Math From Scratch, Vol. 1
W. Blaine Dowler
The first volume in a series designed to make the connections between the different mathematical fields and topics, building the entirety of math from scratch. This first volume covers relations, set theory, whole numbers, the group axioms, simple group theory, permutation groups, combinations, subgroups, mappings, functions, domain, range, injections, surjections, bijections, cosets, cardinality, Lagrange's Theorem, ring theory, cancelable elements, the bases representation theorm, binary numbers, octal numbers, hexadecimal numbers, metric spaces, absolute value, the number line, division, remainder, the Fundamental Theorem of Arithmetic, even numbers, odd numbers, prime numbers, composite numbers, perfect squares, relatively prime numbers (aka coprime numbers), linear diophantine equations, proof by induction, divisibility rules in base 10 for divisors 2-11, modular arithmetic, the Euclidean Algorithm, the Chinese Remainder Theorem, totients and the RSA encryption algorithm.