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Course Criteria
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3.00 Credits
An introduction to the study of "discrete" mathematical objects and number systems, in contrast to the study of the continuous real number line. The course explores many topics at the analytical level of calculus: relations, logic, techniques of proof, counting techniques, algorithms, graph theory, number systems, Boolean algebra, and set theory. Prerequisite: MAT 141 or 170 or permission of the instructor.
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3.00 Credits
A study of the language and structure of mathematics including problem solving, set and number theory, integers, rational and real numbers, probability and statistics, and geometry. NOTE: This course is open to early elementary education majors only.
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3.00 Credits
An extension of the concepts of function, limit, derivative, and integral to three-dimensional space and vector spaces; the course describes many applications and their historical significance, such as planetary motion and magnetic fields. Topics include vector algebra, elementary differential geometry of curves and surfaces, limits, continuity, partial derivatives, directional derivatives, multiple integrals, line integrals, surface integrals, Green's Theorem, Stokes' Theorem, and the Divergence Theorem. Prerequisite: MAT 171 or placement.
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3.00 Credits
The abstract study of systems of linear equations: the determination of whether a system has no, one, or infinitely many solutions and the techniques for obtaining such solutions. The topics include the algebra of matrices, Gaussian elimination, vector spaces, spanning, linear independence, basis, dimension, inner products, Gram-Schmidt orthogonalization, determinants, linear transformations and their matrix representations, eigenvalues and eigenvectors. Prerequisite: MAT 171.
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3.00 Credits
This course explores certain questions in mathematics that do not have answers and will never be answered since mathematicians have logically proven that the hoped for answers simply do not exist. Topics include the insolvability of quintic polynomials, non-Euclidean geometry, the G del Incompleteness Theorems, and the independence of the Continuum Hypothesis. In addition, we consider the history, people, and philosophical consequences of these results. Prerequisite: MAT 171.
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3.00 Credits
An introduction to mathematical tools used for modeling in economics. The tools studied include multivariate calculus with special emphasis on constrained optimization, as well as matrix algebra, diffential and difference equations. Applications focus on the use of marginal analysis, comparative statics, elasticities, isoquants, and Cobb-Douglas functions. Among the models discussed are the IS-LM macroeconomic model, the Solow growth model, and Leontief input-output systems. The course includes an introduction to the computer algebra system Maple. Prerequisite: MAT 141 or 170, and ECO 220.
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3.00 Credits
This course develops the abstract thinking and the writing skills necessary for proof-oriented mathematics courses and surveys various areas of mathematics. Fundamental concepts and questions are studied from mathematical logic, abstract algebra, number theory, and real analysis. Further topics include complex analysis, statistics, graph theory, and/or other areas of mathematics according to the interests of instructor and students. Prerequisite: MAT 171.
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3.00 Credits
A mathematical study of chance, this course uses counting techniques and topics from calculus to develop a mathematical approach that describes the likelihood of events happening. Specific topics include an introduction to the theory of probability, random variables, discrete and continuous probability distributions, expected values, moments and moment-generating functions, distributions of functions of random variables, and multivariate distributions. Prerequisite: MAT 230 or permission of instructor.
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3.00 Credits
A calculus-based course in statistics devoted to techniques for analyzing and interpreting data with the goal of understanding our world and facilitating informed decision-making processes. This course is a continuation of MAT 310 that studies applications of sampling distributions related to the normal distribution. These include estimation of parameters, confidence intervals, hypothesis testing, regression analysis and least-squares estimators, correlation, design of experiments, analysis of variance, chi-square tests, and nonparametric statistics. Prerequisite: MAT 310 or permission of the instructor.
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3.00 Credits
This course defines and investigates the key properties of the mathematical structure called an algebraic group, studying many examples, including groups of numbers, groups of functions, and groups of matrices, with the goal of determining the common properties of all of these mathematical systems. Topics include the basic properties of the integers, permutation groups, subgroups, Lagrange's Theorem, quotient groups, isomorphisms and homomorphisms, and Cayley's Theorem. Prerequisite: MAT 290.
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