**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

**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.

(

**4936**views)

**Basic Real Analysis**

by

**Anthony W. Knapp**-

**BirkhĂ¤user**

A comprehensive treatment with a global view of the subject, emphasizing connections between real analysis and other branches of mathematics. Included throughout are many examples and hundreds of problems, with hints or complete solutions for most.

(

**1252**views)

**Introduction to Mathematical Analysis**

by

**B. Lafferriere, G. Lafferriere, N. Mau Nam**-

**Portland State University Library**

We provide students with a strong foundation in mathematical analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.

(

**3543**views)

**Topics in Real and Functional Analysis**

by

**Gerald Teschl**-

**Universitaet Wien**

This manuscript provides a brief introduction to Real and (linear and nonlinear) Functional Analysis. It covers basic Hilbert and Banach space theory as well as basic measure theory including Lebesgue spaces and the Fourier transform.

(

**8932**views)