Mathematics Books — a Few of the Very Best Jul 2021

Mathematics — my favorites

Of all the books that I’ve ever read — the best.

Author: Herbert S. Wilf
Department of Mathematics
University of Pennsylvania
Philadelphia, Pennsylvania
Copyright 1990 and 1994 by Academic Press, Inc.
Authors: Marko Petkovŝek, Herbert S. Wilf, Doron Zeilberger
Marko Petkovŝek, University of Ljubljana, Ljubljana, Slovenia
Herbert S. Wilf, University of Pennsylvania, Philadelphia, PA, USA
Doron Zeilberger, Temple University, Philadelphia, PA, USA
April 27, 1997
Concrete Mathematics: A Foundation for Computer Science
Authors: Ronald L. Graham, Donald E. Knuth, Oren Patashnik
January 1994
Addison-Wesley Longman Publishing Co, Inc

In computer science and mathematics, the Josephus problem (or Josephus permutation) is a theoretical problem related to a certain counting-out game.

Excerpt from Concrete Mathematics, Section 1.3: “Our final introductory example is a variant of an ancient problem named for Flavius Josephus, a famous historian of the first century. Legend has it that Josephus wouldn’t have lived to become famous without his mathematical talents. During the Jewish-Roman war, he was among a band of 41 Jewish rebels trapped in a cave by the Romans. Preferring suicide to  capture, the rebels decided to form a circle and, proceeding around it, to kill every third remaining person until no one was left. But Josephus, along with an unindicted co-conspirator, wanted none of this suicide nonsense; so he quickly calculated where he and his friend should stand in the vicious circle.”

Interesting Websites Nov 2018
Visual Complex Analysis
Author: Tristan Needham
Oxford University Press 2005 – finite calculus.pdf
Finite Calculus: A Tutorial for Solving Nasty Sums
Author: David Gleich
January 17, 2005

Geometric Tranformations
Author: I. M. Yaglom
The Trachtenberg Speed System of Basic Mathematics
Author: Jakow Trachtenberg, Translated and Adapted by Ann Cutler and Rudolph McShane
Doubleday & Company, 1960

Of the books in this list, the Trachtenberg book is suited to middle school and up.


Do your best work,
Revisit next morning and edit out errors,
Revisit next week and edit out errors,
Revisit and run several arbitrary (though maybe realistic) test cases, edit out errors.


Web Lectures -- a Few of the Very Best
Brilliant Series

Imagine — in the 2020s, we can have Brian Greene as our private physics tutor.

A wonderful gift!

Thank you, Dr. Greene.KLH

Episode 01: Brian Greene kicks off Your Daily Equation with Albert Einstein’s famous equation E = mc2

Your Daily Equation #1: E = mc2



3Blue1Brown is a math YouTube channel created by Grant Sanderson. The channel focuses on teaching higher mathematics from a visual perspective, and on the process of discovery and inquiry-based learning in mathematics, which Sanderson calls “inventing math”.
Three Blue One Brown Feb 2019 (a previous post)

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