Algebra Formulary: Algebra Formulary with Numerous Examples and Illustrations

This algebra formulary is a digest of important results in logic and sets, group, ring and field theory, number theory and RSA cryptography. These results are accompanied by numerous illustrations and good examples.
Here are the sections of the table of contents:

1) Greek alphabet and various symbols

2) Sets and Logic:
Definition, Union and Intersection, Difference and Complement, Inclusion and equality, Properties, Sets of numbers, Intervals on R, Cartesian Product of Two Sets, Cardinality of Sets, Countable and Uncountable Sets, Cardinality of theContinuum, Logic, The liar paradox, Statements, Truth tables and propositional connectives, Statement Forms, Tautology, Quantifiers, notations, Quantifiers, properties, Direct proof, Proof by contraposition,Proof by contradiction, Proof by equivalence, Proof by mathematical induction, Some conjectures

3) Group Theory:
Closed binary operation, Some definitions, Group axioms, Algebra Formulary Section, Abelian group, Subgroup definition, Subgroup properties, Group homomorphisms, Normal subgroup, Quotient group, Cyclic groups, Ring, Field, Field of Real Numbers + Properties, Complex Numbers, olar Form of the Complex Numbers, nth Roots of a Complex Number, Algebraic Properties of The Field of Complex Numbers, Complex Exponential Function

4) Number Theory:
Prime numbers, Divisibility, Properties, Divisibility criteria, Prime number definition, Fundamental Theorem of Arithmetic, Large prime numbers, Mersenne prime numbers, Perfect numbers, Euclid’sTheorem, Prime numbers theorem, Titanic primes, Gigantic primes, Mega primes, Congruence and GCD, Euclidean division in Z, Congruence modulo n, Properties of thec ongruence relation, Congruence classes, Modul ararithmetic, Greatest Common Divisor GCD(a,b), Euclid’s algorithm, GCD Theorem, Gauss Lemma, Unique factorization of an integer, Modular algebra, Linear congruence ax≡b(mod n), Chinese Remainder Theorem, Euler’stotientfunction, Euler’sTheorem, Fermat’sLittleTheorem, Primality Test and Binary Exponentiation

RSA Theorem - Rivest Shamir Adleman
Public Key and Certification Authorities, RSA Encryption Process, RSA Signature Process, ImportantRemarks

Index/Bibliography

This book is the first in a series covering different areas of mathematics, high school and early university level (algebra, geometry, probability and statistics, analysis, linear algebra, etc.).