University Core Curriculum course including such topics as mathematical modeling, problem solving, geometrical concepts, growth patterns, and applications to the physical sciences, social sciences, and economics.
Derivatives and integrals of transcendental functions with additional applications, techniques of integration, calculus in higher dimensions and series.
Differential calculus of algebraic and transcendental functions and applications, antidifferentiation and the Riemann integral. Includes the use of graphing calculators and computer software.Text: Calculus (Early Transcendentals), by James Stewart
Standard techniques of integration, application of the integral, sequences and series, indeterminate forms, and numerical methods. Includes the use of graphing calculators and computer software.Text: Calculus (Early Transcendentals), by James Stewart
Multidimensional calculus and its applications. Topics include three-dimensional vector calculus, Gauss's theorem, Green's theorem, and Stokes's theorem. Includes the use of graphing calculators and computer software.Text: Calculus (Early Transcendentals), by James Stewart
Topics from discrete mathematics, including formal logic, methods of proof, set theory, relations, recursion, combinatorics, and graph theory. A systematic development of number systems via equivalence classes is included as an application of these topics.Text: Discrete Mathematics and Its Applications (Fourth Edition), by Kenneth H. Rosen.
Investigation of selected topics in geometry and measurement, from both historical and contemporary perspectives, with applications in the elementary and middle school curriculum.Texts: 1. Symmetry, shape, and space: an introduction to mathematics through geometry, by L.C. Kinsey and T.E. Moore; 2. Flatland, by E.A. Abbott; 3. Taxicab geometry: an adventure in non-Euclidean geometry, by E.F. Krause.
Consideration of the basic algebraic structures: groups, rings, integral domains, and fields. Examples of these structures and elementary proof will be emphasized as will polynomials over rings, integral domains, and the fields of real and complex numbers.Text: Abstract Algebra: An Introduction, by Thomas Hungerford (Second Edition).
A comparative study of Euclidean and non-Euclidean geometries, their respective histories and technologies, and their applications in mathematics, the sciences, and modern life.
The theory of groups, including subgroups, cyclic groups, normal subgroups, cosets, Lagrange’s
Theorem, quotient structures, homomorphism, automorphisms, group actions, Sylow’s Theorems, structure of finite abelian
groups, generators and relationsText: A First Course in Abstract Algebra, by John B. Fraleigh.
In-depth treatment of ring and field theory covering ideals, quotient rings, homomorphisms, polynomial rings, unique factorization domains, field extensions and geometric constructions, finite fields and additional topics from field automorphisms, Galois theory and applications to coding theory.Text: A First Course in Abstract Algebra, by John B. Fraleigh.
Primes and greatest common divisors, linear and polynomial congruences, primality tests, multiplicative functions, primitive roots, quadratic residues, continued fractions, and applications to cryptography,Text: Elementary Number Theory, by Kenneth H. Rosen.
Introduction to geometric topology, including piecewise linear structures, Euler's formula, surfaces and solids, knots, graphs, and other topics.Text: Topology of Surfaces, Knots, and Manifolds, by Stephan C. Carlson
Differential forms and vector fields; Curves in 3-space, frame fields, Frenet equations; Surfaces in 3-space, tangent bundle, Gauss map; First and second fundamental forms; Principal curvatures: Gauss and mean curvatures; Gauss and Codazzi equations; Theorema Egregium; Asymptotic and principal curves; Geodesics; Minimal surfaces; Gauss-Bonnet Theorem; Riemannian metricsText: Elementary Differential Geometry, by Barrett O'Neill (Second Edition)
Set-theoretic preliminaries, topological spaces, continuous functions, metric spaces, product and quotient spaces, connectedness, compactness, countability and separation axioms, Urysohn’s Metrization Theorem, Tietze’s Extension Theorem, Tychonoff’s Theorem.
Text: Topology, by J.R. Munkres (Second Edition)
Differential and integral calculus: limits; continuity; the derivative and applications; extrema; the definite integral; fundamental theorem of calculus; applications of the integral; transcendental functions.Text: Calculus, by S. Salas and E. Hille (Seventh Edition).
Partial differentiation, differential and integral calculus of function of several variables, and the integral theorems of vector calculus.Text: Calculus, by S. Salas and E. Hille (Seventh Edition).
Rigorous treatment of calculus of single and several variables. Topics include uniform continuity, metric spaces, Riemann integral, implicit function theorem, and the integral theorems of vector calculus.Text: Advanced Calculus, A Course in Mathematical Analysis, by P. Fitzpatrick.
Linear systems, matrices, vectors, vector spaces, linear transformations, determinants, inner product spaces, eigenvalues, and eigenvectors.Text: Linear Algebra and its Applications, by D. Lay (Second Edition).
Groups, quotients, Lagrange's theorem, isomorphism theorems, group actions; rings, quotients, isomorphism theorems, rings of fractions, chinese remainder theorem, Euclidean domains, principle ideal domains, unique factorization domains, polynomial rings, irreducibility criteria.Text: Abstract Algebra, by David S. Dummit and Richard M. Foote.
Algebraic techniques with polynomials, rational expressions and inequalities, exponential and logarithmic functions, rational exponent, conic sections, systems of linear equations.Text: Various texts.
Logical inference, probability and statistical inference, geometric growth, with selected topics such as linear programming, game theory, graph theory.Text: For all Practical Purposes, Contributing Authors: L. Steen, J. Malkevitch, R. Meyer, W. Meyer, D. Moore, W. Lucas, D. Albers, P. Campbell, D. Crowe, S, Schuster, M. Thompson, W. Carlson, Z. Karian, S. Sahni, P. Wang, and J. Blatt. (Second Edition)
A continuation of Math 175 in geometry, statistics, and probability.Text: A Problem Solving Approach to Mathematics for Elementary School Teachers, by R. Billstein, S. Libeskind, and J. Lott (Sixth Edition).
Describing sets of data; probability, independence, conditional probability; random variables and probability distribution; sampling distributions; small and large sample estimation of population means; test of hypothesis; comparing population means.Text: A First Course in Statistics, by J. McClave and T. Sincich (Fifth Edition).
Half of Math 231 correlated with material from algebra, coordinate geometry, trigonometry, and elementary functions.Text: Calculus, by J. Stewart (Third Edition).
Limits and continuity, derivatives, applications of derivatives, integration, fundamental theorem of calculus, applications of the integral.Text: Calculus, by G. Thomas and R. Finney (Ninth Edition).
Continuation of Math 231. Differential and integral calculus of algebraic and transcendental functions; techniques of integration; applications to the physical sciences; infinite series; further topics in analytic geometry such as polar coordinates, parametrized curves, and conic sections.Text: Calculus, by G. Thomas and R. Finney (Ninth Edition).