Topic: Quipu
- General Introduction
- Peruvian Civilization and the Inca Empire. Quick discussion on the Geo-Historical need for a record system.
- Introduction of the chasquis and the Quipukeeper as examples of historical adaptation to the orographic conditions.
- Quipu as written records? Brief analysis of Quipu as possible writing system as suggested by Professor Gary Urton in his analysis of the Historia Piruanorum.
- Structure of Quipu
- General Characteristics and string hierarchy: S and Z Strings. Introductory vs coding segments.
- Types of Knots: Single, Long and E-Knots
- Coding elements: Color of the strings and spacing on the strings.
- Arithmetical Ideas
- Positional base 10 numeral System. Supporting evidences for a possible base 5 system
- Addition with Quipu. Puruchuco quipu are an example of a progressive addition of hierarchical values These Quipu were likely used for bookkeeping and they are an example of summation of values -
- Ratios and Fractions Quipu used in population grouping and tax regulations show a fundamental grasp of set theory and elemental partitions.
- Multiplication with Quipu Quick explanation of possible uses of quipu as calculators in complex multiplications. I will introduce the example of quipu 719 which is one of the few surviving Inca multiplication “tables” .
Topic: Newton vs. Leibniz
- General Introduction o Introduction to who Newton and Leibniz are and their impact on the world of Mathematics.
- What is the Calculus Controversy?
- An Introduction to what the controversy is, why it exists and how it started.
- Introducing Their Ideas o Newton’s Method of Fluxions-
- Talk about the main points in Newton’s version of Calculus. Introduce the terms he uses such as Fluents and discuss how Newton would solve a Calculus problem. o Leibniz’ Differential and Integral Calculus-
- Discuss Leibniz’ construction of quadratures and the notations Leibniz introduced.
- This is the section in which I will provide detailed solutions as to how both men would solve a calculus problem.
- The Controversy o Who Did It First? –
- Discuss the evidence, timeframes, and historians’ viewpoints of both of their works.
- This includes discussing Leibniz’ 1673 visit to London, Leibniz correspondences with Collins, and Leibniz and Newton’s correspondences with each other.
- England’s loyalty to Newton.
- How the controversy has impacted the world of mathematics and present-day calculus.