Mathematica U. and AP Calculus

The Wolfram Company which makes the premier mathematical computing software program "Mathematica" has branched out into all different directions, but one of their core areas of interest is teaching mathematics to all levels of students. They have apparently established a 'University' where online study can be found. Some of their latest work involves advanced placement Calculus.

And from their Facebook presentation we get:

[20180919]

Russian School Mathematics Results

The is an after school enrichment opportunity for grade school-aged students which will help develop mathematical interests (do not be thrown off by the "Russian" part of the name it's just a teaching technique first perfected in Russia). But there is nothing like success to speak well of this endeavor, so without further ado here is some of their recent triumphs:

They aren't everywhere, but if you are lucky enough to  live near a center I would urge you to look into it!

[20180818]

Laugh of the Day, 20180817 xkcd

"All electromagnetic equations: The same as all fluid dynamics equations, but with the 8 and 23 replaced with the permittivity and permeability of free space, respectively."


A complete explanation of why this is funny and/or wrong, depending on your point of view can be found at: "explainxkcd.com"


[20180817]

AP High School Calculus? Ummm...I think not.

Simple enough...unless you are truly a gifted student and have already mastered one of those massive Pre-Calculus Algebra books you should forget about taking high school calculus. High school is the time to truly master algebra. After all, calculus is just the manipulation of algebraic concepts, not some new math that is so way beyond anybody that people taking it are called "Einsteins!" Not really, calculus is just more better algebra...at least for you beginning students. Later on, if you are a math major, it can become something new and exciting, but you'd better have the basics down pat! OK, don't believe me? Well how about Harvard?

You've been so advised, now do it!!!

[20180804]

Proofs from the Book

Paul Erdos used to remark that a particularly elegant of beautiful proof of a mathematical theorem was one for the "Book." This reference is to a hypothetical book Erdos figured God was keeping with only the very best proofs. Oh, if one could only be so lucky as to read this book! As things worked out two mathematicians took his book concept to heart and, after careful consultation with Erdos, decided to give it their best shot. The following link interviews the two authors and gives an interesting background to their book, "Proofs from the Book", 5th edition. As mentioned at the end off the interview there may be a sixth edition available at some point.


Proofs from the Book, authors interview.

[20180322]

More to the point:

A conjecture both deep and profound
Is whether a circle is round.
In a paper of Erdős
Written in Kurdish
A counterexample is found.

Simon's Course in Modern Analysis

Professor Barry Simon of Caltech has a series of books on modern analysis. As a prelude to this set he has written an ~130 page 'companion guide' which is available free from the Am. Math. Society at this link. It's a good read for anyone irrespective of level of math skills. Please avail yourself of this free publication! Give yourself a Valentine's Day present.

Now, right out of the gate, Prof. Simon tells us:

"Analysis is the infinitesimal calculus writ large. Calculus as taught to most high school students and college freshmen is the subject as it existed about 1750—I’ve no doubt that Euler could have gotten a perfect score on the Calculus BC advanced placement exam. Even “rigorous” calculus courses that talk about ε-δ proofs and the intermediate value theorem only bring the subject up to about 1890 after the impact of Cauchy and Weierstrass on real variable calculus was felt.

"This volume [vol 1] can be thought of as the infinitesimal calculus of the twentieth century. From that point of view, the key chapters are Chapter 4, which covers measure theory—the consummate integral calculus—and the first part of Chapter 6 on distribution theory—the ultimate differential calculus.
"But from another point of view, this volume is about the triumph of abstraction. Abstraction is such a central part of modern mathematics that one forgets that it wasn’t until Frechet’s 1906 thesis that sets of points with no a priori underlying structure (not assumed points in or functions on Rn) are considered and given a structure a posteriori (Frechet first defined abstract metric spaces). And after its success in analysis, abstraction took over significant parts of algebra, geometry, topology, and logic."

[20180214]

MathWorld

One freely available resource supporter by Wolfram Research is an online reference called MathWorld, available here. A link to this site should be on everybody's desktop.

[20180214]

Mathematica and all that

At the risk of coming off as a shill for a commercial product (I'm not, I'm just an enthusiastic user) I would like to recommend the entire product line of mathematical tools available from Wolfram Research here. The flagship software is of course Mathematica. If you have not tried Mathematica you owe it to yourself, it's amazing and the number of avenues to access it has grown from Desktops to clouds and iOS availability. One never need be without sophisticated computational power! I urge you to visit their website!

[20140214]

Data collections

Sometimes one just needs to run some data through a calculation just to see if it works, no? Well, given enough complexity in the requirements, i.e. the data should have some fair amount of complexity, it is tedious to develop a database just for dry runs. Enter Wolfram! This software company which makes "Mathematica" and developed and maintains "Wolfram|Alpha" now offers collections of data just for those mathematicians needing to feed their latest creation. A link to the data collection is here.

[20180214]

Online source encyclopedia of math functions

Here's a handy and valuable online list of functions curated by NIST: DLMF.

Historical note. This is the online and updated version of the big, paperback reference book authored and edited by Abramowitz and Stegun. Additionally, the online version has been checked and validated by Professor Tom Apostol.

[20180103]

John A. Wheeler's Papers

A well curated archive of Prof. Wheeler's publications is available at the "JAW Archive."

[20120102]