## subcategories

**Logic** (35)

**Number Theory** (22)

## e-books in Pure Mathematics category

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

by

**John Wesley Young**-

**Macmillan and co.**,

**1917**

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.

(

**1343**views)

**Mathematical Reasoning: Writing and Proof**

by

**Ted Sundstrom**-

**Pearson Education, Inc.**,

**2013**

'Mathematical Reasoning' is designed to be a text for the first course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics.

(

**6946**views)

**Proofs in Mathematics**

by

**Alexander Bogomolny**-

**Interactive Mathematics Miscellany and Puzzles**,

**2013**

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.

(

**6860**views)

**How To Write Proofs**

by

**Larry W. Cusick**-

**California State University, Fresno**,

**2009**

Proofs are the heart of mathematics. What is the secret? The short answer is: there is no secret, no mystery, no magic. All that is needed is some common sense and a basic understanding of a few trusted and easy to understand techniques.

(

**5292**views)

**An Introduction to Mathematical Reasoning**

by

**Peter J. Eccles**-

**Cambridge University Press**,

**2007**

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.

(

**2106**views)

**An Inquiry-Based Introduction to Proofs**

by

**Jim Hefferon**-

**Saint Michael's College**,

**2013**

Introduction to Proofs is a Free undergraduate text. It is inquiry-based, sometimes called the Moore method or the discovery method. It consists of a sequence of exercises, statements for students to prove, along with a few definitions and remarks.

(

**4492**views)

**Blast Into Math!**

by

**Julie Rowlett**-

**BookBoon**,

**2013**

This is a fun and rigorous introduction to pure mathematics, suitable for both students and a general audience interested in learning what pure mathematics is all about. Presented in a friendly, accessible, and nonetheless rigorous style.

(

**6113**views)

**Super Special Codes using Super Matrices**

by

**W.B.V. Kandasamy, F. Smarandache, K.Ilanthenral**-

**arXiv**,

**2010**

Basic properties of codes and super matrices are given. New type of super special vector space is constructed. Three new classes of super special codes namely, super special row code, super special column code and super special codes are introduced.

(

**6249**views)

**Surreal Numbers: An Introduction**

by

**Claus Tondering**,

**2013**

This text will provide the readers with a free and accessible introduction to a very fascinating subject. The author is not a mathematician by profession, the book shows that pure mathematics is not that complicated once you get down to the rules.

(

**8044**views)

**Book of Proof**

by

**Richard Hammack**-

**Virginia Commonwealth University**,

**2009**

This textbook is an introduction to the standard methods of proving mathematical theorems. It is written for an audience of mathematics majors at Virginia Commonwealth University, and is intended to prepare the students for more advanced courses.

(

**26882**views)

**A Gentle Introduction to the Art of Mathematics**

by

**Joseph Fields**-

**Southern Connecticut State University**,

**2009**

The point of this book is to help you with the transition from doing math at an elementary level (concerned mostly with solving problems) to doing math at an advanced level (which is much more concerned with axiomatic systems and proving statements).

(

**8537**views)

**Proofs and Concepts: the fundamentals of abstract mathematics**

by

**Dave Witte Morris, Joy Morris**-

**University of Lethbridge**,

**2009**

This undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. It is designed to be the textbook for a bridge course that introduces undergraduates to abstract mathematics.

(

**8851**views)

**Fundamental Concepts of Mathematics**

by

**Farshid Hajir**-

**University of Massachusetts**,

**2005**

Problem Solving, Inductive vs. Deductive Reasoning, An introduction to Proofs; Logic and Sets; Sets and Maps; Counting Principles and Finite Sets; Relations and Partitions; Induction; Number Theory; Counting and Uncountability; Complex Numbers.

(

**9221**views)

**Foundations of Mathematics**

by

**Stephen G. Simpson**-

**Pennsylvania State University**,

**2008**

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, etc.

(

**14024**views)

**Basic Concepts of Mathematics**

by

**Elias Zakon**-

**The Trillia Group**,

**2007**

The book will help students complete the transition from purely manipulative to rigorous mathematics. It covers basic set theory, induction, quantifiers, functions and relations, equivalence relations, properties of the real numbers, fields, etc.

(

**9579**views)

**Practical Foundations of Mathematics**

by

**Paul Taylor**-

**Cambridge University Press**,

**1999**

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.

(

**14056**views)

**A Introduction to Proofs and the Mathematical Vernacular**

by

**Martin Day**,

**2009**

The book helps students make the transition from freshman-sophomore calculus to more proof-oriented upper-level mathematics courses. Another goal is to train students to read more involved proofs they may encounter in textbooks and journal articles.

(

**14805**views)