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
