Roland S McIntire
Motivating Mathematical Concepts through Problems
This podcast takes the approach of motivating mathematical concepts by way of a compelling problem. This is NOT the same as providing a definition and then showing that it solve a useful problem. The later has the feeling of someone doing mathematics to someone as opposed to giving one the sense that mathematics is a human endeavor; full of practical problems that need to be solved. Instead people often feel like that are being handed a collection of stone tablets handed down from the math gods. This does not mean that the material is easy. It does not mean that the material provides a history...
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Simple Geometric Proof of a Classic result as well as some Conjectures for Pythagorean Triples 12.11.2024 8:55
A new geometric proof of the result that for primitive Pythagorean triples: c is odd one of the legs is divisible by 4 the other leg is odd. Conjectures that partition the set of primitive Pythagorean hypotenuses into two sets. Conjectures that try to examine the complexity of these two partitioning sets.
Computing EMA and Deriving Formulas for Unbiased Moments of Weighted Averages 12.11.2024 10:25
Derives recursive computational formulas for EMA and its standard deviation. Derives formulas for computing higher unbiased moments.
Discrete and Continuous Calculus: The Essentials 12.11.2024 17:58
The general theme is to show that the differencing and summing oof sequences of numbers are inverse operations in some sense. This is easy to do and helps us understand the continuous analogs of these; namely, differentiation and integration. Goes further and examines difference equations and relates them to the continuous notion of differential equations. Once again, it uses the easier discrete p...
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