Topics include: set theory, combinatorics, probability, statistics, matrix algebra, linear programming, Markov chains, graph theory, and mathematics of finance. A student cannot receive credit for this course after credit has been received for MTH-260 or any mathematics course numbered greater than MTH-302.
Ideas in Mathematics
Exploration of some of the great ideas of mathematics, with an emphasis on creative problem solving, effective thinking, and clear writing. Topics will be drawn from areas that include properties of and patterns in numbers, infinity, probability, geometry, topology, fractals, network theory, and statistics.
Integrated Precalc/Calc I
Introduction to the theory and methods of differential calculus. Topics include functions, graphs, limits, continuity and derivatives. May not be enrolled on a pass-fail basis.
Integrated Precalc/Calc II
Introduction to applications of the derivative and the theory and applications of the definite integral. Topics include: trigonometric functions and their derivatives, applications of derivatives, antiderivatives, the definite integral and applications of the integral.
Calc for Life & Social Science
Introduction to the methods of differential and integral calculus with an emphasis on applications in the management, life, and social sciences. Topics include limits and continuity, differentiation and integration of functions of one variable, exponential and logarithmic functions, and applications.
Analytic Geometry/Calculus I
First course in the standard calculus sequence. Introduction to the theory, methods, and applications of differential calculus and an introduction to the definite integral. Topics include: algebraic and trigonometric functions, limits and continuity, rules for differentiation, applications of the derivative, antiderivatives, and the definition and basic properties of the definite integral.
Analytic Geometry/Calculus II
The second course in the standard calculus sequence. An introduction to the logarithmic and exponential functions, the applications of the definite integral, techniques of integration, indeterminate forms, improper integrals, numerical methods, and infinite series.
Vectors and Matrices
Introduction to the theory of vectors and matrices. Among the topics included are: vectors, vector operations, the geometry of Euclidean space, systems of equations, matrices, matrix operations, special transformations, eigenvalues, and applications of matrix theory.
Mathematics of Ranking
From the ranking of the web pages by Google and other search engines, to the ranking of movies and products by Netflix and Amazon, to the ranking of sports teams destined for postseason tournaments --- it is clear that rankings of all types are pervasive in today's society. Introducing students to the mathematical topics that underlie many different ranking systems. May Experience ONLY.
Higher Mathematics Transition
Introduction to the main ideas and proof techniques of mathematics with an emphasis on reading, writing and understanding mathematical reasoning. Among the topics covered are logic, proof techniques, sets, cardinality, combinatorial enumeration, mathematical induction, relations, functions, and others selected by the instructor.
Introduction to the arithmetic properties of the integers including divisibility, congruences, diophantine equations, primes and their distribution, quadratic forms and quadratic reciprocity. Additional topics will be chosen from continued fractions, cryptography, partitions, elliptic curves, modular forms and number fields.
Combinatorics & Graph Theory
A study of the primary methods and fundamental ideas of combinatorics and graph theory. Topics covered include generating functions, set partitions, recurrence relations, inclusion-exclusion, trees, graph connectivity, independence, and graph colorings. Additional topics will be chosen from Ramsey theory, set systems, planarity, directed graphs, matchings, and Hamiltonian and Eulerian graphs.
Linear Algebra & Matrix Theory
Study of finite dimensional real vector spaces, linear transformations, determinants, inner product spaces, eigenvalues and eigenvectors.
A theoretical introduction to some of the basic ideas of real analysis: real numbers and the topology of the real line, sequences and series of real numbers, limits of functions, continuity, uniform continuity, differentiation, the Riemann integral, and sequences and series of functions.
A theoretical introduction to some of the basic ideas of modern abstract algebra. Included is a study of groups, rings, domains, polynomial rings and fields as well as an investigation of their sub-structures and of the fundamental homomorphism theorems.
Topics in Algebra
An in-depth investigation of selected topics in abstract algebra.
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