Solomon W. Golomb

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.

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.

Shift register sequences cover a broad range of applications, from radar signal design, pseudo-random number generation, digital wireless telephony, and many other areas in coded communications. It is the primary area for which the author, Dr Golomb, received the US National Medal of Science. This book is the third, revised edition of the original definitive book on shift register sequences which was published in 1967, which has been widely distributed, read, and cited. It has stood the test of time, and provides a clear, comprehensive, and readily applicable description of both linear and non-linear shift register sequences.

Basic Concepts in Information Theory and Coding is an outgrowth of a one­ semester introductory course that has been taught at the University of Southern California since the mid-1960s. Lecture notes from that course have evolved in response to student reaction, new technological and theoretical develop­ ments, and the insights of faculty members who have taught the course (in­ cluding the three of us). In presenting this material, we have made it accessible to a broad audience by limiting prerequisites to basic calculus and the ele­ mentary concepts of discrete probability theory. To keep the material suitable for a one-semester course, we have limited its scope to discrete information theory and a general discussion of coding theory without detailed treatment of algorithms for encoding and decoding for various specific code classes. Readers will find that this book offers an unusually thorough treatment of noiseless self-synchronizing codes, as well as the advantage of problem sections that have been honed by reactions and interactions of several gen­ erations of bright students, while Agent 00111 provides a context for the discussion of abstract concepts.

Wireless communications, advanced radar and sonar systems, and security systems for Internet transactions are contemporary examples of systems that employ digital signals to transmit information. This volume affords comprehensive, up-to-date treatment of the methodologies and application areas throughout the range of digital communication where individual signals, and sets of signals, with favorable correlation properties, play a central role. Some application areas covered include Code Division Multiple Access (CDMA) signals such as those in use for cell-phone communication; digital systems for coded radar and sonar signals; and methods for secure authentication and stream cipher cryptology. The authors provide the necessary mathematical background to explain how the signals are generated and to show how the signals satisfy the appropriate correlation constraints.

Inspiring popular video games like Tetris while contributing to the study of combinatorial geometry and tiling theory, polyominoes have continued to spark interest ever since their inventor, Solomon Golomb, introduced them to puzzle enthusiasts several decades ago. In this fully revised and expanded edition of his landmark book, the author takes a new generation of readers on a mathematical journey into the world of the deceptively simple polyomino. Golomb incorporates important, recent developments, and poses problems, inviting the reader to play with and develop an understanding of the extraordinary properties of polyominoes.

Basic Concepts in Information Theory and Coding is an outgrowth of a one­ semester introductory course that has been taught at the University of Southern California since the mid-1960s. Lecture notes from that course have evolved in response to student reaction, new technological and theoretical develop­ ments, and the insights of faculty members who have taught the course (in­ cluding the three of us). In presenting this material, we have made it accessible to a broad audience by limiting prerequisites to basic calculus and the ele­ mentary concepts of discrete probability theory. To keep the material suitable for a one-semester course, we have limited its scope to discrete information theory and a general discussion of coding theory without detailed treatment of algorithms for encoding and decoding for various specific code classes. Readers will find that this book offers an unusually thorough treatment of noiseless self-synchronizing codes, as well as the advantage of problem sections that have been honed by reactions and interactions of several gen­ erations of bright students, while Agent 00111 provides a context for the discussion of abstract concepts.