**The Foundations of Analysis**

by Larry Clifton

**Publisher**: arXiv 2013**Number of pages**: 48

**Description**:

This is a detailed and self-contained 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 as presented in Book V of Euclid, and then use these classical results to define the positive real numbers categorically.

Download or read it online for free here:

**Download link**

(370KB, PDF)

## Similar books

**The General Theory of Dirichlet's Series**

by

**G.H. Hardy, Marcel Riesz**-

**Cambridge University Press**

This classic work explains the theory and formulas behind Dirichlet's series and offers the first systematic account of Riesz's theory of the summation of series by typical means. Its authors rank among the most distinguished mathematicians ...

(

**1605**views)

**Introduction to Infinitesimal Analysis: Functions of One Real Variable**

by

**N. J. Lennes**-

**John Wiley & Sons**

This volume is designed as a reference book for a course dealing with the fundamental theorems of infinitesimal calculus in a rigorous manner. The book may also be used as a basis for a rather short theoretical course on real functions.

(

**8623**views)

**An Introductory Single Variable Real Analysis**

by

**Marcel B. Finan**-

**Arkansas Tech University**

The text is designed for an introductory course in real analysis suitable to upper sophomore or junior level students who already had the calculus sequel and a course in discrete mathematics. The content is considered a moderate level of difficulty.

(

**7492**views)

**A Course of Pure Mathematics**

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.

(

**6346**views)