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The Book of Foundational Mathematics
Ordered Pairs and Set Products
Propositions
Sets
The Structure of Basic Arguments
Modeling Logic with Truth Tables
Properties of the Cartesian Product
Rules of Inference
Subsets
Logical Equivalence
Proof Technique: Element Arguments
Relations
Using the Rules of Inference
A Set of Operations on Sets
Logically Equivalent Arguments
The Laws of Logic
Application: Switching Networks
Invalid Arguments
The Laws of Set Theory
Logical Implications
Proof Technique: Exhaustion
Universal Specification
Propositions with Variables
Set Partitions
Universal Generalization
Axioms, Definitions, Theorems, and Proofs
Proof Technique: Casework
Quantifiers
Logic with Quantified Statements
Proof Technique: Direct Proofs
Nested Quantifiers
Proof Technique: Indirect Proofs
Russell’s Paradox and a Formal Resolution
Application: Logic Puzzles
Proof Technique: Contradiction
Set Theory in Maple
A Primer on Fuzzy Logic
Mistakes in Proofs
Further Reading
Mathematical Logic With Maple
Proof Technique: Equivalence
Defining Propositions With Maple
Verifying Mathematical Arguments in Maple
The Book of Probability
Conditional Probability
Sample Spaces and Events
Modeling Events with Venn Diagrams
The Axioms of Probability
Basic Theorems Derived From the Axioms
Uniform Randomness
Probability via Counting
Continuity of the Probability Function
Probabilities of 0 and 1
Geometric Probability
An Example Set That Is Not an Event
Estimating Probability With Simulations
The Book of Real Analysis
Closed Sets
Closure of a Set
Connected Sets
Further Topological Properties of Real Numbers
Metric Spaces
Open Sets
Properties of the Limit Superior and Limit Inferior
The Limit Superior and Limit Inferior of a Sequence
Unions and Intersections of Sets
Why Topology Matters
Tutoring
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Jake Hiance
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Introducing Bishop Polynomials
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General Investigations of Rook Polynomials
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Automating the Calculation of Rook Polynomials
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How Do You Calculate Rook Polynomials?
Uncategorized
What Are Rook Polynomials?
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