Mathematics | Chris Aldrich

🎧 Episode 097 Applied Mathematics & the Evolution of Music: An Interview With Natalia Komarova | HumanCurrent

Listened to Episode 097 Applied Mathematics & the Evolution of Music: An Interview With Natalia Komarova by

Haley Campbell-Gross from HumanCurrent

In this episode, Haley interviews Natalia Komarova, Chancellor's Professor of the School of Physical Sciences at the University of California, Irvine. Komarova talks with Haley at the Ninth International Conference on Complex Systems about her presentation, which explored using applied mathematics to study the spread of mutants, as well as the evolution of popular music.

There’s some interesting sounding research being described here. Be sure to circle back around to some of her papers.

Acquired Category Theory for the Sciences by David I. Spivak

Acquired Category Theory for the Sciences by David I. Spivak (The MIT Press, 1st Edition)

An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences.

Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines.

Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs―categories in disguise. After explaining the “big three” concepts of category theory―categories, functors, and natural transformations―the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions.

Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.

Ordered a copy from Amazon

👓 AI Is Making It Extremely Easy for Students to Cheat | WIRED

Read AI Is Making It Extremely Easy for Students to Cheat (WIRED)

Teachers are being forced to adapt to new tools that execute homework perfectly.

The headline is a bit click-baity, but the article is pretty solid nonetheless.

There is some interesting discussion in here on how digital technology meets pedagogy. We definitely need to think about how we reframe what is happening here. I’m a bit surprised they didn’t look back at the history of the acceptance (or not) of the calculator in math classes from the 60’s onward.

Where it comes to math, some of these tools can be quite useful, but students need to have the correct and incorrect uses of these technologies explained and modeled for them. Rote cheating certainly isn’t going to help them, but if used as a general tutorial of how and why methods work, then it can be invaluable and allow them to jump much further ahead of where they might otherwise be.

I’m reminded of having told many in the past that the general concepts behind the subject of calculus are actually quite simple and relatively easy to master. The typical issue is that students in these classes may be able to do the first step of the problem which is the actual calculus, but get hung up on not having practiced the algebra enough and the 10 steps of algebra after the first step of calculus is where their stumbling block lies in getting the correct answer.

👓 Developing Mathematical Mindsets | American Federation of Teachers

Read Developing Mathematical Mindsets by Jo Boaler (American Federation of Teachers)

Babies and infants love mathematics. Give babies a set of blocks, and they will build and order them, fascinated by the ways the edges line up. Children will look up at the sky and be delighted by the V formations in which birds fly. Count a set of objects with a young child and then move the objects and count them again, and they will be enchanted by the fact they still have the same number. Ask children to make patterns with colored blocks, and they will work happily making repeating patterns—one of the most mathematical of all acts. Mathematician Keith Devlin has written a range of books showing strong evidence that we are all natural mathematics users and thinkers.¹ We want to see patterns in the world and to understand the rhythms of the universe. But the joy and fascination young children experience with mathematics are quickly replaced by dread and dislike when they start school mathematics and are introduced to a dry set of methods they think they just have to accept and remember.

If you think mathematics is difficult, tough, or you’re scared of it, this article will indicate why and potentially show you a way forward for yourself and your children.

Highlights, Quotes, Annotations, & Marginalia

The low achievers did not know less, they just did not use numbers flexibly—probably because they had been set on the wrong pathway, from an early age, of trying to memorize methods and number facts instead of interacting with numbers flexibly. ❧

December 15, 2018 at 08:42AM

Unfortunately for low achievers, they are often identified as struggling with math and therefore given more drill and practice—cementing their beliefs that math success means memorizing methods, not understanding and making sense of situations. They are sent down a damaging pathway that makes them cling to formal procedures, and as a result, they often face a lifetime of difficulty with mathematics. ❧

December 15, 2018 at 08:44AM

Notably, the brain can only compress concepts; it cannot compress rules and methods. ❧

December 15, 2018 at 08:44AM

Unfortunately, many classrooms focus on math facts in isolation, giving students the impression that math facts are the essence of mathematics, and, even worse, that mastering the fast recall of math facts is what it means to be a strong mathematics student. Both of these ideas are wrong, and it is critical that we remove them from classrooms, as they play a key role in creating math-anxious and disaffected students. ❧

This article uses the word “unfortunately quite a lot.
December 15, 2018 at 08:46AM

The hippocampus, like other brain regions, is not fixed and can grow at any time,15 but it will always be the case that some students are faster or slower when memorizing, and this has nothing to do with mathematics potential. ❧

December 15, 2018 at 08:53AM