These are the notes for the Clay Mathematics Institute Senior Scholar Lecture which was delivered by Bernd Sturmfels in Park City, Utah, on July 22, 2004. The topic of this lecture is the ``tropical approach'' in mathematics, which has gotten a lot of attention recently in combinatorics, algebraic geometry and related fields. It offers an an elementary introduction to this subject, touching upon Arithmetic, Polynomials, Curves, Phylogenetics and Linear Spaces. Each section ends with a suggestion for further research. The bibliography contains numerousreferences for further reading in this field.

[See also: https://www.youtube.com/watch?v=ghiZVlfLdVg
"The currently accepted world map dates from 1569 when Gerardus Mercator originally designed it. Hajime Narukawa has been working on a more accurate version of the planet's continents for years now and was awarded the 2016 Good Design Award for his new world map."]

Quantum computers can only cheat so much before they out themselves

Welcome to my online math tutorials and notes. The intent of this site is to provide a complete set of free online (and downloadable) notes and/or tutorials for classes that I teach at Lamar University. I've tried to write the notes/tutorials in such a way that they should be accessible to anyone wanting to learn the subject regardless of whether you are in my classes or not. In other words, they do not assume you've got any prior knowledge other than the standard set of prerequisite material needed for that class. In other words, it is assumed that you know Algebra and Trig prior to reading the Calculus I notes, know Calculus I prior to reading the Calculus II notes, etc. The assumptions about your background that I've made are given with each description below.

Great article on why #mathematics gets left out of mainstream histories of knowledge, gives Heidegger a kick for good measure