## Mathematics CoursesMATH 110 Mathematics in our World 4 hours Quantitative literacy plays an important role in an increasing number of professional fields, as well as in the daily decision-making of informed citizens in our changing society. This course is designed to improve students' quantitative reasoning and problem-solving skills by acquainting them with various real-world applications of mathematical reasoning, such as fair division, voting and apportionment, graph theory, probability, statistics, the mathematics of finance, check digits and coding, and geometry. This course is recommended for students who wish to take a non-calculus-based mathematics class as they prepare for their lives as informed members of a larger world. Prerequisite: high school algebra. (Quant) MATH 115 Introduction to Statistics 4 hours The course uses data sets from the social and natural sciences to help students understand and interpret statistical information. Computer software is used to study data from graphical and numerical perspectives. Topics covered include descriptive statistics, correlation, linear regression, contingency tables, probability distributions, sampling methods, confidence intervals, and tests of hypotheses. This class does not count towards the mathematics major or minor or the mathematics/statistics major. Students who earn credit for BIO 256, MGT 150, PSYC 350, or SOC 350 may not earn credit for MATH 115. Prerequisite: high school algebra. (Quant) MATH 123 Mathematics for Elementary School Teachers 4 hours This course provides pre-service K–8 teachers a strong foundation in the mathematics content areas as described in the NCTM's Principles and Standards for School Mathematics. The content standards include: Numbers and Operations, Algebra, Geometry, and Measurement. This course will engage students in standards-based mathematics learning to prepare them for the pedagogical practices they will learn in EDUC 325. Prerequisite: one year of high school algebra, one year of high school geometry and admission into the teacher education program. Corequisite: EDUC 325, EDUC 326. (Quant) MATH 139, 239, 339, 439 Special Topics Credit arr. MATH 140 Precalculus with Derivatives 4 hours MATH 140 and 141 cover all the material in MATH 151; Calculus I, while concurrently reviewing precalculus material. Algebraic and graphical representations of functions including: polynomial, rational, exponential, and logarithmic; techniques of solving equations and inequalities; modeling with various functions. An introduction to calculus concepts such as instantaneous rates of change: limits, derivatives; continuity; applications of derivatives. Graphing calculator use may be required. Prerequisite: a suggested placement. (Quant) MATH 141 Calculus I with Algebra and Trigonometry 4 hours Continuation of topics of MATH 140: trigonometric functions, derivatives, chain rule, the mean value theorem, Riemann sum approximation for integrals, definite integrals, antiderivatives, and applications. Graphing calculator use may be required. (Students who earn credit for MATH 141 may not earn credit for MATH 151.) Prerequisite: MATH 140. (Quant) MATH 151 Calculus I 4 hours Topics related to instantaneous rates of change: functions, limits, continuity, derivatives, mean value theorem and applications; antiderivatives and definite integrals. Graphing calculator use may be required. (Students who earn credit for MATH 151 may not earn credit for MATH 140 or 141.) Prerequisites: three years of high school mathematics including algebra, trigonometry, and geometry, and a suggested placement. (Quant) MATH 152 Calculus II 4 hours Applications of the definite integral, techniques of integration, differential equations, power series, Taylor series, and an introduction to computer algebra systems. Prerequisite: MATH 141 or 151 or consent of instructor. (Quant) MATH 185 First-Year Seminar 4 hours A variety of seminars for first-year students offered each January Term. MATH 220 Discrete Structures 4 hours The basic topics of discrete mathematics are covered in this course: propositional and predicate logic, methods of proof, induction, recursion and recurrence relations, sets, cardinality, combinatorics, binary relations (including equivalence relations and partial orderings) and functions. Prerequisite: MATH 152 or above; or CS 150 or 160; or consent of instructor. (Quant, W) MATH 240 Linear Algebra 4 hours Theory, computation, abstraction, and application are blended in this course, giving students a sense of what being a mathematics major is all about. Assignments will include computations to practice new techniques and proofs to deepen conceptual understanding. This course starts by solving systems of linear equations, views matrices as linear transformations between Euclidean spaces of various dimensions, makes connections between algebra and geometry, and then extends the theory to more general spaces. Topics include matrix algebra, vector spaces and subspaces, linear independence, determinants, bases, eigenvalues, eigenvectors, orthogonality, and inner product spaces. Prerequisite: MATH 152, or consent of instructor. (Quant, W) MATH 253 Vector Calculus 4 hours The tools of calculus are developed for real-valued functions of several variables: partial derivatives, tangent planes to surfaces, directional derivatives, gradient, maxima and minima, double and triple integrals, and change of variables. Ventor-valued functions are also studied: tangent and normal vectors to curves in space, arc length, vector fields, divergence and curl. The fundamental theorem of calculus is extended to line and surface integrals, resulting in the theorems of Green, Stokes, and Gauss, which have applications to heat conduction, gravity, electricity and magnetism. Prerequisite: MATH 240. (Quant) MATH 258 Chaotic Dynamical Systems 4 hours Why is it so difficult to make accurate predictions about seemingly chaotic physical systems like weather? This course explores the behavior of nonlinear dynamical systems described by iterated functions. A variety of mathematical methods, including computer modeling, is used to show how small changes in initial conditions can drastically change the future behavior of the system. Topics will include periodic orbits, phase portraits, bifurcations, chaos, symbolic dynamics, fractals, Julia sets, and the Mandelbrot set. Offered alternate years. Prerequisite: MATH 240. (Quant) MATH 260 Elementary Number Theory 4 hours Fibonacci numbers, divisibility theory in the integers, prime numbers, Euclidean algorithm, Diophantine equations, congruences, divisibility tests, Euler's theorem, public key cryptography. Usually offered in alternate January terms. Prerequisites: MATH 220 or 240. (Quant) MATH 285/295 Directed Study 2, 4 hours An opportunity to pursue individualized or experiential learning with a faculty member, at the sophomore level or above, either within or outside the major. MATH 285 can be taken only during January Term, MATH 295 can be taken during the fall, spring, or summer terms. MATH 285 cannot be counted toward the mathematics minor. Prerequisite for MATH 285: MATH 240. MATH 321 Probability and Statistics I 4 hours Axioms and laws of probability, conditional probability, combinatorics, counting techniques, independence, discrete and continuous random variables, mathematical expectation, discrete probability distributions, continuous probability distributions, functions of random variables, joint probability distributions and random samples, statistics and their distributions, central limit theorem, distribution of a linear combination of random variables. Prerequisite: MATH 152. (Quant) MATH 322 Probability and Statistics II 4 hours Sampling distribution of mean, standard deviation and proportion, theory of estimation, methods of point estimation, hypothesis testing, large and small sample confidence intervals, inferences for means, proportions and variances. Distribution free procedures. Prerequisite: MATH 321. (Quant) MATH 327 Applied Statistics I 4 hours Regression Analysis: Least square estimates, simple linear regression, multiple linear regression, hypothesis testing and confidence intervals for linear regression models, prediction intervals, and ANOVA. Model diagnostics including tests of constant variance assumptions, serial correlation, and multicollinearity. Time series: Linear time series, moving average, autoregressive and ARIMA models. Estimation and forecasting. Forecast errors and confidence intervals. Prerequisite: college-level statistics course. (Quant, W) MATH 328 Applied Statistics II 4 hours Design and analysis of experiments; analysis of variance techniques; fixed, random, and mixed models; repeated measures. Prerequisite: MATH 327. (Quant, W) MATH 351 Ordinary Differential Equations 4 hours Differential equations is an area of theoretical and applied mathematics in which there are a large number of important problems associated with the physical, biological, and social sciences. Analytic (separation, integration factors, and Laplace transforms), qualitative (phase and bifurcation diagrams), and numerical (Runge-Kutta) methods are developed for linear and nonlinear first- and higher-order single equations as well as linear and nonlinear systems of first-order equations. Emphasis is given to applications and extensive use of a computer algebra system. Prerequisite: MATH 240. (Quant) MATH 365 Geometry 4 hours The course follows the historical development of geometry, including the important question of which parallel postulate to include. This is a proof-oriented course focusing on theorems in plane Euclidean and hyperbolic geometry, with some mention of elliptic geometry. We examine the development of a lean set of axioms (incidence, betweenness, congruence, continuity) and investigate which theorems about points and lines can be derived using them. Prerequisites: MATH 220, MATH 240. (Quant) MATH 380 Internship Credit arr. On-the-job learning experience. The plan must be presented for departmental approval before the experience begins. MATH 395 Independent Study 1, 2, or 4 hours MATH 452 Partial Differential Equations 4 hours An introduction to initial and boundary value problems associated with certain linear partial differential equations (Laplace, heat, and wave equations). Fourier series methods, including the study of best approximation in the mean and convergence, will be a focus. Sturm-Liouville problems and associated eigenfunctions will be included. Numerical methods, such as finite difference, finite element, and finite analytic, may be introduced, including the topics of stability and convergence of numerical algorithms. Extensive use of a computer algebra system. Prerequisite: MATH 351 or consent of instructor. (Quant) MATH 454 Principles of Real Analysis 4 hours This course studies functions of a real variable and examines the foundations of calculus, with an emphasis on writing rigorous analytical proofs, and follows the historical development of analysis from Newton and Leibniz through Lagrange, Cauchy, Bolzano, Weierstrass, Cantor, Riemann, and Lebesgue. Topics include the topology of the reals, sequences, series, limits, continuity, pointwise and uniform convergence, differentiation, Taylor series, and integration. Prerequisites: MATH 220, MATH 240. (Quant, W) MATH 456 Functions of a Complex Variable 4 hours What happens when calculus is extended to functions of a complex variable? Geometry and analysis combine to produce beautiful theorems and surprising applications. Topics include complex numbers, limits and derivatives of complex functions, Cauchy-Riemann equations, harmonic functions, contour integrals, the Cauchy integral formula, Taylor and Laurent series, residues, and conformal mappings with applications in physical sciences. Offered in alternate years. Prerequisite: MATH 253. (Quant) MATH 459 Topology 4 hours What properties of a space are preserved by a continuous transformation? Point-set topology uses the concept of an "open set" to extend the definition of continuity to many different spaces. Topics may include the order, metric, product, and subspace topologies; limit points, connectedness, compactness, countability axioms, separation axioms, the Urysohn lemma, and the Urysohn metrization theorem. Usually offered in alternate January terms. Prerequisites: MATH 220, 240. (Quant) MATH 462 Numerical Analysis 4 hours Numerical analysis is a blend of computational methods and mathematical analysis of their convergence, accuracy, and stability. Topics include roots of equations and solutions of systems of linear equations, function interpolation and approximation, numerical differentiation and integration, optimization, and numerical solutions of ordinary and partial differential equations. Offered in alternate years. Prerequisites: MATH 240, CS 150. (Quant) MATH 471 Abstract Algebra I 4 hours Real numbers and integers satisfy many nice properties under addition and multiplication, but other sets behave differently: matrix multiplication and composition of functions are noncommutative operations. Which properties (associativity, commutativity, identity, inverses) are satisfied by operations on sets determine the basic algebraic structure: group, ring, or field. The internal structure, (subgroups, cosets, factor groups, ideals), and operation-preserving mappings between sets, (isomorphisms, homomorphisms), are examined. Emphasis is on theory and proof, although important applications in symmetry groups, cryptography, and error-correcting codes may also be covered. Prerequisites: MATH 220, MATH 240. (Quant, W) MATH 472 Abstract Algebra II 1, 2, or 4 hours Topics may include simple groups, Sylow theorems, divisibility in integral domains, generators and relations, field extensions, splitting fields, solvability by radicals, Galois theory, symmetry, and geometric constructions. Offered on demand. Prerequisite: MATH 471. (Quant) MATH 490 Senior Project 1, 2, or 4 hours MATH 493 Senior Honors Project 4 hours A yearlong independent research project. Applications are completed on the Honors Program form available at the registrar's office, requiring the signatures of a faculty supervisor, the department head, the honors program director, and the registrar. Interdisciplinary projects require the signatures of two faculty supervisors. The project must be completed by the due date for senior projects. The completed project is evaluated by a review committee consisting of the faculty supervisor, another faculty member from the major department, and a faculty member from outside the major department. All projects must be presented publicly. Only projects awarded an "A-" or "A" qualify for "department honors" designation. The honors project fulfills the all-college senior project requirement. |