- Cover
- Preface
- Possible Beneficial Audiences
- Wow Factors of the Book
- Chapter by Chapter (the nitty‐gritty)
- Note to the Reader
- About the Companion Website
- Chapter 1: Logic and Proofs
- 1.1 Sentential Logic
- 1.1.1 Introduction
- 1.1.2 Getting into Sentential Logic
- 1.1.3 Compound Sentences (“AND,” “OR,” and “NOT”)
- 1.1.4 Compound Sentences
- 1.1.5 Equivalence, Tautology, and Contradiction
- 1.1.6 De Morgan's Laws
- 1.1.7 Tautology
- 1.1.8 Logical Sentences from Truth Tables: DNF and CNF
- 1.1.9 Disjunctive and Conjunctive Normal Forms
- Problems
- 1.2 Conditional and Biconditional Connectives
- 1.3 Predicate Logic
- 1.4 Mathematical Proofs
- 1.5 Proofs in Predicate Logic
- 1.6 Proof by Mathematical Induction
- 1.1 Sentential Logic
- Chapter 2: Sets and Counting
- Chapter 3: Relations
- Chapter 4: The Real and Complex Number Systems
- 4.1 Construction of the Real Numbers
- 4.2 The Complete Ordered Field: The Real Numbers
- 4.3 Complex Numbers
- 4.3.1 An Introductory Tale
- 4.3.2 Complex Numbers
- 4.3.3 Complex Numbers as an Algebraic Field
- 4.3.4 Imaginary Numbers and Two Dimensions
- 4.3.5 Polar Coordinates
- 4.3.6 Complex Exponential and Euler's Theorem
- 4.3.7 Complex Variables in Polar Form
- 4.3.8 Basic Arithmetic of Complex Numbers
- 4.3.9 Roots and Powers of a Complex Number
- Problems
- Chapter 5: Topology
- Chapter 6: Algebra
- 6.1 Symmetries and Algebraic Systems
- 6.1.1 Abstraction and Abstract Algebra
- 6.1.2 Symmetries
- 6.1.3 Symmetries in Two Dimensions
- 6.1.4 Symmetry Transformations
- 6.1.5 Symmetries of a Rectangle
- 6.1.6 Observations
- 6.1.7 Symmetries of an Equilateral Triangle
- 6.1.8 Rotation Symmetries of Polyhedra
- 6.1.9 Rotation Symmetries of a Cube
- Problems
- 6.2 Introduction to the Algebraic Group
- 6.3 Permutation Groups
- 6.4 Subgroups: Groups Inside a Group
- 6.5 Rings and Fields
- 6.1 Symmetries and Algebraic Systems
- Index
- End User License Agreement
-
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