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Course Criteria
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3.00 Credits
Presents the basics of elementary number theory. Topics include the Euclidean algorithm, divisibility, congruences and modular arithmetic, primes, number-theoretic functions, and Diophantine equations.-a Emphasis is placed on making mathematical conjectures and verifying or disproving them, and on writing efficient and mathematically correct proofs. The course is intended for mathematics majors.
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3.00 Credits
Presents mathematical models in financial mathematics and interest theory, and how these concepts are applied in calculating present and accumulated values for various streams of cash flows as a basis for use in reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and valuing contingent cash flows. Financial instruments, including derivatives, and the concept of no-arbitrage are covered. This course covers materials for the second actuarial exam, Exam 2, Financial Mathematics (FM).
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3.00 Credits
Presents the rigorous mathematics of probability theory. There is a thorough treatment of discrete and continuous random variables, both univariate and multivariate, including traditionally discussed examples (including Binomial, Negative Binomial, Poisson, Normal, Gamma), properties of expected value, statistical independence, moment generating functions, and transformations of random variables. This course covers materials for the actuarial exam P (Probability).
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3.00 Credits
Presents a synthesis of mathematical methods utilized to model and solve real-world problems. The emphasis is on developing models that provide the means to analyze and answer questions posed in practical settings. Students will learn a problem-solving approach toward applied problems in optimization, dynamical systems, and stochastic processes. The course is intended for students in mathematics, statistics, and data science.
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3.00 Credits
Presents an introduction to automata, formal languages computability, and computational complexity. Topics include finite automata, pushdown automata, context-free grammars, Turing machines, and algorithmically unsolvable and computationally intractable problems. The course is intended for students interested in the mathematical foundations of computer science theory.
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3.00 Credits
Provides an introduction to the language and methods of abstract mathematics. Topics included are: sets, relations, functions, groups, rings and fields. Emphasis is on the elementary theory of groups. The course is intended for mathematics and secondary education/mathematics majors.
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3.00 Credits
Presents a rigorous treatment of the calculus of functions of a single real variable. The course is designed to fill the gaps left in the development of calculus as it is presented in the elementary courses. Topics include an introduction to the topology of the real line and the rigorous development of the concepts of limit, continuity, derivative, and integral.
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3.00 Credits
Provides a broad overview of partial differential equations, exploring various methods of solution. The topic of boundary value problems will be developed in parallel. The course will equip students who have already completed an introductory course in ordinary differential equations with the tools required to pursue more advanced coursework in mathematics, engineering and the physical sciences.
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3.00 Credits
Exposes students to a rigorous treatment of complex numbers and an introduction to the theory of functions of a complex variable. Central topics are the complex number system, analytic functions, harmonic functions, and conformal mappings. Additional topics may include power series, contour integration, Cauchy's formula, and applications.
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3.00 Credits
Introduces metric spaces; topological spaces; functions and continuity on topological spaces; and the related concepts of compactness, connectedness, and completeness. Optional topics may include homotopy and fundamental groups as well as homology. This course is intended for students in mathematics who wish to pursue research or attend graduate school.
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