of participation in an assigned school and regular group meetings to discuss the classroom experience. (Credit/No Credit only)

### MATH 440A. Mathematical Statistics I (3)

Prerequisites: MATH 262, 340. Point estimation, bias and mean squared error, optimality theory for estimates, maximum likelihood estimation, confidence intervals, test of hypotheses, power, and optimality theory for tests.

### MATH 440B. Mathematical Statistics II (3)

Prerequisite: MATH 440A. Chi-square goodness of fit tests, simple and multiple linear regression, 1- and 2-way analysis of variance, and statistical analysis using the computer.

### MATH 441. Applied Statistics II (3)

Prerequisite: MATH 341. Continuation of MATH 341 with emphasis on statistical inference. Includes design of surveys and experiments, the t-distribution, inference for means, correlation and regression with transformations, and inference for slope.

### MATH 442A-Z. Topics in Mathematical Statistics (3)

Prerequisite: MATH 340 or 440A. Topics selected from statistics and/or probability, such as nonparametric statistics, multivariate statistics, experimental design, decision theory and advanced probability theory.

### MATH 450. Advanced Calculus II (3)

Prerequisite: MATH 350. Topics include sequences and series of functions, Heine-Borel theorem, Jacobians, and inverse and implicit function theorems.

### MATH 455. Complex Variables (3)

Prerequisite: MATH 350. Complex numbers, analytic functions, complex integration, CauchyÕs Theorem, power series, calculus of residues and conformal mappings.

### MATH 460. Abstract Algebra II (3)

Prerequisite: MATH 360. Second course in abstract algebra. Group theory, rings and modules, and field extensions.

### MATH 462. Advanced Linear Algebra (3)

Prerequisites: MATH 262, 320. Finite dimensional vector spaces, linear transformations, matrix polynomials, canonical forms.

### MATH 463. Number Theory (3)

Prerequisite: MATH 320. Recommended Corequisite or Preparatory: MATH 360. Euclidean algorithm and the unique factorization theorem, congruences, primitive roots and indices, quadratic residues and the law of quadratic reciprocity, and distribution of primes.

### MATH 470. Topics of Geometry (3)

Prerequisite: MATH 370 or 350. Non-Euclidean geometries and/or advanced results in Euclidean geometry.

### MATH 480. Partial Differential Equations (3)

Prerequisite: MATH 351 or 280. Orthogonal functions, LaplaceÕs equation, PoissonÕs equation, BesselÕs equation, self-adjoint operators, Sturm-Liouville theory, Fourier series, separation of variables applied to the heat equation and wave equation, nonhomogeneous problems, GreenÕs functions for time-independent problems, and infinite domain problems.

### MATH 481A. Numerical Analysis (3)

Prerequisites: COMP 106/L or 110/L; MATH 262. Techniques of applied mathematics, solution of equations, interpolation, numerical integration and numerical solution of differential equations.

### MATH 481B. Numerical Analysis (3)

Prerequisite: MATH 481A. Numerical solution of linear systems of equations. Included are direct and iterative methods for solving linear systems, iterative techniques in matrix algebra, applications to approximation theory and techniques for finding eigenvalues. Formal instructions are combined with practical assignments in scientific computing.

### MATH 481C. Numerical Methods for Partial Differential Equations (3)

Prerequisite: MATH 481B. Corequisite: MATH 480. Numerical Methods for PDEs are covered, in particular finite difference methods and finite element methods. Application of these methods to linear partial differential equations.

### MATH 481D. Topics in Numerical Mathematics (3)

Prerequisite: MATH 481A. This course explores topics in numerical mathematics that have not been explored elsewhere in the sequence. These include, but are not limited to, topics from statistics and linear and non-linear optimization. The course may be taken twice for credit with the consent of an advisor.

### MATH 482. Combinatorial Algorithms (3)

Prerequisites: MATH 150B, 262; Some computer programming experience. Computer-oriented study of seminumerical and non-numerical algorithms. Sorting, tree searching, generation of combinatorial structures, algorithm proof techniques, best algorithms and programming complexity.

### MATH 483. Mathematical Modeling (3)

Prerequisites: MATH 340; 351. Applications of mathematical techniques to solve selected problems in ecology, biology, economics, finance, social sciences, life sciences, physical sciences and engineering. Models discussed include deterministic, stochastic, optimization, static and dynamic ones. Emphasis is placed on the initial phase of building mathematical models and the final phase of interpreting the solutions in terms of real-life applications.

### MATH 490. Capstone Course (3)

Prerequisite: Senior standing. A course where prospective teachers see high-school level mathematics from a more advanced perspective, where there is considerably more emphasis on issues of pedagogy than in other content courses, and where students will see connections between the mathematics they have learned and some of the activities that they will themselves be engaged in as teachers. MATH 490 is required for the Secondary Teaching Option, but a student may choose, in consultation with his or her advisor, to take the course a second time as an elective.

### MATH 493. Undergraduate Seminar in Mathematics (3)

Prerequisite: Junior standing in the major. Students will study current topics in mathematical and/or statistical literature and will prepare written summaries and give oral presentations to the class. Students will be active participants in all seminars by asking questions and providing written critiques and summaries of the presentations of other students.

### MATH 494. Practical Experience in Mathematics (3)

Prerequisite: Junior standing in the major. Students will gain practical experience in the profession by either participating in an internship doing mathematical/statistical work at an outside organization or by doing directed research within the Department. All students are expected to work a minimum of 8 hours per week on this assignment and meet with the course instructor on a regular basis. All students are required to produce a written report on their work at the end of the semester. Students will give oral reports to the Department and their peers.

### MATH 496A-Z. Experimental Topics in Modern Mathematics (3)

Prerequisites: Senior standing and instructor consent.

### MATH 499A-C. Independent Study (1-3)

See Independent Study under courses of study.