A First Course In Real Analysis

The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. Numbers and Geometry Also, it will serve admirably in courses aimed at giving students from other areas a view of some of the basic ideas in mathematics. This book covers the main ideas of Euclid--geometry, arithmetic and the theory of real numbers, but with 2000 years of extra insights attached.

, via a course in Advanced Calculus or Linear Algebra.

Geometric constructions have been a popular part of mathematics throughout history. The ancient Greeks made the subject an art, which was enriched by the medieval Arabs but which required the algebra of the Renaissance for a thorough understanding. As specified by Plato, the game is played with a ruler and compass. He hopes that readers will learn a little geometry and a little algebra while enjoying the effort.

Interesting problems are nicely scattered throughout the text. In the process of examining geometric objects, the author incorporates the algebra of complex (and hypercomplex) numbers, some graph theory, and some topology.

The first course in Analysis, which follows calculus, along with other courses, such as differential equations and elementary linear algebra, in the curricu­ lum, presents special pedagogical challenges., as they arise naturally in the course of a narrative discussion of the question.

. No prior knowledge of number theory is assumed.

The book's readability has also been improved by the further clarification of many of the proofs, additional explanatory remarks, and clearer notation.. The most noticeable is the addition of many problems and the inclusion of answers to most of the odd-numbered exercises.

A First Course in Real Analysis There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies.. Mathematics is the music of science, and real analysis is the Bach of mathematics. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.

Many changes have been made in this second edition of A First Course in Real Analysis.

Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. Mathematics is the music of science, and real analysis is the Bach of mathematics.