Introduction to Real Analysis
by William F. Trench
Publisher: Prentice Hall 2003
Number of pages: 583
Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The book is written for those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.
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by Larry Clifton - arXiv
This is a detailed introduction to the real number system from a categorical perspective. We begin with the categorical definition of the natural numbers, review the Eudoxus theory of ratios, and then define the positive real numbers categorically.
by A. M. Bruckner, J. B. Bruckner, B. S. Thomson - Prentice Hall
This book provides an introductory chapter containing background material as well as a mini-overview of much of the course, making the book accessible to readers with varied backgrounds. It uses a wealth of examples to illustrate important concepts.
by G.H. Hardy - Cambridge University Press
This classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. Hardy explains the fundamental ideas of the differential and integral calculus, and the properties of infinite series.
by Shlomo Sternberg
The topology of metric spaces, Hilbert spaces and compact operators, the Fourier transform, measure theory, the Lebesgue integral, the Daniell integral, Wiener measure, Brownian motion and white noise, Haar measure, Banach algebras, etc.