Nonlinear Ordinary Differential Equations: An Introduction to Dynamical Systems (Oxford Texts in Applied and Engineering Mathematics) 3rd Edition

by D. W. Jordan and Peter Smith

Nonlinear Ordinary Differential Equations was first published in 1977 and has since become a standard text in the teaching of the subject. It takes a qualitative approach, and is designed for advanced undergraduate and graduate students of dynamical systems in mathematics or mathematics-related subjects. The text of this third edition has been completely revised to bring it into line with current teaching, including an expansion of the material on bifurcations and chaos. The book is directed towards practical applications of the theory, with several hundred examples and problems covering a wide variety of applications. Prerequisites are kept to a minimum, with appendices containing the necessary mathematical theory new to this edition.

"The subject has wide applications in physical, biological, and social sciences which continuously supply new problems of practical and theoretical importance. The book does a good job in motivating the reader in such pursuits, and presents the subject in a simple but elegant style." --P. K. Kythe in Applied Mechanics Reviews

About the Author

Dominic Jordan is at University of Keele. Peter Smith is at University of Keele.

Acclaimed in five prior editions, this text covers all of the standard topics for any introductory logic course in neatly-packaged capsules of learning. Known for its concise, direct style emphasizing clarity, Hurley avoids the peculiar quirks, technicalities, and wordiness of other texts. The material is integrated in such a way that elements fit together as in a puzzle so students can assemble a broad picture of the subject. Visual aids and color are used to reinforce key points and concepts. Additionally, key terms are boldfaced, hundreds of examples serve to illustrate ideas, and more than 2000 carefully selected exercises sharpen student understanding and skill. The adept presentation of the subject matter leads to mastery, even by students with poorer academic preparation.

Patrick Hurley was born in Spokane, Washington in 1942. He received his bachelor's degree in mathematics (with a Physics minor) from Gonzaga University in 1964 and his Ph.D. in philosophy of science with an emphasis in history of philosophy from Saint Louis University in 1973. In 1972 he began teaching at the University of San Diego, where his courses have included logic, philosophy of science, metaphysics, process philosophy, and legal ethics. In 1987 he received his J.D. from the University of San Diego and he is currently a member of the California Bar Association. He retired from teaching in 2008, but continues his research and writing. His interests include music, art, opera, environmental issues, fishing, and skiing.

Personality:  Theories and Processes by Alan O Ross

Comprehensive outline in easy-to-use narrative format supplements major textbooks.  Charts, tables included.

This book is part of an all-new, in-depth series, featuring titles in all areas of study, including Humanities, Social Science, Business, Engineering, Science, Mathematics, and Computer Science.  Featuring the most up-to-date information, each book is written by educators in the field, for students as well as the general reader.  Without sacrificing quality, these outlines summarize the material in a format that assures easy comprehension.

What is the unique and most important feature that distinguishes man from all other living beings?

Why is it that, contrary to the instinct of self-preservation, a parent will throw themselves headlong into fire or water to save their child?

Why do people get married and why do they get divorced? Why do people have extra-marital affairs and why do two people in a couple become jealous of one another? What is Love?

When and why did the type of sex emerge among human beings that is free of any reproductive function?

Why are the social and behavioural distinctions between men and women being rapidly erased?

Why, despite everything, is the world becoming more tolerant than it was in previous centuries?

People are born with different intellectual, spiritual and physical capabilities. So why do we assert that all people are equal?

Can the world without violence exist? If not, under what circumstances and to what kind of violence does man have a right? Wherein lies the origin of this right?

Where is the root of our morality? Why do our moral values change over time? Do absolute moral values exist?

Why has Man, on the whole, never observed (or perhaps is incapable of observing) a set of various religious commandments? Should we observe them? Are they the decree of God?

By which “commandments” do we really live our lives and is it possible to formulate them in such a way that we could realistically observe them?

What is Good? And what is Evil? Is there a simple criterion by which one may distinguish Good from Evil?

In which direction is humanity evolving and is it governed by some universal law?

Is there any meaning to life?

Is it possible to give a clear and straightforward answer to all these questions?

It is, in fact, possible!

“The Last Faith: a book by an atheist believer” provides a clear and scientifically elegant answer to all the questions listed above. The answer which will cause the reader to reconsider many established moral principles and notions about the world around us. The answer which will help the reader to understand the nature of human actions, dilemmas, dramas and passions, in their true light. The answer which will elucidate the current stage in the development of human civilisation and offer unexpected predictions for its future.

“The Last Faith: a book by an atheist believer” is aimed at a wide audience and does not require any specialised knowledge. The author’s thoughts and reflections are presented here in the form of a fictional conversation with God which unfolds over the course of just two hundred pages. The author (PhD in Physics and Mathematics) gives concise and clearly expressed explanations and evidence for his ideas. He cites abundant examples from the world around us which are drawn from his extensive travels through Russia, America, Europe, Africa and Central Asia.

All this makes for an accessible and enjoyable read.

On the night Janie waits for her sister, Hannah, to be born, her grandmother tells her a story: Since the Japanese occupation of Korea, their family has lost a daughter in every generation, so Janie is charged with keeping Hannah safe. As time passes, Janie hears more stories, while facts remain unspoken. Her father tells tales about numbers, and in his stories everything works out. In her mother's stories, deer explode in fields, frogs bury their loved ones in the ocean, and girls jump from cliffs and fall like flowers into the sea. Within all these stories are warnings.

Years later, when Hannah inexplicably cuts all ties and disappears, Janie embarks on a mission to find her sister and finally uncover the truth beneath her family's silence. To do so, she must confront their history, the reason for her parents' sudden move to America twenty years earlier, and ultimately her conflicted feelings toward her sister and her own role in the betrayal behind their estrangement.

Weaving Korean folklore within a modern narrative of immigration and identity, Forgotten Country is a fierce exploration of the inevitability of loss, the conflict between obligation and freedom, and a family struggling to find its way out of silence and back to one another.

Catherine Chung was born in Evanston, Illinois. She grew up in New York, New Jersey and Michigan.  She graduated with a mathematics degree from the University of Chicago, and worked at the think tank The RAND Corporation before attending Cornell University to receive her MFA.

Chung's critically acclaimed debut novel, Forgotten Country, was published in 2012 by Riverhead Books, a division of Penguin Press. She has also published short stories and essays in The New York Times, The Rumpus, and Granta, and was the recipient of a Dorothy Sargent Rosenberg Prize in Poetry.

She has been a fellow at the MacDowell Colony, Yaddo, Hedgebrook, and Jentel, and received support for her writing from The Camargo Foundation, The Jerome Foundation, and the Constance Saltonstall Foundation. She was a Picador Guest Professor at The University of Leipzig, and is currently Assistant Professor of Creative Writing at Adelphi University. Catherine is the recipient of a 2014 National Endowment for the Arts Fellowship in Creative Writing, a Granta New Voice, and a fiction editor at Guernica Magazine.

"A very stimulating book ... in a class by itself." — American MathematicalMonthly
Advanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject.

The book is divided into three parts. Part I is concerned with background material — a synopsis of elementary number theory (including quadratic congruences and the Jacobi symbol), characters of residue class groups via the structure theorem for finite abelian groups, first notions of integral domains, modules and lattices, and such basis theorems as Kronecker's Basis Theorem for Abelian Groups.

Part II discusses ideal theory in quadratic fields, with chapters on unique factorization and units, unique factorization into ideals, norms and ideal classes (in particular, Minkowski's theorem), and class structure in quadratic fields. Applications of this material are made in Part III to class number formulas and primes in arithmetic progression, quadratic reciprocity in the rational domain and the relationship between quadratic forms and ideals, including the theory of composition, orders and genera. In a final concluding survey of more recent developments, Dr. Cohn takes up Cyclotomic Fields and Gaussian Sums, Class Fields and Global and Local Viewpoints.

In addition to numerous helpful diagrams and tables throughout the text, appendices, and an annotated bibliography, Advanced Number Theory also includes over 200 problems specially designed to stimulate the spirit of experimentation which has traditionally ruled number theory.

Can we predict prison riots?  Earthquakes?  Stock Market Crashes?

Hailed by scientists as the most important intellectual development since calculus, catastrophe theory boldly suggests a controversial new way of predicting sudden, "unpredictable" change.  Imagine being able to forecast the raising of oil prices by Arab nations, the outbreak of a revolution, or the erratic behavior of a schizophrenic.  The brainchild of French mathematician Rene Thom, catastrophe theory uses seven basic geometric shapes to transform abstract concepts--fear, anger, love, hate--into concrete visual diagrams, or catastrophes, that represent patterns of behavior.

This vanguard book illustrated with thirty line drawing, explains the catastrophe theory to laymen, explores the controversy surrounding ti, and gives fascinating examples of how it can be used to understand problems in psychology, biology, politics, economics, and history that affect everyone.

The final novel of Hermann Hesse, for which he won the Nobel Prize for Literature in 1946, The Glass Bead Game is a fascinating tale of the complexity of modern life as well as a classic of modern literature

"...a genre blend of science fiction, fantasy, and fictional biography, leavened with musicology, poetry, and Hesse’s unique swirl of Eastern and Western philosophy." -The American Scholar

Set in the 23rd century, The Glass Bead Game is the story of Joseph Knecht, who has been raised in Castalia, the remote place his society has provided for the intellectual elite to grow and flourish. Since childhood, Knecht has been consumed with mastering the Glass Bead Game, which requires a synthesis of aesthetics and scientific arts, such as mathematics, music, logic, and philosophy, which he achieves in adulthood, becoming a Magister Ludi (Master of the Game).

The infamous eco-anarchist John Zerzan whose books have resulted in recent interviews by Vice and Believer magazines, checks in with further provocative articles about the chaotic results of civilization and technology.

Says novelist Lang Gore in his introduction:

"The present collection of essays continues the overarching thrust of John's scholarship, unveiling the post-apocalyptic nature of our times by noting the apocalypse was yesterday, several thousand years ago, to be precise, and that nothing produced by civilization can ever redeem the systematic attempt it has undertaken these (very) few millennia to destroy or alienate any human connection with the earth.

"In fact, when civilized Europeans imposed themselves everywhere on Earth, they created a terminal crisis for themselves by their very contact with indigenous societies. Suddenly, those with eyes to see and ears to hear could recognize that patriarchy, property and authority, and certainly slavery, were neither necessary nor desirable, let alone determined by 'human nature.'"

About the Author

John Zerzan (born 1943) is an American anarchist and primitivist philosopher and author. His works criticize agricultural civilization as inherently oppressive, and advocate drawing upon the ways of life of hunter gatherers as an inspiration for what a free society should look like. Some subjects of his criticism include domestication, language, symbolic thought (such as mathematics and art) and the concept of time.

Expanded, Updated & Greatly Improved

New Expanded Edition Includes:

• More Than 150 Pages of New Material with Greatly Expanded Content and 4 New Chapters
• Over 75 Carefully Devised Practice and Example Poker Hands That Are Analyzed in Great Detail
• Free Enrollment into My Essential Poker Math eLearning Online Video Training Course

Poker Math Is Easy to Learn

Poker math is a vitally important aspect to No Limit Holdem poker, but it's often overlooked or simply not used because many poker players fear it is too difficult to learn. I'm here to tell you it is not. In fact, fundamental poker math is very easy to learn. More importantly, it can yield you a lot more profits at the poker table. Without using simple math at the poker table, you are simply playing a guessing game.

Use Simple Math at the Poker Table & Increase You Winnings

In this book I'll teach you how to use simple arithmetic at the poker table to gain a huge skill advantage over your opponents that will allow you to win more and lose less. Poker players that don't use math are simply guessing and you'll learn to no longer guess and know the correct mathematical move at the poker table. These simple mathematical concepts I'll be teaching you will drastically help improve your poker game and allow you to make the most profitable decisions at the poker.

Contents & Overview

First you'll be introduced to several fundamental overarching poker concepts that apply to poker mathematics. Then we'll begin our journey into poker mathematics where you'll learn about fundamental poker mathematics, including probabilities and odds, pot equity, pot odds, implied odds,the Rule of 2 and 4, expected value (EV) and much more. We'll then embark on a journey of learning about important pre-flop and post-flop poker mathematical concepts, such as pre-flop all-in situations, set-mining, steal attempts, 3-bet bluffing, betting with the best hand, semi-bluffing all-in, bluffs and hero calls. Lastly, you'll learn how to perform basic and intermediate expected value calculations and utilize card combinations, better known as combinatorics.

Effectively Understand & Utilize Essential Poker Math

• Develop a keen understanding of Probability & Odds
• Learn to quickly calculate Pot Odds & Implied Odds at the poker table
• Effectively use Pot Equity & The Rule of 2 & 4 to Determine the correct poker play
• Understand how to use Expected Value (EV) both on & off the table to analyze your plays
• Understand how to properly Set-Mine, Steal & 3-Bet Bluff with basic mathematics
• Learn the important math behind Bluffs & Hero Calls to give you a skill advantage over your opponent
• Learn to utilize EV Calculations to analyze your previous play off the table
• Learn to leverage Card Combinations to further enhance your card reading abilities & develop balanced ranges

What You'll Get out of This Book

Suitable for both beginning and experienced poker players alike you'll learn many essential fundamental poker mathematical concepts that'll help you drastically improve your poker game. After reading this book, you'll have mastered fundamental No Limit Holdem mathematics. You'll have gained a huge skill advantage over your opponents and will be able to effectively use math at the poker table to make profitable moves. Most importantly, you'll become a much better and profitable poker player!

What are you waiting for?

Purchase this book today to start advancing your poker game with simple poker math!

Why seemingly unrelated mathematical truths are connected in simple and beautiful equations continues to stump even mathematicians. This recreational math book takes the reader on a fantastic voyage into the world of natural numbers. From the earliest discoveries of the ancient Greeks to various fundamental characteristics of the natural number sequence, Clawson explains fascinating mathematical mysteries in clear and easy prose. He delves into the heart of number theory to see and understand the exquisite relationships among natural numbers, and ends by exploring the ultimate mystery of mathematics: the Riemann hypothesis, which says that through a point in a plane, no line can be drawn parallel to a given line.While a professional mathematician's treatment of number theory involves the most sophisticated analytical tools, its basic ideas are surprisingly easy to comprehend. By concentrating on the meaning behind various equations and proofs and avoiding technical refinements, Mathematical Mysteries lets the common reader catch a glimpse of this wonderful and exotic world.

Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.

An irreverent and accessible explanation of challenging puzzles within the world of mathematics considers such topics as the link between a pineapple's spirals and the famous Fibonacci numbers, the shape of the universe as reflected by a twisted strip of paper, and the parallels between the Lincoln and Kennedy assassinations. 

In Meta Math!, Gregory Chaitin, one of the world’s foremost mathematicians, leads us on a spellbinding journey of scientific discovery and illuminates the process by which he arrived at his groundbreaking theories.

“A startling vision of the future of mathematics. . . . The Chaitinesque intellectual future will be eternally youthful and anarchic.”–American Scientist 

“Math’s dark secret is out. . . . Chaitin explains why omega, a number he discovered thirty years ago, has him convinced that math is based on randomness.”–Time Magazine 

“Captivating. . . . With extraordinary skill and a gentle humor, Chaitin shares his profound insights.” –Paul Davies, author of How to Build a Time Machine 

All of science is based on mathematics, but mathematicians have become painfully aware that math itself has serious limitations. This notion was first revealed in the work of two giants of twentieth-century mathematics: Kurt Gödel and Alan Turing. Now their successor, Gregory Chaitin, digs even deeper into the foundations of mathematics, demonstrating that mathematics is riddled with randomness, enigmas, and paradoxes.

Chaitin’s revolutionary discovery, the Omega number, is an exquisitely complex representation of unknowability in mathematics. His investigations shed light on what, ultimately, we can know about the universe and the very nature of life. But if unknowability is at the core of Chaitin’s theories, the great gift of his book is its completely engaging knowability. In an infectious and enthusiastic narrative, Chaitin introduces us to his passion for mathematics at its deepest and most philosophical level, and delineates the specific intellectual and intuitive steps he took toward the discovery of Omega. In the final analysis, he shows us that mathematics is as much art as logic, as much experimental science as pure reasoning. And by the end, he has helped us to see and appreciate the art––and the sheer beauty––in the science of math.

In Meta Math!, Gregory Chaitin takes us to the very frontiers of scientific thinking. It is a thrilling ride.

In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Gödel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.

The present volume reprints the first English translation of Gödel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.

This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it

"[Szpiro] turns the abstract mathematics of spheres into a lucid, lovely romantic odyssey."--Sylvia Nasar, author of A Beautiful Mind

In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found.

Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.

Mathematics is driven forward by the quest to solve a small number of major problems--the four most famous challenges being Fermat's Last Theorem, the Riemann Hypothesis, Poincaré's Conjecture, and the quest for the "Monster" of Symmetry. Now, in an exciting, fast-paced historical narrative ranging across two centuries, Mark Ronan takes us on an exhilarating tour of this final mathematical quest. 

Ronan describes how the quest to understand symmetry really began with the tragic young genius Evariste Galois, who died at the age of 20 in a duel. Galois, who spent the night before he died frantically scribbling his unpublished discoveries, used symmetry to understand algebraic equations, and he discovered that there were building blocks or "atoms of symmetry." Most of these building blocks fit into a table, rather like the periodic table of elements, but mathematicians have found 26 exceptions. The biggest of these was dubbed "the Monster"--a giant snowflake in 196,884 dimensions. Ronan, who personally knows the individuals now working on this problem, reveals how the Monster was only dimly seen at first. As more and more mathematicians became involved, the Monster became clearer, and it was found to be not monstrous but a beautiful form that pointed out deep connections between symmetry, string theory, and the very fabric and form of the universe. 

This story of discovery involves extraordinary characters, and Mark Ronan brings these people to life, vividly recreating the growing excitement of what became the biggest joint project ever in the field of mathematics. Vibrantly written, Symmetry and the Monster is a must-read for all fans of popular science--and especially readers of such books as Fermat's Last Theorem.

Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

"A mathematician named Klein
Thought the Moebius band was divine.
Said he: 'If you glue
The edges of two,
You'll get a weird bottle like mine.' " — Stephen Barr

In this lively book, the classic in its field, a master of recreational topology invites readers to venture into such tantalizing topological realms as continuity and connectedness via the Klein bottle and the Moebius strip. Beginning with a definition of topology and a discussion of Euler's theorem, Mr. Barr brings wit and clarity to these topics:

• New Surfaces (Orientability, Dimension, The Klein Bottle, etc.)
• The Shortest Moebius Strip
• The Conical Moebius Strip
• The Klein Bottle
• The Projective Plane (Symmetry)
• Map Coloring
• Networks (Koenigsberg Bridges, Betti Numbers, Knots)
• The Trial of the Punctured Torus
• Continuity and Discreteness ("Next Number," Continuity, Neighborhoods, Limit Points)
• Sets (Valid or Merely True? Venn Diagrams, Open and Closed Sets, Transformations, Mapping, Homotopy)

With this book and a square sheet of paper, the reader can make paper Klein bottles, step by step; then, by intersecting or cutting the bottle, make Moebius strips. Conical Moebius strips, projective planes, the principle of map coloring, the classic problem of the Koenigsberg bridges, and many more aspects of topology are carefully and concisely illuminated by the author's informal and entertaining approach.

Now in this inexpensive paperback edition, Experiments in Topology belongs in the library of any math enthusiast with a taste for brainteasing adventures in the byways of mathematics.

Text deals with subgroups, permutation groups, automorphisms and finitely generated abelian groups, normal series, commutators and derived series, solvable and nilpotent groups, the group ring and monomial representations, Frattini subgroup, factorization, linear gorups, and representations and characters—in all, 431 problems. Full solutions to problems in separate section.

This textbook for advanced courses in group theory focuses on finite groups, with emphasis on the idea of group actions. Early chapters summarize presupposed facts, identify important themes, and establish the notation used throughout the book. Subsequent chapters explore the normal and arithmetical structures of groups as well as applications.

Topics include the normal structure of groups: subgroups; homomorphisms and quotients; series; direct products and the structure of finitely generated Abelian groups; and group action on groups. Additional subjects range from the arithmetical structure of groups to classical notions of transfer and splitting by means of group action arguments. More than 675 exercises, many accompanied by hints, illustrate and extend the material.

Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Originally conceived as a text for a one-semester course, it is directed to undergraduate students whose studies of calculus sequence have included definitions and proofs of theorems. The book's principal aim is to provide a simple, thorough survey of elementary topics in the study of collections of objects, or sets, that possess a mathematical structure.

The author begins with an informal discussion of set theory in Chapter 1, reserving coverage of countability for Chapter 5, where it appears in the context of compactness. In the second chapter Professor Mendelson discusses metric spaces, paying particular attention to various distance functions which may be defined on Euclidean n-space and which lead to the ordinary topology.

Chapter 3 takes up the concept of topological space, presenting it as a generalization of the concept of a metric space. Chapters 4 and 5 are devoted to a discussion of the two most important topological properties: connectedness and compactness. Throughout the text, Dr. Mendelson, a former Professor of Mathematics at Smith College, has included many challenging and stimulating exercises to help students develop a solid grasp of the material presented.

A stimulating excursion into pure mathematics aimed at "the mathematically traumatized," but great fun for mathematical hobbyists and serious mathematicians as well. Requiring only high school algebra as mathematical background, the book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, and a discussion of The Seven Bridges of Konigsberg. Exercises are included at the end of each chapter.

Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.

In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.

Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.

Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated.

George E. Andrews, Evan Pugh Professor of Mathematics at Pennsylvania State University, author of the well-established text Number Theory (first published by Saunders in 1971 and reprinted by Dover in 1994), has led an active career discovering fascinating phenomena in his chosen field — number theory. Perhaps his greatest discovery, however, was not solely one in the intellectual realm but in the physical world as well.

In 1975, on a visit to Trinity College in Cambridge to study the papers of the late mathematician George N. Watson, Andrews found what turned out to be one of the actual Holy Grails of number theory, the document that became known as the "Lost Notebook" of the great Indian mathematician Srinivasa Ramanujan. It happened that the previously unknown notebook thus discovered included an immense amount of Ramanujan's original work bearing on one of Andrews' main mathematical preoccupations — mock theta functions. Collaborating with colleague Bruce C. Berndt of the University of Illinois at Urbana-Champaign, Andrews has since published the first two of a planned three-volume sequence based on Ramanujan's Lost Notebook, and will see the project completed with the appearance of the third volume in the next few years.

In the Author's Own Words:
"It seems to me that there's this grand mathematical world out there, and I am wandering through it and discovering fascinating phenomena that often totally surprise me. I do not think of mathematics as invented but rather discovered." — George E. Andrews

An Introduction to Information Theory : Symbols, Signals and Noise (Dover Books on Mathematics) by John R. Pierce - Paperback

"Uncommonly good...the most satisfying discussion to be found." — Scientific American.

Behind the familiar surfaces of the telephone, radio, and television lies a sophisticated and intriguing body of knowledge known as information theory. This is the theory that has permitted the rapid development of all sorts of communication, from color television to the clear transmission of photographs from the vicinity of Jupiter. Even more revolutionary progress is expected in the future.

To give a solid introduction to this burgeoning field, J. R. Pierce has revised his well-received 1961 study of information theory for a second edition. Beginning with the origins of the field, Dr. Pierce follows the brilliant formulations of Claude Shannon and describes such aspects of the subject as encoding and binary digits, entropy, language and meaning, efficient encoding, and the noisy channel. He then goes beyond the strict confines of the topic to explore the ways in which information theory relates to physics, cybernetics, psychology, and art. Mathematical formulas are introduced at the appropriate points for the benefit of serious students. A glossary of terms and an appendix on mathematical notation are proved to help the less mathematically sophisticated.

J. R. Pierce worked for many years at the Bell Telephone Laboratories, where he became Director of Research in Communications Principles. His Introduction to Information Theory continues to be the most impressive nontechnical account available and a fascinating introduction to the subject for lay readers.

Now available in paperback, Mind Tools connects mathematics to the world around us. Reveals mathematics' great power as an alternative language for understanding things and explores such concepts as logic as a computing tool, digital versus analog processes and communication as information transmission.

This reader-friendly volume groups the patterns of mathematics into five archetypes: numbers, space, logic, infinity, and information. Rudy Rucker presents an accessible introduction to each of these important areas, reflecting intelligence gathered from the frontiers of mathematical thought. More than 100 drawings illuminate explorations of digital versus analog processes, logic as a computing tool, communication as information transmission, and other "mind tools."

"Mind Tools is an original and fascinating look at various aspects of mathematics that is sure to fascinate the nonmathematician." — Isaac Asimov

"A lighthearted romp through contemporary mathematics. . . . Mind Tools is a delight." — San Francisco Chronicle
"For those who gave up college mathematics for what seemed more liberal arts, Rudy Rucker's book, Mind Tools, is a dazzling refresher course. . . . He rekindles the wonder that can come from contemplating logarithms, exponential curves and transcendental numbers." — The New York Times Book Review

"One of Rucker's greatest assets is his ability to make complexities comprehensible to the general reader without lecturing." — The Washington Post

"Approaching all of mathematics, and everything else, by way of information theory, Dr. Rucker's latest and most exciting book opens vistas of dazzling beauty — scenes that blend order with chaos, reality with fantasy, that startle you with their depths of impenetrable mystery." — Martin Gardner

Presents the unifying world-concept long sought by scientists, mystics, and sages: an Integral Theory of Everything 

• Explains how modern science has rediscovered the Akashic Field of perennial philosophy 

• New edition updates ongoing scientific studies, presents new research inspired by the first edition, and includes new case studies and a section on animal telepathy 

Mystics and sages have long maintained that there exists an interconnecting cosmic field at the roots of reality that conserves and conveys information, a field known as the Akashic record. Recent discoveries in vacuum physics show that this Akashic Field is real and has its equivalent in science’s zero-point field that underlies space itself. This field consists of a subtle sea of fluctuating energies from which all things arise: atoms and galaxies, stars and planets, living beings, and even consciousness. This zero-point Akashic Field is the constant and enduring memory of the universe. It holds the record of all that has happened on Earth and in the cosmos and relates it to all that is yet to happen. 

“. . . Ervin Laszlo’s brilliant new work, Science and the Akashic Field, surpasses previous explorations. . . . This is a 'make-sense-of-the-complex' opus, accessible to every reader.” (A. Harris Stone, Ed.D., founder of The Graduate Institute in Milford, Connecticut, and author of The)

“This is a solidly grounded vision of our cosmos, with perspectives that are wide and deep and have profound implications for all of us.” (Henrik B. Tschudi, chairman of the Flux Foundation, Oslo, Norway)

“If you ever wanted to hold the universe in your hand . . . . You can hardly do better than join cosmologist Ervin Laszlo in the ultimate quest: for a theory of everything.” (Christian de Quincey, Ph.D., professor of philosophy, John F. Kennedy University, editor of Institut)

“Ervin Laszlo is, arguably, the most profound thinker alive today.” (Lady Montagu of Beaulieu, First Ambassador of the Club of Budapest)

"Decoding GUTs, WIMPs, and The Big Crunch, Ervin Laszlo brings the ancient Indian concept of akasha into the new millennium and convincingly details how science is turning this metaphor into a viable scientific theory.” (Spirit of Change, March-April 2005)

". . . lends credance to our deepest intuitions of the oneness of life and the whole of creation." (Share Guide, Sept-Oct 2005, Issue #81)

In Science and the Akashic Field, philosopher and scientist Ervin Laszlo conveys the essential element of this information field in language that is accessible and clear. From the world of science he confirms our deepest intuitions of the oneness of creation in the Integral Theory of Everything. We discover that, as philosopher William James stated, “We are like islands in the sea, separate on the surface but connected in the deep.”

A friendly and non-formal approach to a subject of abstract mathematics that has important applications in physics, especially in General Relativity, but also in other sectors.

From the bestselling author of The Theoretical Minimum, a DIY introduction to the math and science of quantum mechanics.

First he taught you classical mechanics. Now, physicist Leonard Susskind has teamed up with data engineer Art Friedman to present the theory and associated mathematics of the strange world of quantum mechanics.

In this follow-up to the New York Times best-selling The Theoretical Minimum, Susskind and Friedman provide a lively introduction to this famously difficult field, which attempts to understand the behavior of sub-atomic objects through mathematical abstractions. Unlike other popularizations that shy away from quantum mechanics' weirdness, Quantum Mechanics embraces the utter strangeness of quantum logic. The authors offer crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics, and each chapter includes exercises to ensure mastery of each area. Like The Theoretical Minimum, this volume runs parallel to Susskind's eponymous Stanford University-hosted continuing education course.

An approachable yet rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.

A Wall Street Journal Best Book of 2013

"What a wonderful and unique resource. For anyone who is determined to learn physics for real, looking beyond conventional popularizations, this is the ideal place to start."―Sean Carroll, physicist, California Institute of Technology, and author of The Particle at the End of the Universe

If you ever regretted not taking physics in college--or simply want to know how to think like a physicist--this is the book for you. In this bestselling introduction, physicist Leonard Susskind and hacker-scientist George Hrabovsky offer a first course in physics and associated math for the ardent amateur. Challenging, lucid, and concise, The Theoretical Minimum provides a tool kit for amateur scientists to learn physics at their own pace.

"Readers ready to embrace their inner applied mathematics will enjoy this brisk, bare-bares introduction to classical mechanics."―Publishers Weekly

About the Author

Leonard Susskind has been the Felix Bloch Professor in Theoretical Physics at Stanford University since 1978. He lives in Palo Alto, California.

George Hrabovsky is the president of Madison Area Science and Technology (MAST), a nonprofit organization dedicated to scientific and technological research and education. He lives in Madison, Wisconsin.

Seven-card stud is an extremely complex game. Deciding on exactly the right strategy in any particular situation can be very difficult. Perhaps this is why very few authors have attempted to analyze this game even though it is widely played. In 1989, the first edition of this text appeared. Many ideas, which were only known to a small, select group of players, were now made available to anyone who was striving to become an expert, and a major gap in the poker literature was closed. It is now a new century, and the authors have again moved the state of the art forward by adding over 100 pages of new material, including an extensive section on "loose games." Anyone who studies this text, is well disciplined, and gets the proper experience should become a significant winner. Some of the other ideas discussed in this 21st century edition include the cards that are out, the number of players in the pot, ante stealing, playing big pairs, playing little and medium pairs, playing three-flushes, playing three-straights, randomizing your play, fourth street, pairing your door card on fourth street, proper play on fifth, sixth, and seventh streets, defending against a possible ante steal, playing against a paired door card, scare card strategy, and buying a free card.

About the Authors

About David Sklansky

David Sklansky is generally considered the number one authority on gambling in the world today. Besides his ten books on the subject, David also has produced two videos and numerous writings for various gaming publications. His occasional poker seminars always receive an enthusiastic reception, including those given at the Taj Mahal in Atlantic City and the World Series of Poker in Las Vegas.

More recently, David has been doing consulting work for casinos, Internet gaming sites, and gaming device companies. He has recently invented several games, soon to appear in casinos.

David attributes his standing in the gambling community to three things:

1. The fact that he presents his ideas as simply as possible (sometimes with Mason Malmuth) even though these ideas frequently involve concepts that are deep, subtle, and not to be found elsewhere.

2. The fact that the things he says and writes can be counted on to be accurate.

3. The fact that to this day a large portion of his income is still derived from gambling (usually poker, but occasionally blackjack, sports betting, horses, video games, casino promotions, or casino tournaments).

Thus, those who depend on David’s advice know that he still depends on it himself.

About Mason Malmuth

Mason Malmuth was born and raised in Coral Gables, Florida. In 1973 he received his BS in Mathematics from Virginia Tech, and completed their Masters’ program in 1975. While working for the United States Census Bureau in 1978, Mason stopped overnight in Las Vegas while driving to his new assignment in California. He was immediately fascinated by the games, and gambling became his major interest.

After arriving in California he discovered that poker was legal and began playing in some of the public cardrooms as well as taking periodic trips to Las Vegas where he would play both poker and blackjack. In 1981 he went to work for the Northrop Corporation as a mathematician and moved to Los Angeles where he could conviently pursue his interest in poker in the large public cardrooms in Gardena, Bell Gardens, and Commerce.

In 1983 his first article "Card Domination — The Ultimate Blackjack Weapon" was published in Gambling Times magazine. In 1987 he left his job with the Northrop Corporation to begin a career as both a full-time gambler and a gambling writer. He has had over 500 articles published in various magazines and is the author or co-author of 12 books. These include Gambling Theory and Other Topics, where he tries to demonstrate why only a small number of people are highly successful at gambling. In this book he introduces the reader to the concept of "non-self weighting strategies" and explains why successful gambling is actually a balance of luck and skill. Other books he has co-authored are Hold ’em Poker For Advanced Players, written with David Sklansky, and Seven-Card Stud For Advanced Players written with David Sklansky and Ray Zee. All the "advanced" books are considered the definitive works on these games.

His company Two Plus Two Publishing has sold over 400,000 books and currently has 22 titles to its credit. These books are recognized as the best in their field and are thoroughly studied by those individuals who take gambling seriously.

“An irresistible literary thriller...Rich mines the terror of our times.” ―Rolling Stone

“The opposite of disaster, a knockout of a book by a young writer to keep your eye on from now on...As terrifically described as any of the best science fiction we have.” ―Alan Cheuse, NPR's All Things Considered

NEW YORK CITY, the near future: Mitchell Zukor, a gifted young mathematician, is hired by a mysterious new financial consulting firm, FutureWorld. The business operates out of a cavernous office in the Empire State Building; Mitchell is employee number two. He is asked to calculate worst-case scenarios in the most intricate detail, and his schemes are sold to corporations to indemnify them against any future disasters. This is the cutting edge of corporate irresponsibility, and business is booming. As Mitchell immerses himself in the mathematics of catastrophe--ecological collapse, global war, natural disasters--he becomes obsessed by a culture's fears. Yet he also loses touch with his last connection to reality: Elsa Bruner, a friend with her own apocalyptic secret, who has started a commune in Maine. Then, just as Mitchell's predictions reach a nightmarish crescendo, an actual worst-case scenario overtakes Manhattan. Mitchell realizes he is uniquely prepared to profit. But at what cost? At once an all-too-plausible literary thriller, an unexpected love story, and a philosophically searching inquiry into the nature of fear, Nathaniel Rich's Odds Against Tomorrow poses the ultimate questions of imagination and civilization. The future is not quite what it used to be.