A study of 10,000 school districts shows how local norms help grow or shrink gender achievement gaps.
Category: Mathematics
👓 Francis Su’s Favorite Theorem | Scientific American Blog Network | Roots of Unity
The Harvey Mudd College mathematician tells us why he loves playing with Brouwer's fixed-point theorem
I need to remember to subscribe to this podcast…
👓 Just teach my kid the <adjective> math | Medium
It is astounding to me that mathematics — of all school subjects — elicits such potent emotional reaction when “reform” is in the air…
An interesting take on the changes in math curriculum over the past few years. Takeaway, we need to think about the pedagogy we use with the public and parents as well.
👓 Squares and prettier graphs | Stuart Landridge
The Futility Closet people recently posted “A Square Circle“, in which they showed: 49² + 73² = 7730 77² + 30² = 6829 68² + 29² = 5465 54² + 65² = 7141 71² + 41² = 6722 67² + 22² = 4973 which is a nice little result. I like this sort of recreational maths, so I spent a little time w...
An interesting cyclic structure here.
🔖 Bulletin of Mathematical Biology, Volume 80, Issue 5 Special Issue: Mathematical Oncology
Special Issue: Mathematical Oncology
h/t to @ara_anderson
Its finally out! Our mammoth special issue of the @SpringerNature Bulletin of Mathematical Biology on #mathonco Mathematical Oncology! Jointly edited with @OxUniMaths Philip Maini and this is the single biggest issue in the journals history! @MoffittNews https://t.co/K9GqAPTjy8 pic.twitter.com/tUDs1ACZCW
— Sandy Anderson (@ara_anderson) April 28, 2018
🔖 The Theory of Quantum Information by John Watrous
To be published by Cambridge University Press in April 2018.
Upon publication this book will be available for purchase through Cambridge University Press and other standard distribution channels. Please see the publisher's web page to pre-order the book or to obtain further details on its publication date.
A draft, pre-publication copy of the book can be found below. This draft copy is made available for personal use only and must not be sold or redistributed.
This largely self-contained book on the theory of quantum information focuses on precise mathematical formulations and proofs of fundamental facts that form the foundation of the subject. It is intended for graduate students and researchers in mathematics, computer science, and theoretical physics seeking to develop a thorough understanding of key results, proof techniques, and methodologies that are relevant to a wide range of research topics within the theory of quantum information and computation. The book is accessible to readers with an understanding of basic mathematics, including linear algebra, mathematical analysis, and probability theory. An introductory chapter summarizes these necessary mathematical prerequisites, and starting from this foundation, the book includes clear and complete proofs of all results it presents. Each subsequent chapter includes challenging exercises intended to help readers to develop their own skills for discovering proofs concerning the theory of quantum information.
h/t to @michael_nielsen via Nuzzel
John Watrous's excellent quantum book just came out. It's still available free on his webpage: https://t.co/D2rr5FTly6
— michael_nielsen (@michael_nielsen) April 28, 2018
🔖 actualham tweet about interactive glossary/encyclopedia for challenging technical/academic jargon that can be layered into textbooks
Robin DeRosa on Twitter (Twitter)Just Skyped with a math student @UofR who has built (beta) an interactive glossary/encyclopedia for challenging technical/academic jargon that can be layered into textbooks. He wants to develop it as an #opensource resource for #OER. More soon, but the future is SO OPEN!
— Robin DeRosa (@actualham) April 27, 2018
Following Ilyas Khan
Co-Founder and CEO at Cambridge Quantum Computing
Dear god, I wish Ilyas had a traditional blog with a true feed, but I’m willing to put up with the inconvenience of manually looking him up from time to time to see what he’s writing about quantum mechanics, quantum computing, category theory, and other areas of math.
Reply to A (very) gentle comment on Algebraic Geometry for the faint-hearted | Ilyas Khan
Ilyas Khan (LinkedIn)This short article is the result of various conversations over the course of the past year or so that arose on the back of two articles/blog pieces that I have previously written about Category Theory (here and here). One of my objectives with such articles, whether they be on aspects of quantum computing or about aspects of maths, is to try and de-mystify as much of the associated jargon as possible, and bring some of the stunning beauty and wonder of the subject to as wide an audience as possible. Whilst it is clearly not possible to become an expert overnight, and it is certainly not my objective to try and provide more than an introduction (hopefully stimulating further research and study), I remain convinced that with a little effort, non-specialists and even self confessed math-phobes can grasp some of the core concepts. In the case of my articles on Category Theory, I felt that even if I could generate one small gasp of excited comprehension where there was previously only confusion, then the articles were worth writing.
I just finished a course on Algebraic Geometry through UCLA Extension, which was geared toward non-traditional math students and professionals, and wish I had known about Smith’s textbook when I’d started. I did spend some time with Cox, Little, and O’Shea’s Ideals, Varieties, and Algorithms which is a pretty good introduction to the area, but written a bit more for computer scientists and engineers in mind rather than the pure mathematician, which might recommend it more toward your audience here as well. It’s certainly more accessible than Hartshorne for the faint-of-heart.
I’ve enjoyed your prior articles on category theory which have spurred me to delve deeper into the area. For others who are interested, I thought I’d also mention that physicist and information theorist John Carlos Baez at UCR has recently started an applied category theory online course which I suspect is a bit more accessible than most of the higher graduate level texts and courses currently out. For more details, I’d suggest starting here: https://johncarlosbaez.wordpress.com/2018/03/26/seven-sketches-in-compositionality/
👓 Decades-Old Graph Problem Yields to Amateur Mathematician | Quanta Magazine
By making the first progress on the “chromatic number of the plane” problem in over 60 years, an anti-aging pundit has achieved mathematical immortality.
🔖 List of geometry topics
This is a list of geometry topics, by Wikipedia page.
h/t to @mathematicsprof
One misconception of the general public is that geometry is the kind of geometry the Greeks studied and nothing else. That’s like asking an engineer if engineering has progressed past the wheel. Here is a list of the many kinds of geometries. https://t.co/4gjGsCVqkX
— math prof (@mathematicsprof) April 19, 2018
👓 Why We Use “X” as the Unknown in Math | Gizmodo
For hundreds of years, x has been the go-to symbol for the unknown quantity in mathematical equations. So who started this practice?
👓 Mathematicians Explore Mirror Link Between Two Geometric Worlds | Quanta Magazine
Decades after physicists happened upon a stunning mathematical coincidence, researchers are getting close to understanding the link between two seemingly unrelated geometric universes.
An interesting story in that physicists found the connection first and mathematicians are tying the two areas together after the fact. More often it’s the case that mathematicians come up with the theory and then physicists are applying it to something. I’m not sure I like some of the naming conventions laid out, but it’ll be another decade or two after it’s all settled before things have more logical sounding names. I’m a bit curious if any category theorists are playing around in either of these areas.
After having spent the last couple of months working through some of the “rigidity” (not the best descriptor in the article as it shows some inherent bias in my opinion) of algebraic geometry, now I’m feeling like symplectic geometry could be fun.
👓 Six ‘X-Rated’ Math Terms That Only Sound Dirty | Huffington Post
Cox-Zucker machine. What sounds like a high-tech device for oral sex is actually an algorithm used in the study of certain curves, including those that arise in cryptography. The story goes that David A. Cox co-authored a paper with fellow mathematician Steven Zucker, just so that the dirty-sounding term would enter the lexicon.
I always thought he was cool before (many of his students didn’t “get” him), but I’m now even more proud to have had Steven Zucker as my first math professor in college.
🔖 [1803.05316] Seven Sketches in Compositionality: An Invitation to Applied Category Theory
This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. It aims to give a tour: a gentle, quick introduction to guide later exploration. The tour takes place over seven sketches, each pairing an evocative application, such as databases, electric circuits, or dynamical systems, with the exploration of a categorical structure, such as adjoint functors, enriched categories, or toposes. No prior knowledge of category theory is assumed. [.pdf]
This is the textbook that John Carlos Baez is going to use for his online course in Applied Category Theory.