Sets, numeration systems, relations and their properties whole numbers, integers, rational numbers, real numbers.  For elementary education majors.  Not intended as a preparation for calculus.  Prerequisite: a year of high school algebra and a year of high school geometry. (Fall) (TOP)

Functions and relations, graphs, equations and inequalities, polynomials, geometric topics, introduction to the metric system, the nature of mathematics and its relation to other fields of knowledge.  Not intended as a preparation for calculus.  Prerequisite: 121, or consent of instructor. (Spring) (TOP)

An introduction to topics chosen from set operation, counting techniques, probability, linear programming, matrix algebra, game theory, statistics, mathematics of finance, and computer programming.  Recommended for students who wish to take a mathematics course at the pre-calculus level, with emphasis on current applications in the social sciences, business, and life sciences.   Prerequisite: high school algebra.  (Fall, Spring) (TOP)

Algebraic and graphical representations of functions: polynomial, logarithmic; techniques of solving equations and inequalities; modeling; introduction to instantaneous rates of change:  limits, derivatives of polynomial functions.  (Students who earn credit for 130 may not earn credit for 23.)   (Fall) (TOP)

Continuation of topics of Math 19 to trigonometric functions and their derivatives; applications; continuity.  (Students who earn credit for 140 may not earn credit for 131.)  (J-Term) (TOP)

Algebraic and graphical representations of functions: polynomial, exponential, logarithmic, and trigonometric; techniques of solving equations and inequalities; modeling; introduction to instantaneous rates of change: limits, derivatives with applications; continuity.  Graphing calculator use is required.  (Students who earn credit for 140 may not earn credit for 130 and 131.)   (Fall) (TOP)

Continuation of derivative topics of Math 131 or 140: chain rule, the mean value theorem; Riemann sum approximating integrals; anti-derivatives; applications.  (Students who earn credit for 141 may not earn credit for 151.)  (Spring) (TOP)

Topics related to instantaneous rates of change: functions, limits, continuity, derivatives, anti-derivatives, definite integrals, the mean value theorem, applications.  Graphing calculator use is required.   Prerequisite: a minimum of 1-1/2 years of algebra, 1/2 year of trigonometry, 1 year of geometry.  (Fall, Spring) (TOP)

Applications of the definite integral, techniques of integration, parametric equations, series, approximations, differential equations, introduction to computer algebra systems.  Prerequisite: 151.  (Fall, Spring) (TOP)

Matrices, abstract vector spaces, subspaces, spanning sets, linear independence, bases, linear transformations, isomorphisms, eigenvalues and eigenvectors, inner product spaces.  Prerequisite: 152, or consent of instructor.  (Fall, Spring) (TOP)

Analytic tools useful to management: linear programming, sensitivity analysis, duality; integer linear programming; goal programming; dynamic programming; networks, PERT-CPM, maximum flow, shortest path; simulation.   Offered alternate years.  Prerequisite: 151. (Same as Management 235.) (January) (TOP)

Theory and problems from the topics of formal logic systems (propositional and predicate logic), methods of proof, recursion and recurrence relations, mathematical induction, analysis of algorithms, sets and combinatorics, relations (including equivalence relations, partial order relations and chains) and functions, boolean algebra and computer logic, groups and error detecting/correcting codes, finite state machines.  Prerequisite: 151, computer science 28, or consent of instructor.  (Same as computer science 245.) (Spring) (TOP)

Vector valued functions: limits, continuity, derivatives, and integrals.  Length of space curves, tangents and normals to curves.   Functions of several variables: limits, continuity, partial derivatives, directional derivatives, the gradient, tangent plane approximation and differentials, extreme value, multiple integrals, vector fields, line integrals, Green's theorem, surface integrals, Strokes' theorem, the divergence theorem.  Prerequisite: 240. (Spring) (TOP)

An introduction to first and second order differential equations, existence and uniqueness theorems, higher order linear differential equations, Laplace transforms, power series solutions, boundary value problems, systems of linear differential equations, and applications in the physical, biological, and social sciences.  Prerequisite: 240.  (Fall) (TOP)

Axioms and laws of probability, independence, conditional probability, combinatorics, discrete and continuous random variables, mathematical expectation, central limit theorem, descriptive statistics, confidence intervals. Prerequisite: 152.  (Fall) (TOP)

Sampling distribution theory, theory of estimation and hypothesis testing, confidence intervals, inferences for means and proportions, correlation and regression, chi-square tests  Prerequisite: 321.  (Spring) (TOP)

Elements of Euclidean and non-Euclidean geometries: incidence, betweenness, separation, congruence, and parallel postulates.   Geometry of physical space.  A proof oriented course.  Prerequisite: 240, 245.  (Fall) (TOP)

The mathematics of real functions, emphasizing rigorous analytical proofs.  The real number system, topology of metric spaces, sequences and series, limit of a function, continuity, differentiation, and the theory of the integral.  Prerequisite: 240, 245.  (Spring) (TOP)

Roots of equations and solutions of systems of linear equations, interpolation and approximation, differences and numerical integration, and numerical solutions of ordinary differential equations.  Offered in alternate years.  Prerequisite: 240.  (Same as computer science 462.) (Spring) (TOP)

A course in applied statistics emphasizing analysis of variance techniques.  Single and multi-factor experiments, fixed and random effects models, randomized block designs, repeated measures, nested designs, Latin Squares, analysis of covariance, and multiple comparisons.  This course applies only toward the mathematics/statistics major.  Prerequisite: a college-level statistics course.  (Same as psychology 63.) (Spring) (TOP)

Analytic functions, integration, series, contour integration, analytic continuation, conformal mapping, boundary value problems, integral transforms, applications in continuum mechanics.  Offered in alternate years.   Prerequisite: 253.  (Spring) (TOP)

Metric spaces, general topological properties, separation axioms, connectivity, compactness, product spaces, quotient spaces, local properties.  Prerequisite: 240, 245.  (January) (TOP)

Introduction to the basic structures of abstract algebra: groups and morphisms of groups, rings, integral domains, fields, Euclidean domains, unique factorization, polynomial rings.  Prerequisite: 240, 245.  (Fall) (TOP)

Topics chosen from: 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 in alternate years.  Prerequisite: 471.  (Spring) (TOP)

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