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Course Criteria
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4.00 Credits
Investigates the modern revolutions in mathematics initiated by Cantor, G del, Turing, and Robinson in the fields of set theory, provability, computability, and analysis respectively, as well as provides background on the controversy over the philosophy and underlying logic of mathematics.
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4.00 Credits
Uses the unifying theme of game theory to explore mathematical techniques for gaining an understanding of real-world problems. Includes matrix algebra, linear programming, probability, trees, von Neumann's minimax theorem, and Nash's theorem on equilibrium points. Considers zero-sum and non-zero-sum games, multiperson games, and the prisoner's dilemma. Explores the applications of game theory, including conflict analysis, and various issues in psychology, sociology, political science, economics, and business.
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4.00 Credits
Presents mathematical connections and foundations for art. Topics vary and may include aspects of linear perspective and vanishing points, symmetry and patterns, tilings and polygons, Platonic solids and polyhedra, golden ratio, non-Euclidean geometry, hyperbolic geometry, fractals, and other topics. Includes connections and examples in different cultures.
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4.00 Credits
Provides the discrete portion of the mathematical background needed by students in electrical and computer engineering. Topics include Boolean algebra and set theory, logic, and logic gates; growth of functions, and algorithms and their complexity; proofs and mathematical induction; and graphs, trees, and their algorithms. As time permits, additional topics may include methods of enumeration and finite-state machines.
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6.00 Credits
Contains the material from the first semester of MTH U241, preceded by material emphasizing the strengthening of precalculus skills. Topics include properties of exponential, logarithmic, and trigonometric functions; differential calculus; and introductory integral calculus.
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4.00 Credits
Covers definition, calculation, and major uses of the derivative, as well as an introduction to integration. Topics include limits; the derivative as a limit; rules for differentiation; and formulas for the derivatives of algebraic, trigonometric, and exponential/logarithmic functions. Also discusses applications of derivatives to motion, density, optimization, linear approximations, and related rates. Topics on integration include the definition of the integral as a limit of sums, antidifferentiation, the fundamental theorem of calculus, and integration by substitution.
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4.00 Credits
Covers further techniques and applications of integration, infinite series, and introduction to vectors. Topics include integration by parts; numerical integration; improper integrals; separable differential equations; and areas, volumes, and work as integrals. Also discusses convergence of sequences and series of numbers, power series representations and approximations, 3D coordinates, parameterizations, vectors and dot products, tangent and normal vectors, velocity, and acceleration in space.
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4.00 Credits
Builds upon the differential and integral calculus topics in MTH U241 to develop additional tools such as partial derivatives and multiple integrals needed by students of engineering technology. This course is not equivalent to MTH U242.
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6.00 Credits
Retired August 31, 2004. Introduces the definite integral, the fundamental theorem of calculus, and methods and applications of integration. Completes all the topics included in MTH U242. Designed for students of computer science (and the physical sciences or engineering) who are familiar with differential calculus at the science/engineering level but are not familiar with integral calculus.
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1.00 Credits
Retired August 31, 2006. Offers additional introductory academic experience by exploring course-related topics in greater depth with the professor. Available only to courses approved by the University Honors Program.
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