Thomas M. Green

Prepare to be intrigued by the many facets of the properties of the amazing array of numbers known as Pascal's Triangle and its many relatives. Some of the topics you will find: Polytopes Simplexes and the Simplex Triangle Tetrahedral, and higher dimensional figurate numbers Duplexes and The Duplex Triangle Geometric Duplication - Cubes and Hypercubes Vandermonde's Identity for the Duplex Triangle and the Triplex Triangle Euler's formula for Simplexes and Duplexes Recurrent Sequences in Pascal's Triangle and its Relatives Including the Fibonacci, Pell and Jacobsthal Sequences Pythagorean Triples - Related to the Sequences Listed Above Properties Involving String Products and more. There is a comprehensive index that will allow readers to easily search for topics of their interest. One goal is to provide a vehicle to the discovery of some higher mathematics related to higher dimensional geometric figures, at an entry level for the young beginning researcher by including many exercises that ask for verification of a pattern by testing specific cases and conjecturing a generalization of the pattern. Another major goal was to make available source materials for mathematics teachers to use in their classes. Included are many topics suitable for introducing students, at the pre-college level, to the sense of satisfaction one receives while exploring and discovering significant parts of advanced mathematics. I hope you will enjoy exploring this amazing Arithmetic Triangle and its relatives as much as I have. There is still much more to be discovered, of that I am certain. Teachers and students are eligible for special discounts for purchases of this book. Send an email to [email protected] for information on qualifying for a discount code to use before ordering.

Pascal's Triangle is one of the most intriguing array of numbers in mathematics. Not only are there seemingly boundless patterns and relationships within the trianglular array itself, but there are also numerous applications in mathematics, probability, statistics and science. Students at all levels, elementary through college, can find something of interest appropriate to their level and beyond. This book has been designed to provide a vehicle to the discovery of many of those patterns and applications. This 2nd Editioncontains new material on Catalan numbers centered polygonal numbers counting paths on grids Euler's formula Pascal's pyramid Vandermonde's identity and more. Teachers and students are eligible for special discounts for purchases of this book. Send an email to [email protected] for information on qualifying for a discount code to use before ordering.

Texas Hold 'Em Poker d104book - Mathematics, Probabilities and Odds of Poker - is a book about understanding the mathematics of permutations, combinations, probability rules and odds relevant to playing cards used in creating poker hands, specifically in the game of Texas Hold 'Em. The discussions and charts show the probabilities of your own hand and the probabilities of the hands the other players could have after the deal, after the flop, at the turn, and after the river.Additionally, separate chapters cover the concepts of expected value, poker odds, pot odds, and basic player strategy and tactics. Numerous illustrations, graphs, charts, and tables augment the discussions. The problem sets in most sections ask (and solve) questions of interest for any serious player. "... I was thinking that I could get lost in this book and never be found " - Deke Castleman, Senior Editor, Huntington Press "An Incredible New Book & Author" - by George 'The Engineer' Epstein, columnist, Poker Player Newspaper, Parts I & II, Jan. 2012 A great starter book for anyone and enough information of value for the advanced player. So, limp in or ante up and buy this book, it will be one of the more rewarding bets you will make.