3 Credit Course
Offered in Lecture Format
Prerequisite required  (MATH 1430)

SYLLABUS

I. THE PREHISTORIC PERIOD

A. Counting and the development of one-to-one correspondence, symmetry in art, simple grouping systems

II. THE ANCIENT CIVILIZATIONS: EGYPTIANS AND BABYLONIANS

A. Development of Egyptian Mathematics; Ahmes papyrus
        1. Egyptian simple additive number system & unit fractions
        2. Egyptian multiplication-duplation and mediation
        3. Rule of False Position
      4. Original formulas to calculate area and volume
B. Development of Babylonian Mathematics; Plympton 322
        1. Babylonian positional sexagesimal number system & fractions
        2. Division by multiplication with reciprocals
        3. Square root extraction by Divide and Average method
        4. General formulas for Pythagorean triples

III. THE GREEK PERIOD

A. Development of Ionic Greek (ciphered) number system
B.    Pythagorean influence in music, geometry, astronomy, number theory
        1. Proofs of theorems
        2. Golden ratio
C. Contents and influence of Euclid's Elements, Demonstration of Euclidean Algorithm
D. University of Alexandria
E. Archimedes
        1. Computation of pi
        2. The law of hydrostatics
        3. Proof and derivations of formulas for volume of sphere, cylinder, cone
        4. Treatise on large numbers
        5. Invention of practical war machines, catapults, pulleys, levers
F. Erathosthenes
        1. Sieve
        2. Calculation of circumference of earth
G. Appollonius Conic Sections
H. Hero's Formula (and other inventions)
I. Diophantus, Algebraic symbols
J. Hypatia, First known woman mathematician
K. History of pi
        1. Approximation of pi by measuring
        2. Mnemonics of pi

IV. THE HINDU-ARABIC PERIOD

A. Development of Hindu-Arabic numerals and algorithms
B. Preservation of Greek mathematical texts
C. Computation in Hindu-Arabic manner
D. Lattice method of multiplication
E. Casting away nines to check addition
F. Bhaskara's Lilavati (Rule of False Position, Rule of Three)
G. Srinivasa Ramanujan
        1. Untrained genius
        2. Approximation to pi
        3. Number theory
H. al-Khwarizmi's Algebra

V. THE TRANSITIONAL PERIOD

A. Spread of Hindu-Arabic numerals to Europe
B. Fibonacci's Liber Abaci
        1. Fibonacci sequence and golden ratio

VI. MODERN EUROPEAN MATHEMATICS

A. Euler and Gauss, complete mathematicians
B. History of computers
C. Euler's invention of Network Theory from study of Platonic solids and Koningsberg bridge problem
D. History of calculus (Newton vs. Leibniz)
E. Introduction to Topology
        1. Donut hole geometry
        2. Mobius bands
F. Non-Euclidean Geometry
        1. Definition of parallel lines, etc.
G. Development of Probability and Statistics

Note: Howard Eve's An Introduction to the History of Mathematics is an excellent resource text.

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