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PODCAST

Motivating Mathematical Concepts through Problems

Roland S McIntire

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

science mathematics

All Episodes

18:46

Measure Theoretic Conditional Expectation in a...

Motivating Mathematical Concepts through Problems ·

2026/07/13

Examines what Modern Conditional Expectation means in a discrete setting.

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19:37

What is a Derivative

Motivating Mathematical Concepts through Problems ·

2026/07/13

Discusses the fundamental notion of a derivative and its extensions.

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20:03

Lebesgue Measure Theory

Motivating Mathematical Concepts through Problems ·

2026/07/13

We motivate Lebesgue Measure theory.

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21:39

Pythagorean Numbers: Conjectures and Results.

Motivating Mathematical Concepts through Problems ·

2026/07/13

We prove a theorem related to primitive Pythagorean Primes as well as present a few conjectures.

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17:11

Singular Probabilty Transformation

Motivating Mathematical Concepts through Problems ·

2026/07/13

Derives a formula for the probability density of a singular transformation of a random variable.

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19:59

Diversification Constraints

Motivating Mathematical Concepts through Problems ·

2026/07/13

Derives Diversification Constraints for Convex Optimization.

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22:38

The Essentails of Calculus

Motivating Mathematical Concepts through Problems ·

2026/07/13

Presents the Discrete and Continuous Calculus: The Essentials.

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21:25

Conditional Expecatation in a Discrete Setting

Motivating Mathematical Concepts through Problems ·

2026/07/13

Examines Lesbesgue Measure theoretic Conditional Expectation in a Discrete Setting.

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19:25

UnBiased Analytics of Exponential Moving Averages

Motivating Mathematical Concepts through Problems ·

2026/07/13

A number of formulas for weighted exponential moving averages and their moments.

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24:20

Where does the Dot Product come from?

Motivating Mathematical Concepts through Problems ·

2026/07/13

Explains how the dot product comes about.

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19:43

Where does the determinant come from?

Motivating Mathematical Concepts through Problems ·

2026/07/13

Explains the formula for the determinant of a matrix.

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20:06

Fractal Dimensions

Motivating Mathematical Concepts through Problems ·

2026/07/13

Explains Fractal Dimensions

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18:32

Why Matrix Multiplication

Motivating Mathematical Concepts through Problems ·

2026/07/13

Explains the reason why Matrix Multiplication is the way it is.

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20:27

Heat Equation and Friends

Motivating Mathematical Concepts through Problems ·

2026/07/13

We discuss the derivation of the Heat Equation and the Fokker-Plank Equation via a balance law.

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12:22

Why_Matrix_Multiplication

Motivating Mathematical Concepts through Problems ·

2024/12/08

Motivates the definition of Matrix/Vector and Matrix/Matrix multiplication by examining a systematic approach to a generalization of the simple equation a * x = b.

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11:14

Diversification Constraints in Convex Optimization

Motivating Mathematical Concepts through Problems ·

2024/11/12

Shows a way to add constraints to an optimization problem which wishes to bound the sum of the 'k' largest components of a given collection whiles minimizing a given objective.

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11:32

A New Property of a Minimal Unbiased Estimator

Motivating Mathematical Concepts through Problems ·

2024/11/12

Examines the problem AX = b + epsilon looking for an unbiased estimator. when using "trace" norms.Shows that the estimator is always the same.The infinite collection of these results imply that the usual "best" estimator has the property that its Maximum Eigenvalue is the smallest amongst all unbiased linear estimators.

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16:37

Develops a Systematic Formula for Computing the...

Motivating Mathematical Concepts through Problems ·

2024/11/12

It is known how to compute the probability distribution of a variable that is transformed in a non-singular way.When this is not the case, people find ad hoc ways of computing the probability distribution for singular transformations.The paper shows a more systematic process that leads to formulas form complex singular transformations.

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11:29

Deriving the Heat and Fokker-Plank Equations from...

Motivating Mathematical Concepts through Problems ·

2024/11/12

Shows how balance laws over arbitrary regions leads to a "local" version which is a Partial Differential Equation.

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17:42

Modern Conditional Expectation in a Discrete Setting

Motivating Mathematical Concepts through Problems ·

2024/11/12

Looks at measure theoretic conditional expectation in a discrete setting using the familiar example of single 6 sided dice.Shows how measure theory helps with the notion of conditional expectation when the conditional event has probability 0.

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29 results

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