Analysis (2 volume set) (Texts and Readings in Mathematics)

Mathematics
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Contents:

  • Secondary menu
  • Real Analysis
  • Chicago undergraduate mathematics bibliography
  • Reading List
  • Thanks to our sponsors, you can download our textbooks for free
  • The History of Mathematics: A Source-Based Approach: Volume 1

    • Secondary menu

    Atiyah, M. Suggested books : T. Becker and V. Adams and P. Sturmfels, Grobner bases and convex polytopes , American Mathematical Society Suggested books : Serre, J. Koblitz, N. Iwaniec, H.

    Diamond, F. Suggested books : Adrian Bondy and U. Springer-Verlag, Berlin, ISBN: Douglas B. West, Introduction to graph theory , Prentice Hall, Inc.

    Suggested books : Bondy, J. Burton, D.

    Real Analysis

    Editorial Reviews. From the Back Cover. This is part two of a two-volume book on real analysis These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and. Buy Analysis II: Third Edition (Texts and Readings in Mathematics) on and set theory, the book discusses the basics of analysis (limits, series, continuity.

    Clark, J. Polya G. Suggested books : Narasimham, R. Niven, I. Apostol, T. Ireland, K.

    Hoffman, K. American Mathematical Society. Serre, Linear representations of finite groups , Graduate Texts in Mathematics. New York-Heidelberg. Suggested books : Rudin, W. Suggested books : Royden, H. Folland, G. Hewitt, E. Suggested books : Rudin, Functional Anaysis 2nd Ed.

    Yosida, K. Goffman, C. Suggested books : Ahlfors, L. Conway, J. Suggested books : Narasimhan, R. Nievergelt , Birkhauser 2nd ed. Greene, R. Suggested books : Spivak, M. Hirsh, M. Suggested books : Armstrong, M. Munkres, K. Viro, O. MA Introduction to algebraic topology Prerequisite courses: MA and MA The fundamental group: Homotopy of maps, multiplication of paths, the fundamental group, induced homomorphisms, the fundamental group of the circle, covering spaces, lifting theorems, the universal covering space, Seifert-van Kampen theorem, applications.

    Hatcher, A. Kosniowski, C.

    Chicago undergraduate mathematics bibliography

    Press, Croom, F. Suggested books : do Carmo, M. Thorpe, J.

    O'Neill, B. Gray, A.

    Reading List

    MA Metric Geometry of Spaces and Groups Prerequisite courses: MA Pre-requisites : A first course in Topology can be taken concurrently Metric geometry is the study of geometric properties such as curvature and dimensions in terms of distances, especially in contexts where the methods of calculus are unavailable, An important instance of this is the study of groups viewed as geometric objects, which constitutes the field of geometric group theory. MA Ordinary Differential Equations Prerequisite courses: MA Basics concepts:Introduction and examples through physical models, First and second order equations, general and particular solutions, linear and nonlinear systems, linear independence, solution techniques.

    Birkhaeuser, Coddington, E. Perko, L. Suggested books : Garabedian, P. Renardy, M. Suggested books : Hoffman, K. Simmons G. Churchill, R. MA Numerical Methods Numerical solution of algebraic and transcendental equations, Iterative algorithms, Convergence, Newton Raphson procedure, Solutions of polynomial and simultaneous linear equations, Gauss method, Relaxation procedure, Error estimates, Numerical integration, Euler-Maclaurin formula.

    Suggested books : Gupta, A. Conte, S. Hildebrand, F. Froberg, C.

    Abstract Algebra

    MA Numerical Methods for Partial Differential Equations Finite difference methods for two point boundary value problems, Laplace equation on the square, heat equation and symmetric hyperbolic systems in 1 D. Suggested books : Smith, G. Evans, G. Blackledge, J.

    Thanks to our sponsors, you can download our textbooks for free

    Suggested books : Faires, J. Stoer, J. Iserlas, A. Suggested books : Ross, S. Taylor, H.

    The History of Mathematics: A Source-Based Approach: Volume 1

    Baby Rudin is one of the clearest introductory level analysis textbooks out there. Seshadri, as well as other distinguished Indian mathematicians have been associated with the series. The foundations of complex dynamics are best introduced in the setting of compact spaces. Morphisms : separated, proper, finite morphisms, finite type morphisms, affine morphisms Sheaves of algebras : affine morphisms as sheaves of algebras Sheaves of modules over a scheme, Quasi-coherent and coherent sheaves Divisors and Line Bundles, Weil divisors, Cartier divisors, Line bundles on Projective spaces, Serre sheaves. Finiteness of class number.

    Suggested books : Luenberger, D. Shiryaev, A. Shreve, S. Suggested books : Lichtenberg, A. Guckenheimer, J. Prerequisites, if any: familiarity with linear algebra - matrices, and ordinary differential equations Desirable: ability to write codes for solving simple problems. Suggested books : S. Alligood, T. Tabor, Chaos and Integrability in Non-linear Dynamics , Rudin, W.

    Rudin, Functional Anaysis 2nd Ed. House, New Delhi, Munkres, J. Milnor, Morse Theory , Ann. Press, Princeton, Zariski spectrum as a frame Refresher on categories : Categories, functors, Yoneda Lemma, equivalence of categories, adjoints. Presheaves and Sheaves Locally ringed spaces and schemes Separated schemes, proper schemes, irreducible schemes, reduced schemes, integral schemes, noetherian schemes.

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    Morphisms : separated, proper, finite morphisms, finite type morphisms, affine morphisms Sheaves of algebras : affine morphisms as sheaves of algebras Sheaves of modules over a scheme, Quasi-coherent and coherent sheaves Divisors and Line Bundles, Weil divisors, Cartier divisors, Line bundles on Projective spaces, Serre sheaves.

    Springer-Verlag, New York-Heidelberg, Robin Hartshorne, Residues and duality , Lecture notes of a seminar on the work of A. With an appendix by P.