## Pure Mathematics for Beginners: A Rigorous Introduction to Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra by Dr. Steve Warner

Table of Contents:

Lesson 1 – Logic: Statements and Truth

Lesson 2 – Set Theory: Sets and Subsets

Lesson 3 – Abstract Algebra: Semigroups, Monoids, and Groups

Lesson 4 – Number Theory: The Ring of Integers

Lesson 5 – Real Analysis: The Complete Ordered Field of Reals

Lesson 6 – Topology: The Topology of ℝ

Lesson 7 – Complex Analysis: The Field of Complex Numbers 7

Lesson 8 – Linear Algebra: Vector Spaces

Lesson 9 – Logic: Logical Arguments

Lesson 10 – Set Theory: Relations and Functions

Lesson 11 – Abstract Algebra: Structures and Homomorphisms

Lesson 12 – Number Theory: Primes, GCD, and LCM

Lesson 13 – Real Analysis: Limits and Continuity

Lesson 14 – Topology: Spaces and Homeomorphisms

Lesson 15 – Complex Analysis: Complex Valued Functions

Lesson 16 – Linear Algebra: Linear Transformations

This book was written to provide a basic but rigorous introduction to pure mathematics, while exposing students to a wide range of mathematical topics in logic, set theory, abstract algebra, number theory, real analysis, topology, complex analysis, and linear algebra.

For students: There are no prerequisites for this book. The content is completely self-contained. Students with a bit of mathematical knowledge may have an easier time getting through some of the material, but no such knowledge is necessary to read this book.

*Pure Mathematics for Beginners is perfect for*

- professors teaching an introductory college course in higher mathematics
- students wishing to see the type of mathematics they would be exposed to as a math major
- high school teachers working with advanced math students.

*The material in this pure math book includes:*

- 16 lessons in eight subject areas.
- A problem set after each lesson arranged by difficulty level.
- A complete solution guide is included as a downloadable PDF file.

Download Pure Mathematics for Beginners: A Rigorous Introduction to Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra by Dr. Steve Warner in free pdf format