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Topics include: Number Systems; The Earliest Mathematics; Additive Systems; The Egyptian Number System; Alphabetic Systems; Positional Systems on a Fixed Base; Historical Examples of Positional Systems with a Base Different from Ten; The Babylonian Number System; The Mayan Number System; Method for Translating Base Ten into Base Two; The Algebra of Sets; Set Theoretic Exponentiation; Cardinal Numbers; Theory of Numbers; Mathematical Induction; Complete Induction; Prime Numbers; The Division Theorem; Testing for Primality; The Greatest Common Divisor; Irrational Numbers; Factorization into Primes; The Least Common Multiple; The Euclidean Algorithm; Some Famous Unsolved Problems (Perfect numbers, Fermat primes, The Goldbach Conjecture); Linear Diophantine Equations; Fractions (How is a fraction represented in diagrams? How are fractions represented on a number line? What is the "unit"? What is the "shifting unit"? What is the multiplicative identity element for fractions? What is a proper fraction? What is an improper fraction? When is a fraction larger than one whole? What is a unit fraction? How are fractions "simplified" (or "reduced")?
When is a fraction in "simplest form" (or "lowest terms")? | 
