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Pure Mathematics for Beginners

Grade Levels
11th - 12th, Higher Education, Adult Education, Homeschool
Formats Included
  • Zip
262 pages
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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.

Pure Mathematics for Beginners is perfect for

  • an introductory college course in higher mathematics.
  • high school teachers working with advanced math students.
  • high school and college 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 friendly but rigorous treatment of all the mathematics covered.
  • Additional analyses before and after proofs to help students gain a deep understanding of the subject matter with the minimum amount of effort.
  • A problem set after each lesson containing problems arranged by difficulty level.
  • A complete solution guide is included.

Pure Math Book Table Of Contents (Selected) Here's a selection from the 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: 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

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

Terms of use: This product may be used by the purchaser for their own use only. All rights reserved. No part of this publication may be reproduced, distributed, or transmitted without written permission from the author. This includes posting this product on the internet in any form, including classroom/personal websites or network drives. If you wish to share this product with colleagues, please contact the author for a discount on multiple licenses.

Total Pages
262 pages
Answer Key
Teaching Duration
1 Semester
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