Mathematics

## Real Mathematical Analysis

Author: Charles C. Pugh

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 456

View: 851

Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.
Mathematics

## Real Mathematical Analysis

Author: Charles Chapman Pugh

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 440

View: 268

Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.
Mathematics

## Elements of Real Analysis

Author: Charles Denlinger

Publisher: Jones & Bartlett Learning

ISBN:

Category: Mathematics

Page: 769

View: 102

A student-friendly guide to learning all the important ideas of elementary real analysis, this resource is based on the author's many years of experience teaching the subject to typical undergraduate mathematics majors.
Mathematics

## Fundamentals of Mathematical Analysis

Author: Paul J. Sally (Jr.)

Publisher: American Mathematical Soc.

ISBN:

Category: Mathematics

Page: 379

View: 482

This is a textbook for a course in Honors Analysis (for freshman/sophomore undergraduates) or Real Analysis (for junior/senior undergraduates) or Analysis-I (beginning graduates). It is intended for students who completed a course in ``AP Calculus'', possibly followed by a routine course in multivariable calculus and a computational course in linear algebra. There are three features that distinguish this book from many other books of a similar nature and which are important for the use of this book as a text. The first, and most important, feature is the collection of exercises. These are spread throughout the chapters and should be regarded as an essential component of the student's learning. Some of these exercises comprise a routine follow-up to the material, while others challenge the student's understanding more deeply. The second feature is the set of independent projects presented at the end of each chapter. These projects supplement the content studied in their respective chapters. They can be used to expand the student's knowledge and understanding or as an opportunity to conduct a seminar in Inquiry Based Learning in which the students present the material to their class. The third really important feature is a series of challenge problems that increase in impossibility as the chapters progress.
Education

## Invitation to Real Analysis

Author: César Ernesto Silva

Publisher: American Mathematical Soc.

ISBN:

Category: Education

Page: 303

View: 291

Preliminaries: Sets, functions and induction; The real numbers and the completeness property; Sequences; Topology of the real numbers and metric spaces; Continuous functions; Differentiable functions; Integration; Series; Sequences and series of functions; Solutions to questions; Bibliographical notes; Bibliography; Index.
Mathematics

## Basic Real Analysis

Author: Houshang H. Sohrab

Publisher: Springer

ISBN:

Category: Mathematics

Page: 683

View: 749

Mathematics

## A Problem Book in Real Analysis

Author: Asuman G. Aksoy

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 254

View: 497

Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.
Mathematical analysis

## Principles of Mathematical Analysis

Author: Walter Rudin

Publisher:

ISBN:

Category: Mathematical analysis

Page: 296

View: 329

Mathematics

## A Course in Calculus and Real Analysis

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 432

View: 436

This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses.
Mathematics

## A Concise Approach to Mathematical Analysis

Author: Mangatiana A. Robdera

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 390

View: 236

This text introduces to undergraduates the more abstract concepts of advanced calculus, smoothing the transition from standard calculus to the more rigorous approach of proof writing and a deeper understanding of mathematical analysis. The first part deals with the basic foundation of analysis on the real line; the second part studies more abstract notions in mathematical analysis. Each topic contains a brief introduction and detailed examples.