Mathematics Books — a Few of the Very Best Jul 2021

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https://www2.math.upenn.edu/~wilf/gfologyLinked2.pdf
generatingfunctionology

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

Author: Herbert S. Wilf
Department of Mathematics
University of Pennsylvania
Philadelphia, Pennsylvania
Copyright 1990 and 1994 by Academic Press, Inc.

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https://www2.math.upenn.edu/~wilf/AeqB.pdf
A=B
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

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https://dl.acm.org/doi/book/10.5555/562056#secAbs
Concrete Mathematics: A Foundation for Computer Science
Authors: Ronald L. Graham, Donald E. Knuth, Oren Patashnik
January 1994
Addison-Wesley Longman Publishing Co, Inc

Tease
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
https://en.wikipedia.org/wiki/Josephus_problem

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https://www.maa.org/press/maa-reviews/visual-complex-analysis
Visual Complex Analysis

A beautiful book — so perfectly written covering amazing jewels of mathematics.

Author: Tristan Needham
2009
Oxford University Press

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https://www.cs.purdue.edu/homes/dgleich/publications/Gleich 2005 – finite calculus.pdf
Finite Calculus: A Tutorial for Solving Nasty Sums
Author: David Gleich
January 17, 2005

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https://www.ams.org/books/nml/008/nml008-endmatter.pdf
Geometric Transformations

''Assume that the problem has been solved''
   (a theme in the book)

Author: I. M. Yaglom
1962

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https://www.amazon.com/Trachtenberg-Speed-System-Basic-Mathematics/dp/4871877094
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.

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https://bookstore.ams.org/view?ProductCode=NML/19
PDF preview
Geometry Revisited
Authors: H. S. M. Coxeter, Samuel L, Greitzer
Publisher: New Mathematical Library
1967

[July 2024] I just bought this (used) book. I love the clear diagrams and text. The presentation is in every way artistic.

Greatest classical geometer of the 20th century
Tribute from Edsger Dijkstra — Coxeter’s rabbit EWD1318-0

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https://www.amazon.com/Complete-Idiots-Guide-Game-Theory/dp/161564055X
The Complete Idiot’s Guide to Game Theory
Authors: Edward C. Rosenthal
Publisher: Alpha
2011

The book has a warm feel to it, a casual lecture style. I like the mix of math, logic, and humanity, and the competitive spectrum (hand games, auctions, negotiations, voting, war games). Two of the most interesting areas within game theory are incomplete knowledge and signalling.