#### College of Science and Mathematics

- Chair: Werner Horn
- Santa Susana Hall (SN) 114
- (818) 677-2721, Fax: (818) 677-3634
- www.csun.edu/math

## Courses

#### MATH 090. Introduction to Problem Solving (2)

Introduction to problem-solving, with an emphasis on basic mathematics skills. Diagnostic tests enable students to identify specific topics for study. Involves collaborative learning, individualized advisement and instruction, and use of media and computers. Normally offered as a Summer Bridge course. Credit will not apply toward the Baccalaureate Degree, but will apply as two units of University credit.

#### MATH 092. Developmental Mathematics I (3)

First in a 2-semester sequence of developmental mathematics courses. Students scoring below 34 on the ELM need to complete MATH 092 and 093 successfully to be remediated. Credit will not apply toward the Baccalaureate Degree but will apply as 3 units of University Credit. Students who earn Credit in MATH 092 are eligible to enroll in MATH 093. Topics covered include fractions, decimal notation, percent, real numbers and algebraic expressions, equations and inequalities. (Credit/No Credit only)

#### MATH 093. Developmental Mathematics II (5)

Prerequisite: Score of 34 or above, but below 50 on the ELM Exam or credit in MATH 092. Credit will not apply toward the Baccalaureate Degree, but will apply as 5 units of University credit. Successful completion of MATH 093 qualifies students for entrance into MATH 102, 131, 140 and 210. Review of elementary algebra topics, such as equations and inequalities, polynomials, factoring, rational expressions, graphing, radical expressions, quadratic equations and functions. (Credit/No Credit only)

#### MATH 099 Developmental Mathematics II Ð Accelerated (3)

Prerequisite: A score of 40 or above but below 50 on the ELM Exam or credit in MATH 092. Credit will not apply toward the Baccalaureate Degree, but will apply as 3 units of University credit. Successful completion of MATH 099 qualifies students for entrance into MATH 102 and 103 (conditionally), 131, 140 and 210. This course is not open to students who are currently enrolled in or who have received credit in MATH 093. This is an accelerated review of elementary algebra topics, including equations and inequalities, polynomials, factoring, rational expressions, graphing, radical expressions, quadratic equations and functions. (Credit/No Credit only)

#### MATH 102. College Algebra (3)

Prerequisites: Listed in Table 1. Students who are conditionally prepared must have credit for or concurrently enroll in MATH 102L. Functions, linear equations, quadratic equations, theory of equations, progressions, inequalities, absolute value, logarithms, permutations, combinations, probability and determinants. Not open to students who have credit in MATH 103, 105 or 106. (Available for General Education, Basic Skills Mathematics.)

#### MATH 102L. College Algebra Lab (1)

Prerequisite: Required for all Conditionally prepared students enrolled in MATH 102. All students in MATH 102 are encouraged to enroll in this course. This is a Credit/No Credit hybrid enrichment laboratory for students in MATH 102. This course will include a self-paced, modular online component. 2 hours lab per week. (Credit/No Credit only)

#### MATH 103. Mathematical Methods for Business (3)

Prerequisites: Passing score on or exemption from the ELM Exam or credit in MATH 093; Passing score on the Mathematics Placement Test, Part I or credit or concurrent enrollment in MATH 103L. Concepts and applications of algebra and calculus to business. Topics include functions, systems of equations, matrices, the derivative and business-related topics in calculus. (Available for General Education, Basic Skills Mathematics.)

#### MATH 103L. Mathematics for Business Laboratory (1)

Prerequisite: Passing score on the ELM Exam. This self-paced, module-based laboratory is designed to give students additional exposure to the applications of college algebra to business and economics beyond what can be done in lecture. The additional hands-on problem-solving skills learned in this class enhance the lecture experience and strengthen the skills necessary for success in MATH 103 and subsequent courses in business majors. The lab environment allows students to both work at their own pace and receive small-group instruction with the laboratory instructor on all modules. Students with an MPT Part I score below 24 may enroll in MATH 103 only if they enroll in this course. 2 hours lab per week. (Credit/No Credit only)

#### MATH 104. Trigonometry and Analytic Geometry (3)

Prerequisites: Listed in Table 1. Students who are Conditionally prepared must have credit for or concurrently enroll in MATH 104L. Rectangular and polar coordinates; trigonometric functions, identities and equations; inverse trigonometric functions; conic sections; complex numbers. Not open to students who have credit in MATH 103, 105 or 106.

#### MATH 104L. Trigonometry Lab (1)

Prerequisite: Required for all conditionally prepared students enrolled in MATH 104. All students in MATH 104 are encouraged to enroll in this course. This is a Credit/No Credit hybrid enrichment laboratory for students in MATH 104. This course will include a self-paced, modular online component. w hours lab per week. (Credit/No Credit only)

#### MATH 105. Pre-Calculus (5)

Prerequisites: Listed in Table 1 above. Students who are Conditionally prepared must have credit for or concurrently enroll in MATH 105L. Number systems and their algebraic properties; systems of equations and inequalities; basic analytic geometry of lines and conic sections; elementary functions, including polynomial, rational, exponential and logarithmic, with emphasis on trigonometric functions; polar equations. Graphing calculators are used and the interplay between graphical and algebraic solutions is stressed. Not open for credit to students who have successfully completed MATH 150A.(Available for General Education, Basic Skills Mathematics)

#### MATH 105L. PreCalculus Lab (1)

Prerequisite: Required for all conditionally prepared students enrolled in MATH 105. All students in MATH 105 are encouraged to enroll in this course. This is a NC/CR hybrid enrichment laboratory for students in MATH 105. This course will include a self-paced, modular online component. 3 hours lab per week. (Credit/No Credit only)

#### MATH 131. Mathematical Ideas (3)

Prerequisites: Passing score on or exemption from the ELM Exam, or credit in MATH 093. General Education course intended to acquaint the student with basic mathematical ideas. (Available for General Education, Basic Skills Mathematics.)

#### MATH 140. Introductory Statistics (4)

Prerequisites: Passing score on or exemption from the ELM Exam, or credit in MATH 093. Methods for displaying, describing and producing data. Normal distribution. Correlation and regression. Sampling distributions and probability. Statistical inference for means and proportions. (Available for General Education, Basic Skills Mathematics.)

#### MATH 150A. Calculus I (5)

Prerequisites: Listed in Table 1. Students who are Conditionally prepared or who transfer the equivalent of MATH 105 or both MATH 102 and 104 must have credit for or concurrently enroll in MATH 150AL. Limits, derivatives, applications of differentiation. Definite and indefinite integrals, and the fundamental theorem of calculus. (Available for General Education, Basic Skills Mathematics.)

#### MATH 150AL: Calculus I Laboratory (1)

Prerequisite: Required for all Conditionally prepared students enrolled in MATH 150B or 255B. All students in MATH 150B and 255B are encouraged to enroll in this course. This is a NC/CR hybrid enrichment laboratory for students in MATH 150B and 255B. This course will include a self-paced, modular online component. 3 hours lab per week. (Credit/No Credit only)

#### MATH 150B. Calculus II (5)

Prerequisites: Listed in Table 1. Students who are Conditionally prepared must have credit for or concurrently enroll in MATH 150BL. Techniques of integration, numerical integration, improper integrals and applications of the integral. Taylor polynomials, sequences and series, and power series.

#### MATH 150BL. Calculus II Laboratory (1)

Prerequisite: Required for all Conditionally prepared students enrolled in MATH 150B or 255B. All students in MATH 150B and 255B are encouraged to enroll in this course. This is a Credit/No Credit hybrid enrichment laboratory for students in MATH 150B and 255B. This course will include a self-paced, modular online component. 3 hours lab per week. (Credit/No Credit only)

#### MATH 210. Basic Number Concepts (3)

Prerequisites: Passing score on or exemption from the ELM Exam or credit in MATH 093. Language of sets, systems of numeration, nature of numbers and fundamentals of operations, relations and functions, domain of integers, and field of rational and real numbers. Designed primarily for students intending to teach in elementary or junior high school. Not available for credit toward the Major or Minor in Mathematics.

#### MATH 250. Calculus III (3)

Prerequisite: Completion of MATH 150B with a grade of ÒCÓ or better. Continuation of MATH 150B. Solid analytic geometry, partial differentiation and multiple integrals with applications.

#### MATH 255A. Calculus for the Life Sciences I (3)

Prerequisites: Listed in Table 1. Students who are Conditionally prepared must have credit for or concurrently enroll in MATH 150AL. Knowledge of trigonometry is assumed. First semester of a short course in calculus. Topics in calculus of functions of one variable including techniques of differentiation, applications to graphing, extreme problems and an introduction to integration. Not open for credit to students who have successfully completed MATH 150A. (Available for General Education, Basic Skills Mathematics.)

#### MATH 255B. Calculus for the Life Sciences II (3)

Prerequisites: Listed in Table 1. Students who are Conditionally prepared must have credit for or concurrently enroll in MATH 150BL. Techniques of integration, series, applications, functions of several variables and partial differentiation. Not open for credit to students who have successfully completed MATH 150AB.

#### MATH 262. Introduction to Linear Algebra (3)

Prerequisite: MATH 150B. Systems of linear equations, matrices, determinants, eigenvalues, vector spaces and linear transformations, as well as introduction to inner products on Rn and spectral theorem for symmetric matrices.

#### MATH 280. Applied Differential Equations (3)

Prerequisite: MATH 150B. Recommended Corequisite or Preparatory: MATH 250. Ordinary differential equations, series solutions, systems of equations and Laplace transforms, with emphasis on applications and introduction to numerical techniques. Course is not open to students who have credit for MATH 351.

#### MATH 310. Basic Concepts of Geometry, Probability and Statistics (3)

Prerequisites: Passing score on or exemption from the ELM Exam or credit in MATH 093 and completion of MATH 210 with a grade of ÒCÓ or better. Articulated course from another college equivalent to MATH 210 may only satisfy the course prerequisite for MATH 310. Students passing such a course with a ÒCÓ or better will still need to fulfill the ELM Exam requirement. Second course for students intending to teach in elementary or junior high school. Geometry as a system; congruence and similarity through construction with straightedge and compass; transformational geometry; the nature of measurement, precision and accuracy; basic principles of probability and statistics. Not available for credit toward the Major or Minor in Mathematics.

#### MATH 310L. Geometry, Probability and Statistics Lab (1)

Recommended Corequisite or Preparatory: MATH 310. Problem solving using models and simulation in mathematics appropriate for the elementary-school classroom. 2 hours of activities per week. (Credit/No Credit only)

#### MATH 311. Basic Geometric Concepts (3)

Prerequisites: Passing score on the ELM Exam and completion of MATH 210 and 310 with a grade of ÒCÓ or better, or instructor consent. Continuation of the investigation of elementary geometry begun in MATH 310. Topics selected from topology, motion geometry, metric geometry, geometry as a mathematical system, absolute geometry, Euclidean geometry and non-Euclidean geometry. Not available for credit toward the Math Major or Minor.

#### MATH 312. Basic Algebraic Concepts (3)

Prerequisites: Passing score on the ELM Exam and completion of MATH 210 and 310 with a grade of ÒCÓ or better, or instructor consent. Topics selected from: abstract algebra and applied algebra using elementary mathematical models. Not available for credit toward the Math Major or Minor.

#### 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.

#### MATH 501. Topology (3)

Prerequisite: MATH 350. Metric spaces, topological spaces, compactness, completeness and connectedness. Introduction to function spaces, with emphasis on the uniform topology.

#### MATH 510A/B. Algebra and Number Theory (3-3)

Prerequisite: Admission to the Graduate Program. A 2-course sequence on integers and prime numbers, rational and complex algebraic numbers, symmetry and group theory, rings of polynomials and algebraic integers, basic algebraic geometry and algebraic extensions, elementary Galois Theory and the theory of equations. MATH 510A is the prerequisite for MATH 510B. These courses cannot be taken for credit toward the MasterÕs Degree in Options I and II.

#### MATH 511A/B. Linear Algebra and Geometry (3-3)

Prerequisite: Admission to the Graduate Program. A 2-course sequence on modern applications of mathematics that involve matrices, basic properties of vectors of R2 and R3, dot product, orthonormal basis, cross product, linear transformations of Euclidean 2- and 3-Space and the classification of its rigid motions, symmetric bilinear forms, conics and quadrics, basic topology of Rn, spherical geometry, PoincarŽÕs models of the hyperbolic plane and their isometries. MATH 511A is the prerequisite for MATH 511B. These courses cannot be taken for credit toward the MasterÕs Degree in Options I and II.

#### MATH 512A/B. Concepts of Analysis (3-3)

Prerequisite: Admission to the Graduate Program. A 2-course sequence on the real number system, countable and uncountable sets, cardinal numbers, Cantor diagonal argument, well-ordered sets, ordinal numbers, numerical sequences and numerical series of real numbers, continuity, differentiability and integration of functions of one variable, sequences and series of functions, uniform convergence and ordinary differential equations. MATH 512A is the prerequisite for MATH 512B. These courses cannot be taken for credit toward the MasterÕs Degree in Options I and II.

#### MATH 513A/B. Discrete Mathematics (3-3)

Prerequisite: Admission to the Graduate Program. A 2-course sequence on permutations, combinations, multinomial coefficients and Pascal triangles, pigeon hole principle, inclusion-exclusion principle, Ramsey numbers, vharacteristic functions and algorithms, generating functions, finite probabilities, recurrence relations, vonnected graphs, graph volorings, planar graphs, trees, adjacency matrices, Eulerian paths, Hamiltonian paths, tournaments, matching and covering, networks, information transmission, coding and decoding, and error correcting codes. MATH 513A is the prerequisite for MATH 513 B. These courses cannot be taken for credit toward the MasterÕs Degree in Options I and II.

#### MATH 514A/B. Probability and Statistics (3-3)

Prerequisite: Admission to the Graduate Program. A 2-course sequence on probability rules, discrete and continuous random variables and their distributions, central limit theorem, and on elementary topics in statistics from the advanced point of view, including exploratory analysis, graphical display, random phenomena, probability distributions, simulation, correlation and regression, survey sampling and experimental design, sampling distributions, confidence intervals and significance tests for proportions and means, and chi-square tests. MATH 514A is the prerequisite for MATH 514B. These courses cannot be taken for credit toward the MasterÕs Degree in Options I and II.

#### MATH 540. Regression Analysis (3)

Prerequisite: MATH 440A. General linear model in matrix form, simple and multiple regression analysis, transformations, variable selection, multicollinearity, analysis of variance, robust regression, logistic regression, principal components and factor analysis. Statistical software utilized.

#### MATH 542A-D. Probability and Statistics (3-3-3-3)

Prerequisite: MATH 340 or 440A. This course will cover topics in probability and statistics not covered elsewhere in the program. Part A is usually devoted to multivariate statistics, Part B to stochastic processes, and Part C to probability theory. Part D is left to a topic chosen by the individual instructor.

#### MATH 550. Calculus On Manifolds (3)

Prerequisite: MATH 450. Integration of functions of several variables. Differential forms and differential manifolds, Line integrals, integration on manifolds, StokesÕ Theorem and PoincarŽÕs Lemma.

#### MATH 552. Real Analysis (3)

Prerequisite: MATH 501. Introduction to measure theory and Lebesgue integration, and their application to probability theory. Monotone and dominated convergence theorems, FubiniÕs theorem, Fourier analysis and Banach spaces.

#### MATH 560. Abstract Algebra III (3)

Prerequisite: MATH 460. Graduate course in abstract algebra. Group theory, Galois theory and other topics.

#### MATH 570. Differential Geometry (3)

Prerequisite: MATH 450. The local theory of regular curves in R3 and Frenet formulas. Regular surfaces in R3, the first and second fundamental forms, Gaussian and mean curvatures, and the Egregium Gauss theorem. Geodesics and the Gauss-Bonnet theorem.

#### MATH 581. Numerical Methods for Linear Systems (3)

Prerequisite: MATH 462. Methods for solving large linear problems and eigenvalue problems are presented at an advanced level. Direct methods such as LU factorization, Cholesky factorization and the Least Squares method, and Iterative methods, such as the Jacobi, Gauss-Seidel, SOR and conjugate Gradient methods, are discussed in detail. Eigenvalue problems are solved via power iteration, the QR method and the Jacobi method.

#### MATH 582 A-D. Topics in Numerical Analysis (3-3-3-3)

Prerequisite: MATH 581 or consent of instructor. The course will cover topics in numerical analysis which are important in many applications and which are not covered elsewhere in the program. Part A usually covers numerical methods in optimization, Part B covers numerical methods for ordinary differential equations ,and Part C covers numerical solution of partial differential equations. Part D covers a subject chosen by the instructor.

#### MATH 589. Seminar in Mathematics (1)

Prerequisite: Senior or graduate standing in the Mathematics Department. Students will read about advanced topics in the recent literature in mMathematics and report on them in a lecture. This course may be taken up to two times with the consent of the advisor. (Credit/No Credit only)

#### MATH 592A-D. Topics in Applied Mathematics (3-3-3-3)

Prerequisites: MATH 552 or consent of instructor. This course is devoted to a variety of important topics in applied Mmathematics that are not covered elsewhere in the Program. In particular, Part A will cover the mathematical theory of partial differential equations, Part B covers mathematical optimization and operations research, and Part C covers mathematical biology. The topic of Part D is left to the individual instructor.

#### MATH 595A-Z. Experimental Topics (1-3)

Prerequisite: Consent of instructor. Specialized topics from a concentrated field of current interest presented at an advanced level.

#### MATH 625. Advanced Mathematical Modeling (3)

Selected problems in ecology, biology, economics, finance, social sciences, life sciences, physical sciences and engineering are used to develop advanced techniques of mathematical modeling.

#### MATH 651 ABC. Advanced Topics in Analysis, Geometry and Topology (3-3-3)

Prerequisite: Consent of instructor. Advanced topics not covered in the previous classes on the subject. Part A covers topics in analysis, Part B covers topics in geometry, and Part C covers topics in topology. May be repeated with the consent of the advisor.

#### MATH 655. Complex Analysis (3)

Prerequisites: MATH 501, 455. Topics covered incluyde the general Cauchy theorem, power series and analytic continuation, series and product expansions, conformal mapping and the Dirichlet problem.

#### MATH 661 ABC. Advanced Topics in Algebra, Number Theory and Discrete Mathematics (3-3-3)

Prerequisite: Consent of instructor. Advanced topics not covered in the previous classes on the subject. Part A covers topics in algebra, Part B covers topics in number theory, and Part C covers other topics in discrete mathematics. May be repeated with the consent of the advisor.

#### MATH 680A/B. Applied Functional Analysis (3-3)

Prerequisites: MATH 501, 552. This 2-semester sequence gives an introduction to Banach and Hilbert spaces and their applications. Fixed Point Theorems and their applications to differential and integral equations and variational principles. Adjoint and self-adjoint operators and spectral theory of linear operators. MATH 680A is a prerequisite for MATH 680B.

#### MATH 697A-C. Directed Comprehensive Studies (1-3)

No course description.

#### MATH 698A-C. Thesis or Graduate Project (1-3)

No course description.

#### MATH 699A-F. Independent Study (1-6)

See Independent Study under courses of study.