I Arithmetic
1 What is a Number?
1.1 Various Numerals to Represent
2 Arithmetic in Different Bases
3 Arithmetic in Euclid’s Elements
4 Gauss–Advent of Modern Number Theory
4.1 Number Theory of Gauss
4.2 Cryptography
4.3 Complex Numbers
4.4 Application of Number Theory – Construction of Septadecagon
4.5 How Did Gauss Do It?
4.6 Equations over Finite Fields*
4.7 Law of Quadratic Reciprocity*
4.8 Cubic Equations*
4.9 Riemann Hypothesis*
5 Numbers beyond Rationals
5.1 Arithmetic of Rational Numbers
5.2 Real Numbers
II Geometry
6 Basic Geometry
7 Greece: Beginning of Theoretical Mathematics
8 Euclid: The Founder of Pure Mathematics
8.1 Some Comments on Euclid’s Proof
9 Famous Problems from Greek Geometry
III Contributions of Some Prominent Mathematicians
10 Fibonacci’s Time and Legacy
10.1 Liber Abaci
10.2 Liber Quadratorum
10.3 Equivalent Formulations of the Problems
11 Solution of the Cubic
11.1 Introduction
11.2 History
12 Leibniz, Newton, and Calculus
12.1 Differential Calculus
12.2 Integral Calculus
12.3 Proof of FTC
12.4 Application of FTC
13 Euler and Modern Mathematics
13.1 Algebraic Number Theory
13.2 Analytical Number Theory
13.3 Euler’s Discovery of eπi + 1 = 0
13.4 Graph Theory and Topology
13.5 Traveling Salesman Problem
13.6 Planar Graphs
13.7 Euler-Poincaré Characteristic
13.8 Euler Characteristic Formula
14 Non-European Roots of Mathematics
15 Mathematics of the 20th Century*
15.1 Hilbert’s 23 Problems
15.2 Fermat’s Last Theorem
15.3 Miscellaneous
Biography
Dr. J. S. Chahal is a professor of mathematics at Brigham Young University. He earned a PhD from Johns Hopkins University. After spending a couple of years at the University of Wisconsin as a postdoc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes in and has published several papers in number theory. For hobbies, he likes to travel and hike. His books, Fundamentals of Linear Algebra, and Algebraic Number Theory, are also published by CRC Press.
