Pure Mathematics for Beginners
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
- 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: 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
Author(s): Steve Warner
Edition: 1
Publisher: Get 800
Year: 2018
Language: English
Pages: 262
Cover
Legal Notice
Title Page
Table of Contents
Introduction
For students
For instructors
Lesson 1 – Logic: Statements and Truth
Statements with Words
Statements with Symbols
Truth Tables
Problem Set 1
Lesson 2 – Set Theory: Sets and Subsets
Describing Sets
Subsets
Unions and Intersections
Problem Set 2
Lesson 3 – Abstract Algebra: Semigroups, Monoids, and Groups
Binary Operations and Closure
Semigroups and Associativity
Monoids and Identity
Groups and Inverses
Problem Set 3
Lesson 4 – Number Theory: The Ring of Integers
Rings and Distributivity
Divisibility
Induction
Problem Set 4
Lesson 5 – Real Analysis: The Complete Ordered Field of Reals
Fields
Ordered Rings and Fields
Why Isn’t ℚ enough?
Completeness
Problem Set 5
Lesson 6 – Topology: The Topology of ℝ
Intervals of Real Numbers
Operations on Sets
Open and Closed Sets
Problem Set 6
Lesson 7 – Complex Analysis: The Field of Complex Numbers
A Limitation of the Reals
The Complex Field
Absolute Value and Distance
Basic Topology of ℂ
Problem Set 7
Lesson 8 – Linear Algebra: Vector Spaces
Vector Spaces Over Fields
Subspaces
Bases
Problem Set 8
Lesson 9 – Logic: Logical Arguments
Statements and Substatements
Logical Equivalence
Validity in Sentential Logic
Problem Set 9
Lesson 10 – Set Theory: Relations and Functions
Relations
Equivalence Relations and Partitions
Orderings
Functions
Equinumerosity
Problem Set 10
Lesson 11 – Abstract Algebra: Structures and Homomorphisms
Structures and Substructures
Homomorphisms
Images and Kernels
Normal Subgroups and Ring Ideals
Problem Set 11
Lesson 12 – Number Theory: Primes, GCD, and LCM
Prime Numbers
The Division Algorithm
GCD and LCM
Problem Set 12
Lesson 13 – Real Analysis: Limits and Continuity
Strips and Rectangles
Limits and Continuity
Equivalent Definitions of Limits and Continuity
Basic Examples
Limit and Continuity Theorems
Limits Involving Infinity
One-sided Limits
Problem Set 13
Lesson 14 – Topology: Spaces and Homeomorphisms
Topological Spaces
Bases
Types of Topological Spaces
Continuous Functions and Homeomorphisms
Problem Set 14
Lesson 15 – Complex Analysis: Complex Valued Functions
The Unit Circle
Exponential Form of a Complex Number
Functions of a Complex Variable
Limits and Continuity
The Reimann Sphere
Problem Set 15
Lesson 16 – Linear Algebra: Linear Transformations
Linear Transformations
Matrices
The Matrix of a Linear Transformation
Images and Kernels
Eigenvalues and Eigenvectors
Problem Set 16
Index
About the Author
Books by Dr. Steve Warner
