**Foundations of Mathematics**

by Stephen G. Simpson

**Publisher**: Pennsylvania State University 2008**Number of pages**: 123

**Description**:

These are lecture notes for an introductory graduate-level course in foundations of mathematics. The topics covered are: computability, unsolvable problems, undecidability of the natural number system, decidability of the real number system, informal set theory, axiomatic set theory. This course is suitable for all mathematics graduate students.

Download or read it online here:

**Download link**

(750KB, PDF)

## Similar books

**Lectures on Fundamental Concepts of Algebra and Geometry**

by

**John Wesley Young**-

**Macmillan and co.**

The following lectures contain an elementary account of the logical foundations of algebra and geometry. Except in a very few instances, no knowledge of mathematics beyond the most elementary portions of algebra and geometry has been assumed.

(

**1334**views)

**Proofs in Mathematics**

by

**Alexander Bogomolny**-

**Interactive Mathematics Miscellany and Puzzles**

I'll distinguish between two broad categories. The first is characterized by simplicity. In the second group the proofs will be selected mainly for their charm. Most of the proofs in this book should be accessible to a middle grade school student.

(

**6858**views)

**Practical Foundations of Mathematics**

by

**Paul Taylor**-

**Cambridge University Press**

It explains the basis of mathematical reasoning both in pure mathematics itself and in computer science. In addition to the formal logic, this volume examines the relationship between computer languages and plain English mathematical proofs.

(

**14048**views)

**An Introduction to Mathematical Reasoning**

by

**Peter J. Eccles**-

**Cambridge University Press**

This book introduces basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory.

(

**2099**views)