# 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

- A. Development of Egyptian Mathematics; Ahmes papyrus
- 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.