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  • MATH 221: Vectors and Matrices

    1.00 Credits
    Wesleyan University

    This is a course in the algebra of matrices and Euclidean spaces that emphasizes the concrete and geometric. Topics to be developed include solving systems of linear equations; matrix addition, scalar multiplication, and multiplication; properties of invertible matrices; determinants; elements of the theory of abstract finite dimensional real vector spaces; dimension of vector spaces; and the rank of a matrix. These ideas are used to develop basic ideas of Euclidean geometry and to illustrate the behavior of linear systems. We conclude with a discussion of eigenvalues and the diagonalization of matrices.
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  • MATH 222: Multivariable Calculus

    1.00 Credits
    Wesleyan University

    This course treats the basic aspects of differential and integral calculus of functions of several real variables, with emphasis on the development of calculational skills. The areas covered include scalar- and vector-valued functions of several variables, their derivatives, and their integrals; the nature of extremal values of such functions and methods for calculating these values; and the theorems of Green and Stokes.
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  • MATH 226: Complex Analysis

    1.00 Credits
    Wesleyan University

    We will present the basic properties of complex analytic functions. We begin with the complex numbers themselves and elementary functions and their mapping properties, then discuss Cauchy's integral theorem and Cauchy's integral formula and applications. Then we discuss Taylor and Laurent series, zeros and poles and residue theorems, the argument principle, and Rouche's theorem. In addition to a rigorous introduction to complex analysis, students will gain experience in communicating mathematical ideas and proofs effectively.
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  • MATH 228: Discrete Mathematics

    1.00 Credits
    Wesleyan University

    In this introduction to discrete mathematical processes, topics may include mathematical induction, with applications; number theory; finite fields; elementary combinatorics; and graph theory.
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  • MATH 233: Linear Programming

    1.00 Credits
    Wesleyan University

    Linear programming develops practical techniques for optimizing linear functions on sets defined by systems of linear inequalities. Because many mathematical models in the physical and social sciences are expressed by such systems, the techniques developed in linear programming are very useful. This course will present the mathematics behind linear programming and related subjects. Topics covered may include the following: the simplex method, duality in linear programming, interior-point methods, two-person games, some integer-programming problems, Wolfe's method in quadratic programming, the Kuhn-Tucker conditions, and geometric programming.
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  • MATH 244: Topology: Point Set

    1.00 Credits
    Wesleyan University

    This is an introduction to general topology, the study of topological spaces. We will begin with the most natural examples, metric spaces, and then move on to more general spaces. This subject, fundamental to mathematics, enables us to discuss notions of continuity and approximation in their broadest sense. We will illustrate its power by seeing important applications to other areas of mathematics.
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  • MATH 261: Abstract Algebra: Groups, Rings, and Fields

    1.00 Credits
    Wesleyan University

    An introduction to abstract algebra: groups, rings, and fields. Development of fundamental properties of those algebraic structures that are important throughout mathematics.
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  • MATH 272: Elementary Number Theory

    1.00 Credits
    Wesleyan University

    This is a course in the elements of the theory of numbers. Topics covered include divisibility, congruences, quadratic reciprocity, Diophantine equations, and a brief introduction to algebraic numbers.
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  • MATH 513: Analysis I

    1.00 Credits
    Wesleyan University

    MATH513 and MATH514 constitute the first-year graduate course in real and complex analysis. One semester will be devoted to real analysis, covering such topics as Lebesgue measure and integration on the line, abstract measure spaces and integrals, product measures, decomposition and differentiation of measures, and elementary functional analysis. One semester will be devoted to complex analysis, covering such topics as analytic functions, power series, Mobius transformations, Cauchy's integral theorem and formula in its general form, classification of singularities, residues, argument principle, maximum modulus principle, Schwarz's lemma, and the Riemann mapping theorem.
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  • MATH 515: Analysis II

    1.00 Credits
    Wesleyan University

    Topics in analysis to be announced.
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