
Why_Matrix_Multiplication
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.

Hosted by Roland S McIntire · EN · 14 episodes
Established thought leaders with verified media credentials.
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 of how a given concept was created; rather, it provides at best, a pseudo history of how a given concept may have come about. The podcast also contains episodes on new material and some conjectures.
Roland S McIntire hosts Motivating Mathematical Concepts through Problems, a science show with 14 episodes published.

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.

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.

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" estimat

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 t

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

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 e

Tries to motivate Lebesgue Integration by trying to find an improved limit theorem for Riemann Integration. In the process, find that this seems a lot like trying to find limit results when only dealing with rational num

Defines fractal dimension Why it is a useful concept. Computes the fractal length of a simple non-fractal set Computes the "length" of a self-similar fractal in its "natural" fractional dimension.

Inner Product can be thought of coming from the notion of Projection. If follows from doing a Mathematical "re-factoring", something that one usually only hears in the context of software engineering.

Rather than giving a formula for the determinant, one tries to derive it from first principles. The principles come about by looking at the volume of a parallelepiped. Uses the properties that such a formula would have t

Uses a motivationing example to show: How a matrix comes up naturally.How to define matrix/vector multiplication.How to define matrix/matrix multiplication.How to define an identity matrix.

Shows that the notion of what a derivative is -- NOT what one learns in first year calculus -- that it is the "best" linear approximation to a function. This idea allows us to extend the derivative beyond what one sees i

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 tw

Derives recursive computational formulas for EMA and its standard deviation. Derives formulas for computing higher unbiased moments.

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, differenti
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Motivating Mathematical Concepts through Problems is hosted by Roland S McIntire. The show is categorised under science (mathematics) and has published 14 episodes.
Motivating Mathematical Concepts through Problems has published 14 episodes.
Motivating Mathematical Concepts through Problems regularly covers science, mathematics. It sits in the science category, with a mathematics focus.
Motivating Mathematical Concepts through Problems is accessible for guests with genuine science expertise. A personalised, episode-aware pitch will still outperform a generic one every time.
Motivating Mathematical Concepts through Problems hasn't explicitly signalled guest openness in recent episodes. That doesn't rule out pitching. your hook just needs to be especially compelling and relevant to their recent content.
Episodes of Motivating Mathematical Concepts through Problems average 14 minutes. a focused format where a clear narrative arc and tight preparation matter most.
Our data rates Motivating Mathematical Concepts through Problems's guest bar at 80/100 (Premium tier). Established thought leaders with verified media credentials. Sign in to PitchCentric to see how your own Pod Score compares against this show.
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