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# 2.19 AOK: Mathematics

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## James Conner

on 6 April 2018

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#### Transcript of 2.19 AOK: Mathematics

Scope and Application
Concepts and Languages
Methodology

Historical Development

Links to Personal Knowledge
Algebra
Calculus and analysis
Geometry and topology
Number theory
Combinatorics
Logic

PURE MATHEMATICS
APPLIED MATHEMATICS
Dynamical systems and differential equations
Mathematical physics
Computing
Information theory and signal processing
Probability and statistics
Game theory
Operations research
Mathematical Language
Numbers and Symbols
1.2.3.4.5.6.7.8.9....
I, II, III, IV, V, VI...
Mathematical language follows a set of rules, used to express ideas.
Sets- a collection of elements which can themselves be sets.

The Natural Numbers
Infinite Sets
Fractals
PROOF
What it is about the methods of mathematics that give us this cast-iron guarantee that its results are absolutely certain and that there is not a glimmer of doubt attached to them?
Knowledge Question:
THEOREM
AXIOMS
Proof is a formal method that establishes the truth of statements in mathematics.
SHIP
SHOP

DOCK
a conjecture – a mathematical statement that has not yet been proven.
a set of rules;
ie. distributive property, associative property
PROOF
AXIOMS
THEOREM
}
Each word differs from the one above it by changing only one letter. The aim is to arrive at the word DOCK.
the constructivist view
human invention
the Platonic view
humans discover it
1. Is there a point in this number where there is a sequence of digits that matches your telephone number?

2. Is there a definite answer to (1)?
Are you a constructivist or a Platonist.

Consider the decimal expansion of Piπ = 3.141592653589793... The decimal goes on forever without terminating or repeating.

Now think about these two questions:

Pythagoras, Archimedes,
Euclid,
Diophantus,
Galileo,
Newton,
Leibniz,
Euler,
Gauss,
Contributors
Riemann,
Laplace,
Lagrange, Weierstrass,
Cauchy,
Hardy,
David Hilbert,
John von Neumann, Alain Connes, William Thurston, Andrew Wiles, Grigori Perelman
Probability and Intuition
Personal Finances
Business Management
Matrices/ Life's Riddles
the result of a finished proof
it exists independently of human thought
N= {1,2,3,4,5,6, ...}
THEORY OF KNOWLEDGE

AOK: Mathematics

LESSON #19

Objective: develop an awareness of how individuals and communities construct knowledge and how this is critically examined
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