Pure Mathematics for Beginners - Accelerated and Expanded Edition: A Rigorous Introduction to Logic, Set Theory, Abstract Algebra, Number Theory, Real . Complex Analysis, and Linear Algebra

Pure Mathematics for Beginners - Accelerated and Expanded Edition

Pure Mathematics for Beginners consists of a series of lessons in Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra. The 16 lessons in this book cover basic through intermediate material from each of these 8 topics. In addition, all the proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively. This accelerated and expanded edition of the book moves at a faster pace and contains much more content than the standard edition. Pure Mathematics for Beginners is perfect for

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

The material in this pure math book includes:

• 16 lessons in 8 subject areas.
• A problem set after each lesson arranged by difficulty level.
• A complete solution guide is included as a downloadable PDF file.

Pure Math Book Table Of Contents (Selected)
Here's a selection from the table of contents:
Introduction
Lesson 1 - Logic: Propositional Logic
Lesson 2 - Set Theory: Sets, Relations and Functions
Lesson 3 - Abstract Algebra: Algebraic Structures
Lesson 4 - Number Theory: Induction and Divisibility
Lesson 5 - Real Analysis: Completeness and Continuity
Lesson 6 - Topology: The Topology of R
Lesson 7 - Complex Analysis: The Field of Complex Numbers
Lesson 8 - Linear Algebra: Vector Spaces
Lesson 9 - Logic: First-order Logic
Lesson 10 - Set Theory: Axioms, Ordinals, and Cardinals
Lesson 11 - Abstract Algebra: Quotients and Structure Theorems
Lesson 12 - Number Theory: Cyclic Groups and Modular Arithmetic
Lesson 13 - Real Analysis: Differentiation and Integration
Lesson 14 - Topology: Topological Spaces and Homeomorphisms
Lesson 15 - Complex Analysis: Analytic Functions and Integration
Lesson 16 - Linear Algebra: Determinants and Banach Spaces