Solomon W. Golomb

Andy Liu

This textbook offers an accessible introduction to combinatorics, infused with Solomon Golomb’s insights and illustrative examples. Core concepts in combinatorics are presented with an engaging narrative that suits undergraduate study at any level. Featuring early coverage of the Principle of Inclusion-Exclusion and a unified treatment of permutations later on, the structure emphasizes the cohesive development of ideas. Combined with the conversational style, this approach is especially well suited to independent study. Falling naturally into three parts, the book begins with a flexible Chapter Zero that can be used to cover essential background topics, or as a standalone problem-solving course. The following three chapters cover core topics in combinatorics, such as combinations, generating functions, and permutations. The final three chapters present additional topics, such as Fibonacci numbers, finite groups, and combinatorial structures. Numerous illuminating examples are included throughout, along with exercises of all levels. Three appendices include additional exercises, examples, and solutions to a selection of problems. Solomon Golomb’s Course on Undergraduate Combinatorics is ideal for introducing mathematics students to combinatorics at any stage in their program. There are no formal prerequisites, but readers will benefit from mathematical curiosity and a willingness to engage in the book’s many entertaining challenges.

Solomon Golomb’s Course on Undergraduate Combinatorics

This book provides an overview of how to run a Mathematical “Circle,” i.e., an organization that discovers and nurtures young mathematical talents through meaningful extra-curricular activities. This is the first volume in a trilogy describing in particular the S.M.A.R.T. Circle project, which was founded in Edmonton, Canada in 1981. The acronym S.M.A.R.T. stands for Saturday Mathematical Activities, Recreations & Tutorials. This book, Volume I, offers a sampling of many aspects, including projects and mini-courses. Volume II, which consists of student projects, addresses the purpose of the Circle, and Volume III, consisting of mini-courses, explains what actually takes place in the Circle. All three volumes provide a wealth of resources (mathematical problems, quizzes and games, together with their solutions). The books will be of interest to self-motivated students who want to conduct independent research, teachers who work with these students, and teachers who are currently running or planning to run Mathematical Circles of their own.

S.M.A.R.T. Circle Overview

George Sicherman

Takayuki Yoshigahara

This book convenes a selection of 200 mathematical puzzles with original solutions, all celebrating the inquisitive and inspiring spirit of Nobuyuki “Nob” Yoshigahara – a legend in the worldwide community of mathematical and mechanical puzzles. A graduate from the Tokyo Institute of Technology, Yoshigahara invented numerous mechanical puzzles and published over 80 puzzle books. In 2003, he was honored with the Sam Loyd Award, given by the Association for Games & Puzzles International to individuals who have been made a significant contribution to the world of mechanical puzzles. In this work, the reader will find some of the most ingenious puzzles ever created, organized in ten categories: Logic, matchstick, maze, algorithmic, combinatorial, digital, number, geometric, dissection, and others. Some of them could rivalry with those found at Mathematical Olympiads tests around the globe; others will work as powerful brain teasers for those with an interest in problem-solving. Math teachers, curious students of any age and even experienced mathematicians with a taste for the fun in science can find in this book unconventional paths to develop their problem-solving skills in a creative way.

The Puzzles of Nobuyuki Yoshigahara

Arithmetical Wonderland is intended as an unorthodox mathematics textbook for students in elementary education, in a contents course offered by a mathematics department. The scope is deliberately restricted to cover only arithmetic, even though geometric elements are introduced whenever warranted. For example, what the Euclidean Algorithm for finding the greatest common divisors of two numbers has to do with Euclid is showcased. Many students find mathematics somewhat daunting. It is the [Author];'s belief that much of that is caused not by the subject itself, but by the language of mathematics. In this book, much of the discussion is in dialogues between Alice, of Wonderland fame, and the twins Tweedledum and Tweedledee who hailed from Through the Looking Glass. The boys are learning High Arithmetic or Elementary Number Theory from Alice, and the reader is carried along in this academic exploration. Thus many formal proofs are converted to soothing everyday language. Nevertheless, the book has considerable depth. It examines many arcane corners of the subject, and raises rather unorthodox questions. For instance, Alice tells the twins that six divided by three is two only because of an implicit assumption that division is supposed to be fair, whereas fairness does not come into addition, subtraction or multiplication. Some topics often not covered are introduced rather early, such as the concepts of divisibility and congruence.

Arithmetical Wonderland

Kseniya Garaschuk

This unique book presents mathematical competition problems primarily aimed at upper elementary school students, but are challenging for students at any age. These problems are drawn from the complete papers of the legendary Leningrad Mathematical Olympiads that were presented to the city’s Grade Five students. The period covered is between 1979 – the earliest year for which relevant records could be retrieved – and 1992, when the former Soviet Union was dissolved. The respective chapters reflect the famous four-step approach to problem solving developed by the great Hungarian mathematics educator Gyorgy Pólya. In Chapter One, the Grade Five Competition problems from the Leningrad Mathematical Olympiads from 1979 to 1992 are presented in chronological order. In Chapter Two, the 83 problems are loosely divided into 26 sets of three or four related problems, and an example is provided for each one. Chapter Three provides full solutions to all problems, while Chapter Four offers generalizations of the problems. This book can be used by any mathematically advanced student at the upper elementary school level. Teachers and organizers of outreach activities such as mathematical circles will also find this book useful. But the primary value of the book lies in the problems themselves, which were crafted by experts; therefore, anyone interested in problem solving will find this book a welcome addition to their library./div

Andy Liu

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