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Author(s): Ronald T. Kneusel
Year: 2025
ISBN: 9781718503588,9781718503595
Table of contents :
Brief Contents
Contents in Detail
Foreword
Acknowledgments
Introduction
Who Is This Book For?
What I Expect You to Know Already
What Can You Expect to Learn?
1Computers and Numbers
Numbers and Number Bases
Binary, Octal, and Hexadecimal Numbers
Conversions Between Number Bases
How Computers Represent Numbers
Integers
Floating-Point Numbers
What You Need to Know About Floating-Point Arithmetic
Round-Off Error
Unrepresentable Numbers
Summary
2Sets and Abstract Algebra
Concerning Sets
Special Sets
Set Operations
Set Operations in Python
Venn Diagrams
Subsets and Supersets
Power Sets
The Laws of Set Theory
Experimenting with Number Sets in Python
Abstract Algebra and Groups
Examples of Groups, Magmas, and Monoids
Special Groups
Cantor to Infinity and Beyond
The Cardinality of Infinite Sets
The Continuum Hypothesis and Infinities Without End
Computable and Uncomputable Numbers
Uncomputable Python
Summary
3Boolean Algebra
Definition and Laws
Boolean Algebra Leads to Digital Logic
Set Theory as a Boolean Algebra
Propositional Logic as a Boolean Algebra
The Set {0,1} as a Boolean Algebra
The Truth Tables of Digital Logic
Boolean Functions
Duals and Complements
Boolean Functions in Code
Canonical Normal Forms
Sum of Products
Product of Sums
Karnaugh Maps
Algebraic Simplification of Boolean Expressions
Digital Circuits
Boolean Functions as Digital Circuits
All You Need Is NAND (or NOR)
A Binary Adder
Logic Gate Construction
Summary
Ronald T. Kneusel - Math for Programming (Early Access) (2025).pdf
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