Reddit reviews Winning Ways for Your Mathematical Plays: Volume 1

Knizia is a mathematician. For anyone who's ever studied game theory, Knizia's designs are usually pretty obviously derivative of "mathematical games" (this isn't a criticism.) Sometimes I think he just whips out his copy of winning ways and riffs on stuff until he finds a design he likes. Or at least that's how it seems to me.

Like another commenter said, I think Knizia definitely falls into the camp of "experimental genius." I think SUSD put it aptly "Reiner Knizia has designed 1000's of games, literally some of which are good."

If you find this interesting, check out Winning Ways for Your Mathematical Plays, it covers this in more depth, as well as a host of other combinatorial games. This game is in v1.

Linear programming:

• Vanderbei, Linear Programming: Foundations and Extensions
  
  Combinatorial optimization:
  
  
• Papadimitriou and Steiglitz, Combinatorial Optimization: Algorithms and Complexity
  
• Cook, Cunningham, Pulleyblank, and Schrijver, Combinatorial Optimization
  
  Game theory:
  
  
• Fudenberg and Tirole, Game Theory
  
• Osborne and Rubinstein, A Course in Game Theory
  
  Combinatorial game theory:
  
  
• Berlekamp, Conway, and Guy, Winning Ways for Your Mathematical Plays (volume 1, volume 2, volume 3, volume 4)
  
• Berlekamp, The Dots and Boxes Game: Sophisticated Child's Play
  
• Albert, Nowakowski, and Wolfe, Lessons in Play: An Introduction to Combinatorial Game Theory
  
• Conway, On Numbers and Games

The Beauty of Geometry: Twelve Essays, H. S. M. Coxeter
This requires a little background, and may require a few brain cells, but Coxeter is a great expositor. I find myself rereading this every couple of years.

The Pleasures of Counting, TW Korner
This is a tour through applied math. It needs almost no background, but does more than scratch the surface. It is the perfect response to "... bur what is this good for?". I'd also recommend his 'Fourier Analysis', but I'm pretty sure that it does not qualify as light.

Winning Ways, J. H. Conway, et. al.
Light in tone, but heavy in content. I love these books. Other people, including competent mathematicians, have declared them as impossible to learn from.

If you do not mind reading from the screen, try this collection of Martin Gardner's books.

Pricey

do you want stuff to get ahead in university or just fun stuff?

if you just want fun stuff, i highly recommend a book called Winning Ways. it's about 2 player games... hard to explain exactly what it is, but after finishing my B.A. in Mathematics, it is easily the most fun book i've ever read.

EDIT: Amazon link: http://www.amazon.com/Winning-Ways-Your-Mathematical-Plays/dp/1568811306

Please go check out Winning Ways for Your Mathematical Plays.

1. LOVE this book: Pearls in Graph Theory
   
   Chapters are short and engaging. Great exercises. Very visual and creative which should make mathematical structure more appealing to a lay person.
   
   
2. Winning Ways for your Mathematical Plays by Berlekamp, Conway, and Guy may not satisfy your rigorous criterion but should blow the mind of anyone who thinks of math as primarily computational tools.
   
   
3. Visual Complex Analysis by Needham is an amazing book, but may be too technically difficult (particularly if her calculus is rusty).

My copy of Winning Ways For Your Mathematical Plays signed for me personally by Berlekamp, Conway and Guy is pretty high on my list.

Winning Ways for Your Mathematical Plays is a fantastic book to work through. Berlekamp also has a great Dots and Boxes book.

SG is the start of it. Berkelkam et al. created the necessary rules to extend this for partial, misere and other forms. Winning Ways for Mathematical Plays series does this well. You have to expand Nim to a multistacked version with some extra rules, but it is essentially the same thing.