About

The Math Lover’s Book Vol.1 series presents important branches of mathematics, including complex numbers, group theory, computation and fractals.

Table of Contents

Part I: Numbers

1. Numbers and Number Systems
1.1. What Are Numbers?
1.2. Number Systems

2. Natural Numbers
2.1. Figurate Numbers
2.2. Primes
2.3. Greatest Common Divisor (GCD)
2.4. Least Common Multiple (LCM)
2.5. Aliquot Sequences
2.6. Pythagorean Triples and Fermat’s Last Theorem
2.7. Really Large Numbers
2.8. Number Tricks
2.9. Magic Squares

3. Real Numbers
3.1. Fractions and Decimals
3.2. Irrational Numbers
3.3. Continued Fractions
3.4. Fibonacci Numbers and the Golden Ratio

4. Complex Numbers
4.1. Imaginary Numbers
4.2. The Argand Diagram (The Complex Plane)
4.3. Complex Arithmetic
4.4. Euler’s Formula
4.5. Polar Form
4.6. Roots of Complex Numbers
4.7. The Fundamental Theorem of Algebra

Part II: Abstract Algebra

5. Sets
5.1. What Is a Set?
5.2. Operations on Sets
5.3. Venn Diagrams
5.4. Relations
5.5. Functions
5.6. Cardinal Number

6. Group Theory and Symmetry
6.1. What Is a Group?
6.2. Finite Groups
6.3. Infinite Groups
6.4. Quasicrystals: Forbidden Symmetry

7. Logic
7.1. Syllogisms
7.2. Propositional Logic (Boolean Algebra)
7.3. Predicate Logic
7.4. Gödel’s Incompleteness Theorems

8. Computation
8.1. What Is a Computer?
8.2. Parts of a Computer
8.3. Turing Machines
8.4. Sequential Programming
8.5. Computational Complexity
8.6. Quantum Computation

Part III: Chaos and Fractals

9. Dynamical Systems and Chaos
9.1. Discrete Dynamical Systems
9.2. Continuous Dynamical Systems

10. Fractals
10.1. What Is a Fractal?
10.2. Examples