A Guide to Topology

Author: Steven G. Krantz
Publisher: MAA
ISBN: 0883853469
Release Date: 2009-09-24
Genre: Mathematics

This book is an outline of the core material in the standard graduate-level real analysis course. It is intended as a resource for students in such a course as well as others who wish to learn or review the subject. On the abstract level, it covers the theory of measure and integration and the basics of point set topology, functional analysis, and the most important types of function spaces. On the more concrete level, it also deals with the applications of these general theories to analysis on Euclidean space: the Lebesgue integral, Hausdorff measure, convolutions, Fourier series and transforms, and distributions. The relevant definitions and major theorems are stated in detail. Proofs, however, are generally presented only as sketches, in such a way that the key ideas are explained but the technical details are omitted. In this way a large amount of material is presented in a concise and readable form.

A Guide to Advanced Real Analysis

Author: G. B. Folland
Publisher: MAA
ISBN: 0883853434
Release Date: 2009-11-30
Genre: Mathematics

A concise guide to the core material in a graduate level real analysis course.

A Guide to Advanced Linear Algebra

Author: Steven H. Weintraub
Publisher: MAA
ISBN: 9780883853511
Release Date: 2011-07-07
Genre: Mathematics

Linear algebra occupies a central place in modern mathematics. This book provides a rigorous and thorough development of linear algebra at an advanced level, and is directed at graduate students and professional mathematicians. It approaches linear algebra from an algebraic point of view, but its selection of topics is governed not only for their importance in linear algebra itself, but also for their applications throughout mathematics. Students in algebra, analysis, and topology will find much of interest and use to them, and the careful treatment and breadth of subject matter will make this book a valuable reference for mathematicians throughout their professional lives.Topics treated in this book include: vector spaces and linear transformations; dimension counting and applications; representation of linear transformations by matrices; duality; determinants and their uses; rational and especially Jordan canonical form; bilinear forms; inner product spaces; normal linear transformations and the spectral theorem; and an introduction to matrix groups as Lie groups.The book treats vector spaces in full generality, though it concentrates on the finite dimensional case. Also, it treats vector spaces over arbitrary fields, specializing to algebraically closed fields or to the fields of real and complex numbers as necessary.

A Guide to Real Variables

Author: Steven G. Krantz
Publisher: MAA
ISBN: 0883853442
Release Date: 2009-08-13
Genre: Mathematics

The purpose of A Guide to Real Variables is to provide an aid and conceptual support for the student studying for the qualifying exam in real variables. Beginning with the foundations of the subject, the text moves rapidly but thoroughly through basic topics like completeness, convergence, sequences, series, compactness, topology and the like. All the basic examples like the Cantor set, the Weierstrass nowhere differentiable function, the Weierstrass approximation theory, the Baire category theorem, and the Ascoli-Arzela theorem are treated.The book contains over 100 examples, and most of the basic proofs. It illustrates both the theory and the practice of this sophisticated subject. Graduate students studying for the qualifying exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too.

A Guide to Plane Algebraic Curves

Author: Keith Kendig
Publisher: MAA
ISBN: 9780883853535
Release Date: 2011
Genre: Mathematics

This Guide is a friendly introduction to plane algebraic curves. It emphasizes geometry and intuition, and the presentation is kept concrete. You'll find an abundance of pictures and examples to help develop your intuition about the subject, which is so basic to understanding and asking fruitful questions. Highlights of the elementary theory are covered, which for some could be an end in itself, and for others an invitation to investigate further. Proofs, when given, are mostly sketched, some in more detail, but typically with less. References to texts that provide further discussion are often included. Computer algebra software has made getting around in algebraic geometry much easier. Algebraic curves and geometry are now being applied to areas such as cryptography, complexity and coding theory, robotics, biological networks, and coupled dynamical systems. Algebraic curves were used in Andrew Wiles' proof of Fermat's Last Theorem, and to understand string theory, you need to know some algebraic geometry. There are other areas on the horizon for which the concepts and tools of algebraic curves and geometry hold tantalizing promise. This introduction to algebraic curves will be appropriate for a wide segment of scientists and engineers wanting an entrance to this burgeoning subject.

A Guide to Functional Analysis

Author: Steven G. Krantz
Publisher: MAA
ISBN: 9780883853573
Release Date: 2013-06-06
Genre: Mathematics

This book is a quick but precise and careful introduction to the subject of functional analysis. It covers the basic topics that can be found in a basic graduate analysis text. But it also covers more sophisticated topics such as spectral theory, convexity, and fixed-point theorems. A special feature of the book is that it contains a great many examples and even some applications. It concludes with a statement and proof of Lomonosov's dramatic result about invariant subspaces.

A Guide to Advanced Real Analysis

Author: G. B. Folland
Publisher: MAA
ISBN: 0883853434
Release Date: 2009-11-30
Genre: Mathematics

A concise guide to the core material in a graduate level real analysis course.

A Guide to Groups Rings and Fields

Author: Fernando Q. Gouvêa
Publisher: MAA
ISBN: 9780883853559
Release Date: 2012
Genre: Mathematics

This Guide offers a concise overview of the theory of groups, rings, and fields at the graduate level, emphasizing those aspects that are useful in other parts of mathematics. It focuses on the main ideas and how they hang together. It will be useful to both students and professionals.In addition to the standard material on groups, rings, modules, fields, and Galois theory, the book includes discussions of other important topics that are often omitted in the standard graduate course, including linear groups, group representations, the structure of Artinian rings, projective, injective and flat modules, Dedekind domains, and central simple algebras. All of the important theorems are discussed, without proofs but often with a discussion of the intuitive ideas behind those proofs.Those looking for a way to review and refresh their basic algebra will benefit from reading this Guide, and it will also serve as a ready reference for mathematicians who make use of algebra in their work.

Match

Author:
Publisher:
ISBN: STANFORD:36105123660800
Release Date: 2008
Genre: Chemistry


Graphs

Author: Robin J. Wilson
Publisher: John Wiley & Sons Inc
ISBN: UOM:39015019005720
Release Date: 1990-01-02
Genre: Mathematics

The only text available on graph theory at the freshman/sophomore level, it covers properties of graphs, presents numerous algorithms, and describes actual applications to chemistry, genetics, music, linguistics, control theory and the social sciences. Illustrated.

Subject Guide to Forthcoming Books

Author: Reginald Clark
Publisher:
ISBN: UOM:39015058398242
Release Date: 1983
Genre: American literature

Presents by subject the same titles that are listed by author and title in Forthcoming books.