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Course Criteria
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The calculus of vector-valued functions, including Green's and Stokes's theorems, l'Hopital's rule and indeterminate forms, improper integrals, and sequences and series. Prerequisite: Grade of C- or better in Mathematics 231. Prerequisite: C- or better in Mathematics 132. 1.00 units, Lecture
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An introduction to techniques for solving ordinary differential equations. Series solutions, initial value problems, and Laplace transforms. Prerequisite: C- or better in Mathematics 132 or 142. 1.00 units, Lecture
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An introduction to the basic mathematical tools used in the financial world. Topics may include simple and compound interest, periodic loans, present and future value, amortization, sinking funds, bonds and money market funds, tax-exempt, and tax-deferred investments. Life annuities, perpetual annuities, and the mechanics of life insurance. Students may also do calculations and modeling using spreadsheets; instructions on their use will be given as needed. Basic ideas from probability theory will also be introduced as needed. Additional topics may include linear programming, finite differences, and some actuarial mathematics. However, this course does not prepare students for the examinations of the Society of Actuaries. Prerequisite: C- or better in Mathematics 132 or 142 and Mathematics 107 or permission of the instructor. 1.00 units, Lecture
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Application of elementary mathematics through first-year calculus to the construction and analysis of mathematical models. Applications will be selected from the natural sciences and social sciences, with an emphasis on the natural sciences. Several models will be analyzed in detail, and the computer will be used as necessary. The analysis will consider the basic steps in mathematical modeling: recognition of the non-mathematical problem, construction of the mathematical model, solution of the resulting mathematical problems, and analysis and application of the results. Both Mathematics 252 and 254 may be taken for credit. Prerequisite: Computer Science 115L and a C- or better in either Mathematics 132 or 142. 1.00 units, Lecture
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An introduction to the standard topics in number theory. Topics will include congruences, representation of integers, number theoretic functions, primitive roots, continued fractions and Pythagorean triples. Applications may include cryptology, primality testing, and pseudorandom numbers. Prerequisite: C- or better in Mathematics 132 or 142. 1.00 units, Lecture
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A companion to Mathematics 252, with an alternate set of topics and an emphasis on applications selected from the social sciences, especially economics. See description of Mathematics 252. Both Mathematics 252 and 254 may be taken for credit. Prerequisite: C- or better in Computer Science 115 and one year of calculus. 1.00 units, Lecture
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A broad introduction to, and exploration of, modern algebra. Examples of algebraic structures may be drawn from among the following areas: symmetry, number theory, solutions to equations, modular arithmetic, permutations, matrices, and wallpaper patterns. This course may not be repeated for credit. Students with credit for Mathematics 307 are not normally eligible to receive credit for this course. Prerequisite: C- or better in Mathematics 228, or permission of the instructor. 1.00 units, Lecture
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We will develop tools from calculus and analysis in order to study a variety of continuous structures: mathematical objects which embody in different ways the notions of limit and continuity. Equal emphasis will be placed on proving and applying analytical tools. This is not a survey course. Rather, one or two topics will be explored in detail. Such topics may include sequences and series, Fourier series and differential equations, dynamical systems, special functions, approximation theory, analytic theory of continued fractions, integration theory, and complex analysis. Students with credit for Mathematics 331 are not normally eligible to receive credit for this course. Prerequisite: C- or better in Mathematics 132. 1.00 units, Lecture
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Discrete and continuous probability, combinatorial analysis, random variables, random vectors, density and distribution functions, moment generating functions, and particular probability distributions including the binomial, hypergeometric, and normal. Prerequisite: C- or better in Mathematics 132. 1.00 units, Lecture
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We consider confidence intervals and hypothesis testing from a theoretical viewpoint, with emphasis on sufficiency, completeness, minimum variance, the Cramer-Rao lower bound, the Rao-Blackwell theorem, and the Neyman-Pearson theorem. Other topics as time permits. Prerequisite: Mathematics 305 with a grade of C- or better. 1.00 units, Lecture
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