A Second Course in Mathematical Analysis

Author: J. C. Burkill
Publisher: Cambridge University Press
ISBN: 0521523435
Release Date: 2002-10-24
Genre: Mathematics

A classic calculus text reissued in the Cambridge Mathematical Library. Clear and logical, with many examples.

LOGIC SETS AND THE TECHNIQUES OF MATHEMATICAL PROOFS

Author: Brahima MBODJE, Ph.D.
Publisher: Author House
ISBN: 9781463429669
Release Date: 2011-06-30
Genre: Education

As its title indicates, this book is about logic, sets and mathematical proofs. It is a careful, patient and rigorous introduction for readers with very limited mathematical maturity. It teaches the reader not only how to read a mathematical proof, but also how to write one. To achieve this, we carefully lay out all the various proof methods encountered in mathematical discourse, give their logical justifications, and apply them to the study of topics [such as real numbers, relations, functions, sequences, fine sets, infinite sets, countable sets, uncountable sets and transfinite numbers] whose mastery is important for anyone contemplating advanced studies in mathematics. The book is completely self-contained; since the prerequisites for reading it are only a sound background in high school algebra. Though this book is meant to be a companion specifically for senior high school pupils and college undergraduate students, it will also be of immense value to anyone interested in acquiring the tools and way of thinking of the mathematician.

A Course of Pure Mathematics

Author: G. H. Hardy
Publisher: Cambridge University Press
ISBN: 0521092272
Release Date: 1952
Genre: Mathematics

There can be few textbooks of mathematics as well-known as Hardy's Pure Mathematics. Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of a missionary with the rigor of a purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit.

A Course in Mathematical Analysis

Author: D. J. H. Garling
Publisher: Cambridge University Press
ISBN: 9781107032026
Release Date: 2013-04-25
Genre: Mathematics

The first volume of three providing a full and detailed account of undergraduate mathematical analysis.

Advanced Courses of Mathematical Analysis II

Author: A. Rodriguez-Palacios
Publisher: World Scientific
ISBN: 9789812708441
Release Date: 2007
Genre: Mathematical analysis

This volume comprises a collection of articles by leading researchers in mathematical analysis. It provides the reader with an extensive overview of new directions and advances in topics for current and future research in the field.

A Second Course in Mathematical Analysis

Author: Dorairaj Somasundaram
Publisher: Alpha Science International Limited
ISBN: 1842655337
Release Date: 2010
Genre: Mathematics

A Second Course in Mathematical Analysis makes an in-depth study of Infinite series, Double sequences and series, power series, sequences and series of functions, Functions of bounded variation, Riemann - Stieltjes integrals, Lebesgue integrals, Fourier series, Multivariable differential calculus, Implicit functions and Extremum problems.

An Interactive Introduction to Mathematical Analysis Hardback with CD ROM

Author: Jonathan Lewin
Publisher: Cambridge University Press
ISBN: 0521815894
Release Date: 2003-01-13
Genre: Mathematics

This book provides a rigorous course in the calculus of functions of a real variable. Its gentle approach, particularly in its early chapters, makes it especially suitable for students who are not headed for graduate school but, for those who are, this book also provides the opportunity to engage in a penetrating study of real analysis.The companion onscreen version of this text contains hundreds of links to alternative approaches, more complete explanations and solutions to exercises; links that make it more friendly than any printed book could be. In addition, there are links to a wealth of optional material that an instructor can select for a more advanced course, and that students can use as a reference long after their first course has ended. The on-screen version also provides exercises that can be worked interactively with the help of the computer algebra systems that are bundled with Scientific Notebook.

A Course of Modern Analysis

Author: E. T. Whittaker
Publisher: Cambridge University Press
ISBN: 0521588073
Release Date: 1996-09-13
Genre: Mathematics

This classic text has entered and held the field as the standard book on the applications of analysis to the transcendental functions. The authors explain the methods of modern analysis in the first part of the book and then proceed to a detailed discussion of the transcendental function, unhampered by the necessity of continually proving new theorems for special applications. In this way the authors have succeeded in being rigorous without imposing on the reader the mass of detail that so often tends to make a rigorous demonstration tedious. Researchers and students will find this book as valuable as ever.

A Second Course in Linear Algebra

Author: Stephan Ramon Garcia
Publisher: Cambridge University Press
ISBN: 9781107103818
Release Date: 2017-05-11
Genre: Mathematics

A second course in linear algebra for undergraduates in mathematics, computer science, physics, statistics, and the biological sciences.

A Companion to Analysis

Author: Thomas William Körner
Publisher: American Mathematical Soc.
ISBN: 9780821834473
Release Date: 2004
Genre: Mathematics

This book not only provides a lot of solid information about real analysis, it also answers those questions which students want to ask but cannot figure how to formulate. To read this book is to spend time with one of the modern masters in the subject. --Steven G. Krantz, Washington University, St. Louis One of the major assets of the book is Korner's very personal writing style. By keeping his own engagement with the material continually in view, he invites the reader to a similarly high level of involvement. And the witty and erudite asides that are sprinkled throughout the book are a real pleasure. --Gerald Folland, University of Washingtion, Seattle Many students acquire knowledge of a large number of theorems and methods of calculus without being able to say how they hang together. This book provides such students with the coherent account that they need. A Companion to Analysis explains the problems which must be resolved in order to obtain a rigorous development of the calculus and shows the student how those problems are dealt with. Starting with the real line, it moves on to finite dimensional spaces and then to metric spaces. Readers who work through this text will be ready for such courses as measure theory, functional analysis, complex analysis and differential geometry. Moreover, they will be well on the road which leads from mathematics student to mathematician. Able and hard working students can use this book for independent study, or it can be used as the basis for an advanced undergraduate or elementary graduate course. An appendix contains a large number of accessible but non-routine problems to improve knowledge and technique.

Principia Mathematica

Author: Alfred North Whitehead
Publisher:
ISBN: STANFORD:36105039675058
Release Date: 1984-01
Genre: Logic, Symbolic and mathematical


Amstat News

Author:
Publisher:
ISBN: UOM:39015057314281
Release Date: 2003
Genre: Statistics


Elementary Real and Complex Analysis

Author: Georgi E. Shilov
Publisher: Courier Corporation
ISBN: 9780486135007
Release Date: 2012-07-31
Genre: Mathematics

DIVExcellent undergraduate-level text offers coverage of real numbers, sets, metric spaces, limits, continuous functions, much more. Each chapter contains a problem set with hints and answers. 1973 edition. /div

The Geometry of Moduli Spaces of Sheaves

Author: Daniel Huybrechts
Publisher: Vieweg+Teubner Verlag
ISBN: 3663116255
Release Date: 2013-11-13
Genre: Technology & Engineering

This book is intended to serve as an introduction to the theory of semistable sheaves and at the same time to provide a survey of recent research results on the geometry of moduli spaces. The first part introduces the basic concepts in the theory: Hilbert polynomial, slope, stability, Harder-Narasimhan filtration, Grothendieck's Quot-scheme. It presents detailed proofs of the Grauert-Mülich Theorem, the Bogomolov Inequality, the semistability of tensor products, and the boundedness of the family of semistable sheaves. It also gives a self-contained account of the construction of moduli spaces of semistable sheaves on a projective variety à la Gieseker, Maruyama, and Simpson. The second part presents some of the recent results of the geometry of moduli spaces of sheaves on an algebraic surface, following work of Mukai, O'Grady, Gieseker, Li and many others. In particular, moduli spaces of sheaves on K3 surfaces and determinant line bundles on the moduli spaces are treated in some detail. Other topics include the Serre correspondence, restriction of stable bundles to curves, symplectic structures, irreducibility and Kodaira-dimension of moduli spaces.