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Course Criteria
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3.00 Credits
Full course for one semester. Field axioms, the real and complex fields, sequences and series. Complex functions, continuity and differentiation; power series and the complex exponential. Prerequisite: Mathematics 111 or equivalent. Lecture-conference.
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3.00 Credits
Full course for one semester. An introduction to computer science, covering topics such as elementary data structures, algorithms, computability, floating point computations, and programming in a high-level language. Prerequisite: three years of high school mathematics. Lecture-conference and lab.
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3.00 Credits
Full course for one semester. A rigorous introduction to the theorems of elementary number theory. Topics may include: axioms for the integers, Euclidean algorithm, Fermat's Little Theorem, unique factorization, primitive roots, primality testing, public-key encryption systems, Gaussian integers. Prerequisite: three years of high school mathematics or consent of instructor. Lecture-conference. Not offered 2009-10.
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3.00 Credits
Full course for one semester. Permutations and combinations, finite mathematical structures, inclusion-exclusion principle, elements of the theory of graphs, permutation groups, and the rudiments of Pólya theory will be discussed. Prerequisite: three years of high school mathematics. Lecture-conference.
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3.00 Credits
Full course for one semester. The basic ideas of probability including properties of expectation, the Law of Large Numbers, and the Central Limit Theorem are discussed. These ideas are applied to the problems of statistical inference, including estimation and hypothesis testing. The linear regression model is introduced, and the problems of statistical inference and model validation are studied in this context. A portion of the course is devoted to statistical computing and graphics. Prerequisite: three years of high school mathematics. Lecture-conference and lab.
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3.00 Credits
Full course for one semester. A development of the basic theorems of multivariable differential calculus, optimization, and Taylor series. Inverse and implicit function theorems may be included. Prerequisite: Mathematics 112 or consent of the instructor. Lecture-conference.
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3.00 Credits
Full course for one semester. A study of line, multiple, and surface integrals, including Green's and Stokes's theorems, linear differential equations. Differential geometry of curves and surfaces or Fourier series may be included. Prerequisite: Mathematics 211 or consent of the instructor. Lecture-conference.
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3.00 Credits
Full course for one semester. A study of complex valued functions: Cauchy's Theorem and residue theorem, Laurent series, and analytic continuation. Prerequisite: Mathematics 212. Lecture-conference.
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3.00 Credits
Full course for one semester. A careful study of continuity and convergence in metric spaces. Sequences and series of functions, uniform convergence, normed linear spaces. Prerequisite: Mathematics 212. Mathematics 331 must be taken before or at the same time as this course. Lecture-conference.
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3.00 Credits
Full course for one semester. An introduction to the theory of ordinary differential equations. Existence and uniqueness theorems, global behavior of solutions, qualitative theory, numerical methods. Prerequisite: Mathematics 212 and Mathematics 331. Lecture-conference. Offered in alternate years.
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