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Mathematics Course Descriptions More information about course groupings, academic requirements, available majors, and sample curriculum can be found in the Undergraduate Bulletin of Information. MATH 10005. Processes of Mathematical Thought For students in arts and letters or business administration. A study of mathematical thought as an analytical tool to solve real-life problems. The class is divided into teams, each analyzing a topic from such areas as commercial games, consensus within diversity, governmental economic planning, and chaos theory. Teams will present their findings in a seminar format. MATH 10015. Mathematical Way of Thinking Topics in undergraduate mathematics. MATH 10110. Principles of Finite Mathematics For students in arts and letters. For first-year students who lack the necessary background for MATH 10120. (Students who take this course cannot take MATH 10120. Topics include the fundamental principles of counting systematically, probability, statistics, linear programming, optimization problems, game theory and mathematical finance, population problems, and coding information. There is a wealth of applications of these topics to contemporary social, economic, and political issues appealing to liberal arts students. Also, these topics broaden a student's mathematical horizon in an interesting direction not covered by calculus, which deals mostly with continuous models. MATH 10120. Finite Mathematics For students in arts and letters or as an elective for students in business administration. Topics include the fundamental principles of counting systematically, probability, statistics, linear programming, optimization problems, game theory, and mathematical finance. Other topics that may be covered include population problems, difference equations and modeling, and coding information. There is a wealth of applications of these topics to contemporary social, economic, and political issues appealing to liberal arts students. Also, these topics broaden a student's mathematical horizon in an interesting direction not covered by calculus, which deals mostly with continuous models. MATH 10130. Beginning Logic For students in arts and letters. Provide the students with some formal tools for analyzing arguments. By writing proofs in a formal system, students see the importance of stating the basic premises in an argument and giving intermediate steps that lead to the conclusion. They learn strategies for thinking up proofs. They see that proof checking is, in principle, something that a machine could do. Students learn truth tables and see an effective procedure that they could apply to any argument stated in propositional logic, to determine whether the conclusion follows logically from the premises. There is nothing like truth tables for predicate logic. Students get to experience doing what mathematicians do, trying to determine whether a particular conclusion follows from some premises by searching simultaneously for a proof or a counterexample. Writing papers gives students an opportunity to explore other topics in logic of their interest. MATH 10140. Introduction to Statistics This course is aimed to those students who may or may not plan to use statistics in their chosen careers, but wish nevertheless to become informed and astute consumers. Topics include: statistical decision making, sampling, data representation, random variables, least square regression lines, elementary probability theory, conditional probabilities, independence, and Bayes' rule. The methodology will focus on a "hands-on" approach, with use of computer simulation and representation. Concepts and terminology will be introduced only after thorough exposure to situations that necessitate the concepts and terms. Care will be exercised to select a variety of situations from the many fields where statistics are used in modern society. Examples will be taken from biology and medicine (e.g., drug testing, wild animal counts), the social sciences, psychology, and economics. MATH 10240. Principles of Calculus For students in arts and letters. Note: Credit is not given for both this course and any other calculus course. A terminal course introducing the principles of calculus. Topics include basic properties of functions, derivatives and integrals, with interesting real-life applications throughout. This course is not intended to prepare students for more advanced work in calculus. MATH 10250. Elements of Calculus I For students in arts and letters, architecture, or business. A study of basic calculus as part of a liberal education. It emphasizes conceptual learning and stresses the connections between mathematics and modern society. Topics include functions, limits, derivatives, and an introduction to integral, with interesting real-life applications throughout. Students are familiarized with the many different interpretations of the derivative as a rate of change, and the integral as a total rate of change. This enables them to learn and practice modeling in a variety of situations from economics the social and the life sciences. MATH 10260. Elements of Calculus II for Business Prerequisite: (MATH 10250 OR MATH 105) OR (MATH 10350 OR MATH 119 OR MATH 119A OR MATH 119B OR MATH 119C OR MATH 119E OR MATH 119F OR MATH 119G) OR (MATH 10550 OR MATH 125 OR MATH 125A OR MATH 125B OR MATH 125C OR MATH 125E OR MATH 125F) OR (MATH 10850 OR MATH 165) Credit is not given for both MATH 10280 and either of the following courses: MATH 10260 and MATH 10360. For students in business. An introduction to mathematical concepts, techniques, and ideas that are useful in understanding and solving problems that arise in economics and business. Most mathematical concepts are introduced through interesting business problems. Furthermore, by using available computer technology, real-life problems, that may lead to non-trivial computations and graphics,are considered. Topics include integration, differential equations, Taylor polynomial approximations, unconstrained and constrained optimization for functions of several variables, probability and statistics, with interesting real-life applications throughout. MATH 10270. Elementary Calculus in Action Prerequisite: (MATH 10250 OR MATH 105) OR (MATH 10550 OR MATH 125 OR MATH 125A OR MATH 125B OR MATH 125C OR MATH 125E OR MATH 125F) OR (MATH 10850 OR MATH 165) A second calculus course for Arts and Letters and Architecture students. This course uses typical mathematical strategies of elementary calculus and shows these "in action" with studies of the suspension bridge, various nuclear clocks, growth patterns of human and bacterial populations, the dynamics of money, and basic economics. MATH 10350. Calculus A Corequisite: MATH 12350 Primarily for students in science whose programs require a one-year terminal course in calculus of one variable but also open to students in arts and letters. Topics include sets, functions, limits, continuity, derivatives, integrals, and applications. MATH 10360. Calculus B Prerequisite: (MATH 10350 OR MATH 119 OR MATH 119A OR MATH 119B OR MATH 119C OR MATH 119E OR MATH 119F OR MATH 119G) OR (MATH 10550 OR MATH 125 OR MATH 125A OR MATH 125B OR MATH 125C OR MATH 125E OR MATH 125F) OR (MATH 10850 OR MATH 165) Corequisite: MATH 12360 Primarily for students in science whose programs require a one-year terminal course in calculus of one variable but also open to students in arts and letters. Topics include sets, functions, limits, continuity, derivatives, integrals, and applications. MATH 10450. Honors Mathematics I Corequisite: MATH 12450 A survey of several mathematical topics, emphasizing the relevance of mathematics to many diverse areas of study. Calculus is also studied at the level of MATH 10350-10360. MATH 10460. Honors Mathematics II Prerequisite: (MATH 10450 OR MATH 195) Corequisite: MATH 12460 A survey of several mathematical topics, emphasizing the relevance of mathematics to many diverse areas of study. Calculus is also studied at the level of MATH 10350-10360. MATH 10550. Calculus I Corequisite: MATH 12550 For students in science and engineering. Topics include sets, functions, limits, continuity, derivatives, integrals, and applications. Also covered are transcendental functions and their inverses, infinite sequences and series, parameterized curves in the plane, and polar coordinates. MATH 10560. Calculus II Prerequisite: (MATH 10550 OR MATH 125 OR MATH 125A OR MATH 125B OR MATH 125C OR MATH 125E OR MATH 125F) OR (MATH 10850 OR MATH 165) Corequisite: MATH 12560 For students in science and engineering. Topics include sets, functions, limits, continuity, derivatives, integrals, and applications. Also covered are transcendental functions and their inverses, infinite sequences and series, parameterized curves in the plane, and polar coordinates. MATH 10850. Honors Calculus I Corequisite: MATH 12850 Required of honors mathematics majors. A rigorous course in differential and integral calculus of one variable. Topics include an axiomatic formulation of the real numbers, mathematical induction, infima and suprema, functions, continuity, derivatives, integrals, infinite sequences and series, transcendental functions and their inverses, and applications. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject. MATH 10860. Honors Calculus II Prerequisite: (MATH 10850 OR MATH 165) Corequisite: MATH 12860 Required of honors mathematics majors. A rigorous course in differential and integral calculus of one variable. Topics include an axiomatic formulation of the real numbers, mathematical induction, infima and suprema, functions, continuity, derivatives, integrals, infinite sequences and series, transcendental functions and their inverses, and applications. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject. MATH 12350. Calculus A Tutorial Corequisite: MATH 10350 Perfecting problem-solving skills in smaller group settings. MATH 12360. Calculus B Tutorial Corequisite: MATH 10360 Perfecting problem-solving skills in smaller group settings. MATH 12450. Honors Mathematics Tutorial Corequisite: MATH 10450 Perfecting problem-solving skills in smaller group settings. MATH 12460. Honors Mathematics II Tutorial Corequisite: MATH 10460 Perfecting problem-solving skills in smaller group settings. MATH 12550. Calculus I Tutorial Corequisite: MATH 10550 Perfecting problem-solving skills in smaller group settings. MATH 12560. Calculus II Tutorial Corequisite: MATH 10560 Perfecting problem-solving skills in smaller group settings. MATH 12850. Honors Calculus I Tutorial Corequisite: MATH 10850 Perfecting problem-solving skills in smaller group settings. MATH 12860. Honors Calculus II Tutorial Corequisite: MATH 10860 Perfecting problem-solving skills in smaller group settings. MATH 13150. First Year Math Seminar The goal of this new course is to give students a panoramic view of mathematics by considering a variety of topics displaying its enormous power and beauty. It aspires to present the first year students with an opportunity to participate in the excitement of discovering ideas of their own by practicing the mathematical way of thinking. This topical course will be rich, in content and context. It will stress the connections between mathematics and modern society by considering a wide variety of problems ranging from environmental and economic issues to social and political situations that can be modeled and solved by mathematical means. Also by giving appropriate assignments and projects, it will allow students to make contributions in areas of their interest and expertise."The Magic of Numbers" is the first theme of this seminar course. MATH 20210. Computer Programming and Problem Solving Prerequisite: (MATH 20610 OR MATH 221) OR (MATH 20580 OR MATH 228) An introduction to solving mathematical problems using computer programming in high-level languages such as C. MATH 20340. Introduction to Statistics Prerequisite: (MATH 10360 OR MATH 120 OR MATH 120A OR MATH 120B OR MATH 120C OR MATH 120E OR MATH 120F OR MATH 120G OR MATH 120H) OR (MATH 10560 OR MATH 126 OR MATH 126A OR MATH 126B OR MATH 126C OR MATH 126E OR MATH 126F) An introduction to the principles of statistical inference following a brief introduction to probability theory. This course does not count as a science or mathematics elective for mathematics majors. NOTE: Students may not take both BIOS 40411 (411) and MATH 20340 (214). Not open to students who have taken MATH 30540 (324). MATH 20550. Calculus III Prerequisite: (MATH 10560 OR MATH 126 OR MATH 126A OR MATH 126B OR MATH 126C OR MATH 126E OR MATH 126F) OR (MATH 10860 OR MATH 166) Corequisite: MATH 22550 A comprehensive treatment of differential and integral calculus of several variables. Topics include space curves, surfaces, functions of several variables, partial derivatives, multiple integrals, line integrals, surface integrals, Stokes theorem, and applications. MATH 20570. Mathematical Methods in Physics I Prerequisite: (MATH 10560 OR MATH 10860 OR MATH 126 OR MATH 126A OR MATH 126B OR MATH 126C OR MATH 126E OR MATH 126F) Corequisite: MATH 22570 A study of methods of mathematical physics. Topics include matrices, linear algebra (including matrices and determinants), vector and tensor analysis, vector calculus, curvilinear coordinates, series, ordinary differential equations, partial differential equations, orthogonal functions and vector spaces, special functions (including Bessel, Legendre, and Hermite), calculus of variations, Fourier series, and group theory. Weekly tutorial sessions. Cross-listed with PHYS 20451 (271). MATH 20580. Introduction to Linear Algebra and Differential Equations Prerequisite: (MATH 20550 OR MATH 225 OR MATH 225A OR MATH 225B OR MATH 225C OR MATH 225E) Corequisite: MATH 22580 An introduction to linear algebra and to first-and second-order differential equations. Topics include elementary matrices, LU factorization, QR factorization, the matrix of a linear transformation, change of basis, eigenvalues and eigenvectors, solving first-order differential equations and second-order linear differential equations, and initial value problems. This course is part of a two-course sequence that continues with Math 30650 (325). Credit is not given for both Math 20580 (228) and Math 20710 (221). MATH 20610. Linear Algebra Open to all students. An introduction to vector spaces, matrices, linear transformations, inner products, determinants and eigenvalues. Emphasis is given to careful mathematical definitions and understanding the basic theorems of the subject. Credit is not given for both MATH 20710 (221) and MATH 20580 (228). MATH 20630. Introduction to Mathematical Reasoning Prerequisite This course serves as a transition to upper-level math courses. The general subject is numbers of all sorts-integers, rationals, reals, etc. The main point will be to treat everything the way a mathematician would. That is, we will give precise definitions of the objects we consider and careful statements of the assertions we make about them. And, most importantly, we will justify our assertions by giving mathematical proofs. Topics covered include basic language of sets, common methods of proof, integers, factorization, modular arithmetic, rational numbers, completeness, real numbers, cardinality, limits, and continuity. MATH 20670. Mathematical Methods in Physics II A study of methods of mathematical physics. Topics include linear algebra (including matrices and determinants), vector and tensor analysis, vector calculus, curvilinear coordinates, series, ordinary differential equations, partial differential equations, orthogonal functions and vector spaces, special functions (including Bessel, Legendre, and Hermite), calculus of variations, Fourier series, and group theory. Weekly tutorial sessions. MATH 20750. Ordinary Differential Equations Corequisite: MATH 22750 An introduction to differential equations. Topics include first-order equations, n-th order linear equations, power series methods, systems of first order linear equations, non-linear systems and stability. Credit is not given for both MATH 20750 (230) and MATH 30650 (325). MATH 20810. Honors Algebra I A comprehensive treatment of vector spaces, linear transformations, inner products, determinants, eigenvalues, tensor and exterior algebras, spectral decompositions of finite-dimensional symmetric operators, and canonical forms of matrices. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject. MATH 20820. Honors Algebra II Prerequisite: (MATH 20810 OR MATH 261) A comprehensive treatment of vector spaces, linear transformations, inner products, determinants, eigenvalues, tensor and exterior algebras, spectral decompositions of finite-dimensional symmetric operators, and canonical forms of matrices. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject. MATH 20850. Honors Calculus III Prerequisite: (MATH 10860 OR MATH 166) Corequisite: MATH 22850 Required of honors mathematics majors. A rigorous course in differential and integral calculus of several variables. Topics include functions of several variables, the inverse function theorem, partial derivatives, multiple integrals, line integrals, surface integrals, Stokes' theorem, an introduction to ordinary differential equations and applications. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject. MATH 20860. Honors Calculus IV Prerequisite: (MATH 20850 OR MATH 265) Corequisite: MATH 22860 Required of honors mathematics majors. A rigorous course in differential and integral calculus of several variables. Topics include functions of several variables, the inverse function theorem, partial derivatives, multiple integrals, line integrals, surface integrals, Stokes' theorem, an introduction to ordinary differential equations and applications. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject. MATH 22550. Calculus III Tutorial Corequisite: MATH 20550 Perfecting problem-solving skills in smaller group settings. MATH 22570. Mathematical Methods in Physics I Tutorial Corequisite: MATH 20570 Perfecting problem-solving skills in smaller group settings. MATH 22580. Linear Algebra and Differential Equations Tutorial Corequisite: MATH 20580 Perfecting problem-solving skills in smaller group settings. MATH 22670. Mathematical Methods in Physics II Tutorial A study of methods of mathematical physics. Topics include linear algebra (including matrices and determinants), vector and tensor analysis, vector calculus, curvilinear coordinates, series, ordinary differential equations, partial differential equations, orthogonal functions and vector spaces, special functions (including Bessel, Legendre, and Hermite), calculus of variations, Fourier series, and group theory. Weekly tutorial sessions. MATH 22750. Oridinary Differential Equations Tutorial Corequisite: MATH 20750 Perfecting problem-solving skills in smaller group settings. MATH 22850. Honor Calculus III Tutorial Corequisite: MATH 20850 Perfecting problem-solving skills in smaller group settings. MATH 22860. Honors Calculus IV Tutorial Corequisite: MATH 20860 Perfecting problem-solving skills in smaller group settings. MATH 30210. Introduction to Operations Research Prerequisite: (MATH 20580 OR MATH 228 OR MATH 228A OR MATH 228B OR MATH 228C) OR (MATH 20610 OR MATH 221) OR (MATH 20750 OR MATH 230) OR (MATH 20810 OR MATH 261) An introduction to linear programming, duality theory, simplex algorithm, the transportation problem, network analysis, dynamic programming and game theory. MATH 30390. Introduction to Numerical Methods Prerequisite: (MATH 20210 OR MATH 211) OR (CSE 20232 OR CSE 232) An introduction to numerical methods for solving algebraic and differential equations. Topics include numerical solution of systems of linear equations, approximating functions with polynomials and splines, solutions of nonlinear equations, numerical integration, numerical solution of ordinary differential equations and eigenvalue problems. Some computer programming is required. Credit is not given for both MATH 30390 (318) and MATH 40390 (423). MATH 30440. Probability and Statistics An introduction to the theory of probability and statistics, with applications to the computer sciences and engineering. Topics include discrete and continuous random variables, joint probability distributions, the central limit theorem, point and interval estimation and hypothesis testing. MATH 30530. Introduction to Probability Prerequisite: (MATH 20850 OR MATH 265) An introduction to the theory of probability, with applications to the physical sciences and engineering. Topics include discrete and continuous random variables, conditional probability and independent events, generating functions, special discrete and continuous random variables, laws of large numbers and the central limit theorem. The course emphasizes computations with the standard distributions of probability theory and classical applications of them. MATH 30540. Mathematical Statistics Prerequisite: (MATH 30530 OR MATH 323) An introduction to mathematical statistics. Topics include distributions involved in random sampling, estimators and their properties, confidence intervals, hypothesis testing including the goodness-of-fit test and contingency tables, the general linear model and analysis of variance. MATH 30650. Differential Equations Prerequisite: (MATH 20580 OR MATH 228 OR MATH 228A OR MATH 228B OR MATH 228C) OR (MATH 20750 OR MATH 230) A second course in differential equations. Topics include higher order linear equations, numerical methods, Laplace transforms, linear systems, non-linear systems and stability, and an introduction to partial differential equations and Fourier series. Credit is not given for both MATH 20750 (230) and MATH 30650 (325). MATH 30705. Algebraic Structures Prerequisite: (MATH 20610 OR MATH 221) OR (MATH 20810 OR MATH 261) An introduction to groups, rings and fields, homomorphisms, ideals, polynomial rings and extensions fields Emphasis is given to careful mathematical definitions and understanding the basic theorems of the subject. Prerequisite: (MATH 20630 OR MATH 223) OR (MATH 20610 OR MATH 221) An introduction to groups, rings and fields. Topics include permutations, divisibility, modular arithmetic, cryptography, cyclic and dihedral groups, Lagrange's theorem, homomorphisms, ideals, integral and Euclidean domains, extension fields. MATH 30745. Real Analysis I Prerequisite: (MATH 20850 OR MATH 265) AND (MATH 30705 OR MATH 222) A precise treatment of fundamentals of differential and integral calculus. Topics include sequences, limits, continuity, differentiability, convergence of sequences of functions, infinite series, and the Riemann-Stieltjes integral. Emphasis is given to careful mathematical definitions and understanding the basic theorems of the subject. MATH 30750. Real Analysis Prerequisite: (MATH 20630 OR MATH 223) A rigorous treatment of differential and integral calculus. Topics include a review of sequences and continuity, differentiability, Taylor's theorem, integration, the fundamental theorem of Calculus, pointwise and uniform convergence, and power series. Additional topics are likely and will depend on the instructor. Emphasis throughout will be on careful mathematical definitions and thorough understanding of basic results. MATH 30755. Real Analysis II Prerequisite: (MATH 30745 OR MATH 335) A precise treatment of fundamentals of differential and integral calculus. Topics include sequences, limits, continuity, differentiability, convergence of sequences of functions, infinite series, and the Riemann-Stieltjes integral. Emphasis is given to careful mathematical definitions and understanding the basic theorems of the subject. MATH 30810. Honors Algebra III Prerequisite: (MATH 20820 OR MATH 262) A comprehensive treatment of groups, polynomials, rings, homomorphisms, isomorphism theorems, field theory, and Galois theory. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject. MATH 30820. Honors Algebra IV Prerequisite: (MATH 30810 OR MATH 361) Required of honors mathematics majors. A comprehensive treatment of groups, polynomials, rings, homomorphisms, isomorphism theorems, field theory, and Galois theory. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject. MATH 30850. Honors Analysis I Prerequisite: (MATH 20860 OR MATH 266) Required of honors mathematics majors. An advanced course in mathematical analysis in one and several variables. Topics include an axiomatic formulation of the real and complex number systems, compactness, connectedness, metric spaces, limits, continuity, infinite sequences and series, differentiation, the Riemann-Stieltjes integral, the Stone-Weierstrass theorem, the implicit function theorem, differential forms, partitions of unity, simplexes and chains, and Stokes' theorem. MATH 30860. Honors Analysis II Prerequisite: (MATH 30850 OR MATH 365) Required of honors mathematics majors. An advanced course in mathematical analysis in one and several variables. Topics include an axiomatic formulation of the real and complex number systems, compactness, connectedness, metric spaces, limits, continuity, infinite sequences and series, differentiation, the Riemann-Stieltjes integral, the Stone-Weierstrass theorem, the implicit function theorem, differential forms, partitions of unity, simplexes and chains, and Stokes' theorem.
MATH 40210. Basic Combinatorics An introduction to the theory of combinatorics. Topics include permutations, multinomial coefficients, the theory of enumerative combinatorics, pairing problems, recurrence relations, the inclusion-exclusion principle, graph theory, algebraic coding theory and symbolic dynamics. MATH 40390. Numerical Analysis Prerequisite: (MATH 20750 OR MATH 230) OR (MATH 20860 OR MATH 266) OR (MATH 30650 OR MATH 325) An introduction to the numerical solution of ordinary and partial differential equations. Topics include the finite difference method, projection methods, cubic splines, interpolation, numerical integration methods, analysis of numerical errors, numerical linear algebra and eigenvalue problems, and continuation methods. MATH 40480. Complex Variables Prerequisite: (MATH 20550 OR MATH 20850 OR MATH 225 OR MATH 225A OR MATH 225B OR MATH 225C OR MATH 225D OR MATH 225E OR MATH 265) An introduction to the theory of functions of one complex variable. Topics include analytic functions, Cauchy integral theorems, power series, Laurent series, poles and residues, applications of conformal mapping, and Schwarz-Christoffel transformations. MATH 40510. Intro to Algebraic Geometry Algebraic Geometry is the study of systems of polynomial equations and their vanishing loci. It has important components that lie in the realm of geometry, of algebra and of computation (among others) and countless applications. This course tries to give a flavor of these different aspects of the field and how they fit together. Indeed, much of the fascination of this subject comes from the myriad ways in which arguments squarely in one realm give surprising consequences that fall squarely in a different realm. MATH 40520. Number Theory Prerequisite: (MATH 30705 OR MATH 222) OR (MATH 20820 OR MATH 262) An introduction to elementary number theory. Topics include the Euclidean algorithm, congruencies, primitive roots and indices, quadratic residues, quadratic reciprocity, distribution of primes, and Waring's problem. MATH 40570. Mathematical Methods in Financial Economics Prerequisite: ( (MATH 30530 OR MATH 323) AND (MATH 20750 OR MATH 30650 OR MATH 226 OR MATH 230 OR MATH 325) AND (MATH 30750 OR MATH 30850 OR MATH 338 OR MATH 365) ) OR (FIN 30700) OR (FIN 70670) An introduction to financial economic problems using mathematical methods, including the portfolio decision of an investor and the determination of the equilibrium price of stocks in both discrete and continuous time, will be discussed. The pricing of derivative securities in continuous time including various stock and interest rate options will also be included. Projects reflecting students' interests and background are an integral part of this course. MATH 40710. Computability and Logic Prerequisite: (MATH 10560 OR MATH 126 OR MATH 126A OR MATH 126B OR MATH 126C OR MATH 126D OR MATH 126E OR MATH 126F OR MATH 10860 OR MATH 166) An introduction to formal notions of computability. Topics include finite automata, regular languages and expressions, pushdown automata, context-free grammars and languages, Turing machines, primitive recursive and ?-recursive functions, Church's Thesis, and absolutely unsolvable problems. MATH 40720. Topics in Algebra Prerequisite: (MATH 30705 OR MATH 222) OR (MATH 30820 OR MATH 362) Topics in algebra, number theory and algebraic geometry. MATH 40730. Mathematical Modeling Prerequisite: ( (MATH 20210 OR MATH 211) OR (CSE 20232 OR CSE 232) ) AND ( (MATH 30650 OR MATH 325) OR (MATH 20750 OR MATH 230) ) Introductory course on applied mathematics methods with emphasis on modeling of physical, mechanical and biological problems in terms of differential equations and stochastic dynamical systems. Students will be working in groups on several projects and will present them in class at the end of the course. Prerequisite: (MATH 20630 OR MATH 223) An introduction to topology. Topics include the theory of surfaces, knot theory, and the theory of metric spaces. MATH 40750. Partial Differential Equations Prerequisite: (MATH 20750 OR MATH 230) OR (MATH 30650 OR MATH 325) OR (MATH 30850 OR MATH 365) An introduction to partial differential equations. Topics include Fourier series, solutions of boundary value problems for the heat equation, wave equation and Laplace's equation, Fourier transforms, and applications to solving heat, wave and Laplace's equations in unbounded domains. MATH 40760. Differential Geometry Prerequisite: (MATH 20750 OR MATH 230) OR (MATH 20860 OR MATH 266) OR (MATH 30650 OR MATH 325) An introduction to differential geometry. Topics include analysis of curves and surfaces in space, the first and second fundamental forms of surfaces, torsion, curvature and the Gauss-Bonnet theorem. MATH 40960. Topics in Geometry The symmetry of a geometric figure may be described by an associated algebraic object called a group. This course will study the interplay of groups and symmetry in a variety of geometric situations. We will for example study the symmetry groups of figures like cubes, study the "braid group" which is related to classification of knots, examine the action of groups on trees, classify wall-paper patterns by their symmetry and classify the finite symmetries built up from the symmetries provided by mirrors (reflection groups). Prerequisites for the course will be minimal; familiarity with basic linear algebra and prior exposure to the notion of a group should suffice.
MATH 46800. Directed Readings Prerequisite: Consent of director of undergraduate studies in mathematics. Seniors in the mathematics program have the option of writing a senior thesis on a more advanced subject than is provided in the normal undergraduate courses. A program of readings on the topic must be begun with a faculty advisor by the spring semester of the junior year. MATH 50510. Computer Programming/ Problem Solving An introduction to solving mathematical problems using computer programming in high-level languages such as C. MATH 50570. Math Meth. in Fin. Econ. An introduction to financial economic problems using mathematical methods, including the portfolio decision of an investor and the determination of the equilibrium price of stocks in both discrete and continuous time, will be discussed. The pricing of derivative securities in continuous time including various stock and interest rate options will also be included. Projects reflecting students' interests and background are an integral part of this course. MATH 50590. Foundations of Computational Mathematics The course is a solid theoretical introduction to numerical analysis. Topics covered include polynomial interpolation, least squares, numerical integration, numerical linear algebra, and an introduction to numerical solutions of ordinary and partial differential equations. MATH 50730. Mathematical Modeling Introductory course on applied mathematics methods with emphasis on modeling of physical, mechanical, and biological problems in terms of differential equations and stochastic dynamical systems. Students will be working in groups on several projects and will present them in class at the end of the course. MATH 50780. Special Topics - Riemannian Geometry Differentiable Manifolds; Tangent Space; Vector Fields; Lie Bracket; One Parameter Groups; Riemannian Manifolds; Affine Connections; The Levi-Civita Connection; Lie Groups and Lie Algebras; Geodesics; The Geodesic Flow; The Curvature Tensor; Sectional Curvature; Ricci Curvature Tensor; Manifolds of Constant Curvature; Jacobi fields. The text of this course is: M. DoCarmo, Riemannian Geometry, Birkhauser, 1992. MATH 56800. Directed Readings Readings not covered in the curriculum that relate to the student's area of interest. MATH 58900. Thesis Direction Students in the Applied Mathematics Masters Program have the option of writing a thesis on an advanced subject under the direction of a faculty advisor. |
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