The Society for Mathematical Biology - e-Conference 2020.
August 17 - 20, 2020
a fast way to write and share mathematics
I LATEXed up lecture notes for many of the classes I have taken; feel free to read through them or use them to review. If you find a mistake or typo, please let me know. If you want to look over the .tex source for any of these notes, please send me an email.
via Rama Kunapuli.
Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.
Module 4: -- Edward Frenkel: Harmonic Analysis
Module 1: -- Edward Frenkel: The Continents of Mathematics
Module 3: -- Edward Frenkel: Galois Groups
Module 2: -- Edward Frenkel: Symmetry and Unification
I find myself seeing some immediate and excellent historical examples in Dr. Ibram X. Kendi‘s book Stamped from the Beginning. In chapter nine of the book he discusses the variety and flavors of racism espoused by Thomas Jefferson in his book Notes on the State of Virginia (1785), which would become the most consumed American nonfiction book until well into the mid-nineteenth century.
Shortly afterward Samuel Stanhope Smith countered portions of Jefferson’s racist ideas in the 1787 annual oration to the august American Philosophical Society. This annual lecture was already one of the most heralded scholarly lectures in America and was attended by the wealthy and elite leaders and thinkers in the country. The lecture would be published as the influential Essay on the Causes of Variety of Complexion and Figure in the Human Species.
Samuel Stanhope Smith joined those preeminent intellectuals in Boston’s American Academy of Arts and Sciences and Philadelphia’s American Philosophical Society in attacking polygenesists, in reviving climate theory in America. His scholarly defense of scripture was quickly printed in Philadelphia, in London, and in Lord Kames’s back-yard, Edinburgh. By the time he sat down in Princeton’s presidential chair in 1795, he had amassed an international scholarly reputation.
So in just a few pages Kendi lays out some serious evidence of the direct spread of a wide variety of racist ideas by not only by the academic elite, but the leaders of multiple influential universities and scientific and philosophical institutions in America. The reverberating echos of these wrongs are still haunting us today. They still need to be addressed and righted. We need to use our moral alembic and distill these racist ideas out of science in America.
Lest one wonder about the influence of Samuel Stanhope Smith’s essay, I’ll note that Noah Webster cited Smith directly in Webster’s 1828 Dictionary in the definition of philosophy. The citation was from Smith’s second edition of his Essay on the Causes of Variety of Complexion and Figure in the Human Species (1810). The quote as given: “True religion, and true philosophy must ultimately arrive at the same principle.”
We’re obviously still seeking both true religion and true philosophy.
While you’re thinking about #shutdownSTEM on June 10th and long thereafter, I recommend you spend some time sitting with the ideas that have been handed down to us and question them closely, for this is what science and philosophy are all about. If you find you can’t do that hard work–and it is hard, then perhaps read a bit of Dr. Kendi’s excellent and ardent text Stamped from the Beginning.
An unsolved conjecture, and a clever topological solution to a weaker version of the question.
Mathematics Research Reports is a journal run for and by mathematicians, committed to the mission of providing high-quality scientific content, while adhering to the principles of Fair Open Access. This includes being freely available for a scientific audience worldwide, with no author publication charges, thanks to support from the Anatole Katok Center for Dynamical Systems and Geometry at the Pennsylvania State University. This journal publishes research announcements of significant advances in all branches of mathematics, short complete papers of original research (up to about 15 journal pages), and review articles (up to about 30 journal pages). All articles should be designed to communicate their contents to a broad mathematical audience and should meet high standards for mathematical content and clarity. All papers are reviewed, and the entire Editorial Board must approve the acceptance of any paper. Founded by members of the editorial board of Electronic Research Announcements in Mathematical Sciences (published by the American Institute of Mathematical Sciences and preceded by Electronic Research Announcements of the American Mathematical Society), Mathematics Research Reports is owned and operated by its editorial board, and supported by senior editors drawn from among former editors of both Electronic Research Announcements in Mathematical Sciences and Electronic Research Announcements of the American Mathematical Society.