Volume 1 covers numbers and number systems, natural numbers, real numbers, complex numbers, sets, groups and symmetry, logic, computation, dynamical systems and chaos, and fractals.

Table of Contents:

Part I: Numbers

Numbers and Number Systems

1.What Are Numbers?

2.Number Systems

Natural Numbers

1.Figurate Numbers

2.Primes

3.Greatest Common Divisor (GCD)

4.Least Common Multiple (LCM)

5.Aliquot Sequences

6.Pythagorean Triples and Fermat’s Last Theorem

7.Really Large Numbers

8.Number Tricks

9.Magic Squares

Real Numbers

1.Fractions and Decimals

2.Irrational Numbers

3.Continued Fractions

4.Fibonacci Numbers and the Golden Ratio

Complex Numbers

1.Imaginary Numbers

2.The Argand Diagram (The Complex Plane)

3.Complex Arithmetic

4.Euler’s Formula

5.Polar Form

6.Roots of Complex Numbers

7.The Fundamental Theorem of Algebra

Part II: Abstract Algebra

Sets

1.What Is a Set?

2.Operations on Sets

3.Venn Diagrams

4.Relations

5.Functions

6.Cardinal Number

Groups and Symmetry

1.What Is a Group?

2.Finite Groups

3.Infinite Groups

4.Quasicrystals: Forbidden Symmetry

Logic

1.Syllogisms

2.Propositional Logic (Boolean Algebra)

3.Predicate Logic

4.Gödel’s Incompleteness Theorems

Computation

1.What Is a Computer?

2.Parts of a Computer

3.Turing Machines

4.Sequential Programming

5.Computational Complexity

6.Quantum Computation

Part III: Chaos and Fractals

Dynamical Systems and Chaos

1.Discrete Dynamical Systems

2.Continuous Dynamical Systems

Fractals

1.What Is a Fractal?

2.Examples

Dimensions (in inches)

8x10x1.25"

Weight

2 lb. 3 oz.