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.