Community College of Rhode Island

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Math 1472: History of Mathematics

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.


Last Updated: 3/18/13