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Course Criteria
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4.00 Credits
An overview of one of the oldest areas of mathematics that is designed for any student who wants a taste of mathematics outside the calculus sequence. Topics include number puzzles, prime numbers, congruences, quadratic reciprocity, sums of squares, Diophantine equations, cryptography, coding theory, and continued fractions. Prerequisite: Mathematics 110 or permission of the instructor.
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4.00 Credits
In the 20th century the theory of games gained prominence due to its application to the social sciences. Game theory is a mathematical approach to modeling situations of conflict, whether real or theoretical. Using algebra and some analytical geometry, students explore the mathematical foundations of game theory. At the same time, they encounter a wide range of applications of the theory of games. Topics include zero-sum games, nonzero-sum games, pure and mixed strategies, von Neumann's minimax theorem, Nash equilibria, and cooperative games. Prerequisite: Mathematics 110 or permission of the instructor.
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4.00 Credits
An introduction to the basic ideas of differentiation and integration of functions of one variable. Topics include limits, techniques of differentiation, definite integrals, the fundamental theorem of calculus, and applications. Prerequisite: Mathematics 110 or the equivalent.
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4.00 Credits
This course, a continuation of Calculus I, reinforces the fundamental ideas of the derivative and the definite integral. Topics covered include L'H?pital's rule, integration techniques, improperintegrals, volumes, arc length, sequences and series, power series, continuous random variables, and separable differential equations. Prerequisite: Mathematics 141 or the equivalent.
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4.00 Credits
Cognitive Science This course is organized around methods for solving ordinary differential equations and incorporates many ideas from calculus. Topics include the classification of differential equations; determining the existence and uniqueness of ordinary differential equations; and solving first- and second-order differential equations using a variety of mathematical tools, such as integrating factors, Laplace transforms, and power series. Prerequisites: Mathematics 141 and 142 or permission of the instructor.
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4.00 Credits
This course investigates differentiation and integration of multivariable functions. Topics covered include vectors, coordinate systems, vector-valued functions, partial derivatives, gradients, Lagrange multipliers, multiple integrals, change of variables, line integrals, Green's theorem, and Stokes's theorem. Prerequisites: Mathematics 141 and 142 or the equivalent.
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4.00 Credits
As a complement to calculus, which models continuous phenomena, this course studies discrete processes and structures. Discrete mathematics provides the mathematical foundation for many areas of computation and can be applied to such diverse problems as designing an optimal phone-switching network and designing a computer circuit. Five core areas are covered: enumeration and recurrence relations; fundamentals of logic; sets, relations, and functions; recursion and induction; and basic graph theory. Other topics include elementary probability theory, generating functions, discrete optimization, modular arithmetic and finite groups, and Boolean algebra. Prerequisite: one semester of calculus or permission of the instructor.
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4.00 Credits
This course covers the basics of linear algebra in n-dimensional Euclidean space, including vectors, matrices, systems of linear equations, determinants, and eigenvalues and eigenvectors, as well as applications of these concepts to the natural, physical, and social sciences. Equal time is given to computational, applied, and theoretical aspects of the course material. Prerequisite: Mathematics 141 or permission of the instructor.
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4.00 Credits
An introduction to the methodology of the mathematical proof. The logic of compound and quantified statements; mathematical induction; and basic set theory, including functions and cardinality, are covered. Topics from foundational mathematics are developed to provide students with an opportunity to apply proof techniques. Prerequisite: Mathematics 142 or permission of the instructor.
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4.00 Credits
Economics Every day we make decisions based on numerical data in the face of uncertainty. We do so while reading the latest political polls, playing a card game, or analyzing a scientific experiment. Probabilistic models and statistical methods help us think through such decisions in a precise mathematical fashion. This course provides a calculus-based introduction to the techniques and applications of probability and statistics. Applications are selected from the natural and social sciences. Prerequisite: Mathematics 142 or the equivalent.
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