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The book may serve as a first or second course in undergraduate abstract algebra and with some supplementation perhaps, for beginning graduate level courses in algebraic geometry or computational algebra. Prerequisites for the reader include linear algebra and a proof-oriented course. It is assumed that the reader has access to a computer algebra system. Appendix C describes features of MapleTM, Mathematica® and Sage, as well as other systems that are most relevant to the text. Pseudocode is used in the text; Appendix B carefully describes the pseudocode used.

From the reviews of previous editions:

“...The book gives an introduction to Buchberger’s algorithm with applications to syzygies, Hilbert polynomials, primary decompositions. There is an introduction to classical algebraic geometry with applications to the ideal membership problem, solving polynomial equations and elimination theory. ...The book is well-written. ...The reviewer is sure that it will be an excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry.”

—Peter Schenzel, zbMATH, 2007

“I consider the book to be wonderful. ... The exposition is very clear, there are many helpful pictures and there are a great many instructive exercises, some quite challenging ... offers the heart and soul of modern commutative and algebraic geometry.”

—The American Mathematical Monthly

Skyhorse Publishing, as well as our Sports Publishing imprint, is proud to publish a broad range of books for readers interested in sports—books about baseball, pro football, college football, pro and college basketball, hockey, or soccer, we have a book about your sport or your team.

In addition to books on popular team sports, we also publish books for a wide variety of athletes and sports enthusiasts, including books on running, cycling, horseback riding, swimming, tennis, martial arts, golf, camping, hiking, aviation, boating, and so much more. While not every title we publish becomes a New York Times bestseller or a national bestseller, we are committed to publishing books on subjects that are sometimes overlooked by other publishers and to authors whose work might not otherwise find a home.

In the pages of Bruce Lee: The Celebrated Life of the Golden Dragon, we invite you to examine the real Bruce Lee, the man behind the image—the man who was so much more than an international film and martial arts superstar. In a brilliantly assembled photographic essay compiled and edited by John Little, this history of the life and career of Bruce Lee covers Bruce from childhood to international stardom, from the charismatic public persona to the quiet family man. With a preface by Shannon Lee and a foreword by Linda Lee Cadwell, the text is drawn directly from Bruce Lee's own words, as recorded in his diaries and journals, as well as from interviews and the documentary Bruce Lee: In His Own Words

This Bruce Lee book is part of Tuttle Publishing's Bruce Lee Library which also features:Bruce Lee's Striking ThoughtsBruce Lee's The Tao of Gung FuBruce Lee Artist of LifeBruce Lee: Letters of the DragonBruce Lee: The Art of Expressing the Human BodyBruce Lee Jeet Kune Do

Words of the Dragon is an anthology of rare newspaper and magazine interviews with Bruce Lee, many not previously published in the United States, revealing new words and explanations of Bruce about himself, his art, and philosophy.

Interesting and insightful, Words of the Dragon provides the reader a means to understand the real Bruce Lee, offering us a unique keyhole through which to view the private life and personal struggles of the late martial arts superstar. These interviews provide us with Lee's own interpretations of life, the martial arts, international stardom, and his cross-cultural marriage during a time of racism.

John Little is considered one of the world's foremost authorities on Bruce Lee, his training methods, and philosophies. Little is the only person who has ever been authorized to review the entirety of Lee's personal notes, sketches, and reading annotations. He is currently the Associate Publisher of Bruce Lee magazine and the managing editor of Knowing Is Not Enough, the official newsletter of the Jun Fan Jeet Kune Do Nucleus. Little's articles have appeared in every martial arts and health and fitness magazine in North America. He is the author of The Warrior Within:The Philosophies of Bruce Lee, and co-author of Power Factor Training, The Golfer's 2-Minute Workout, and Static Contraction Training For Bodybuilders.

This Bruce Lee Book is part of Tuttle Publishing's Bruce Lee Library which also features:Bruce Lee's Striking ThoughtsBruce Lee's The Tao of Gung FuBruce Lee Artist of LifeBruce Lee: Letters of the DragonBruce Lee: The Art of Expressing the Human BodyBruce Lee Jeet Kune Do

Until now, no one has ever stepped back and taken a critical look at why this art’s techniques are presented and performed the way they are. This book, by Wing Chun master Danny Xuan and martial-arts authority John Little, is the first to decipher these techniques that until now have been encrypted within this art.

Xuan and Little reveal how Wing Chun was designed holistically, based on the laws of physics, human nature, and biomechanics. It was also designed with economy, efficiency, and productivity in mind. Unlike other martial arts, Wing Chun doesn’t focus on making a person larger, more rugged, acrobatic or animal-like; rather, it focuses on making optimal use of one’s own bodily structure and power potential by applying the sciences of biomechanics and physics. Thus, it is possible for males and females of all ages and sizes to excel in this art.

The Tao of Wing Chun provides a readable, authoritative means of cultivating personal protection skills, enhanced flexibility, improved coordination, greater stamina, and physical and mental fitness while simultaneously cultivating humility, focus, determination, self-confidence, character, camaraderie, and deep inner strength. Foremost, this book offers the reader the means by which to apply Wing Chun principles in daily life.

Enhanced by forty-eight full-color illustrations, The Tao of Wing Chun will fascinate, educate, and entertain a wide range of readers—from beginner to master.

Filled with unforgettable characters, adventure, humour and pathos, this is the inspiring story of a fishing dynasty – showing just how extraordinary the ordinary can be.

Small Green Roofs is the first book to focus on small-scale and domestic green roofs. More than forty profiles of small and domestic-scale projects of all shapes and sizes include green roofs on sheds, garden offices, studios, garages, houses, bicycle sheds, and other small structures, as well as several community projects. For each project, details are given for design, construction, and installation, as well as how-to tips on how the roof was planted and cared for.

For readers looking for inspiration when hiring a contractor or taking the adventurous step of building their own, Small Green Roofs provides the knowledge and encouragement to make it possible.

Little argues that while loyalties were highly localized, American border raids during the war caused a defensive reaction north of the 45th parallel. The resulting sense of distinction from neighbouring Vermont, with its radical religious and political culture, did not prevent a strong regional reform movement from emerging in the eastern townships during the 1820s and 1830s. This movement undermines the argument of Quebec's nationalist historians that the political contest in Lower Canada was essentially a French-English one, but the dual threat of French-Canadian and American nationalism did ensure the border townships's loyalty to the government during the rebellions. The following years would witness the development of an increasingly conservative and distinctly Canadian cultural identity in the region.

A rigorous study of a pivotal period in North American history, Loyalties in Conflict is a fascinating account of conflicting forces in one region that, like the rest of Canada, has been largely shaped by the interaction of American and British influences, as well as French-language and English-language ones.

Over the past forty years he has covered wars and disasters all over the world. He filmed the fall of Saigon. He was in Moscow during the collapse of communism. He has covered countless other conflicts and natural disasters in Asia, Africa and North and South America.

He has been single-mindedly dedicated to the pursuit of his craft: to get the story, get the film - always to preserve and present the human dimension, no matter how large or mindless the conflict or event.

David Brill has paid a high price for this uncompromising style. He has two failed marriages, and at times has been overcome by demons such as alcohol. This biography is also a great adventure story, a journey through war zones and various hell holes of the world. And it is an inside look at what makes some people follow a profession where their life is on the line - as a standard feature of their day.

Catherine Hamlin is still operating though now in her late eighties. Many of the nurses - and some of the surgeons! - now working first came to the hospital as patients, then stayed on to recuperate and picked up skills as they lent a hand. The book is full of stories interspersed with accounts of the dedicated and painstaking techniques that had to be devised for the undernourished, small-boned patients who come in a steady stream to their doors. Behind all this is the figure of Catherine, described by the New York Times as 'the new Mother Teresa of our age'.

Out of fear and pain and blood on a dark desert road in Iraq emerges a story of optimism and hope, made all the more powerful because it ie recounted in the shadow of the dark forces that the world now faces.

This tender study of a father and his son is a tale for our times.

Joly’s life serves as a prism through which author J.I. Little elucidates important themes in Quebec and Canadian society, economy, politics, and culture during the Victorian and Edwardian eras. As Little reveals, Joly’s story is particularly fascinating for how closely the conflicting forces in his life – religious, cultural, and social – mirrored those of a Canadian society straining to forge a cohesive and distinctive national identity.

Christine Townend is an extraordinary person, who has dedicated her life to helping the most vulnerable creatures in our society – the animals that we rely on for food, labour or just companionship.

In the 1970s she founded Animal Liberation in an attempt to prevent cruel farming practices. It made her a highly controversial figure yet Christine never turned away from her mission to lessen animal suffering.

While Animal Liberation did enormous good, Christine's real lifework was still ahead of her. A visit to India in 1990 offered her the opportunity to take over a decrepit animal shelter just outside the city of Jaipur, called Help in Suffering. When she first arrived it contained little more than a few stray dogs and the odd goat. Yet from that small beginning Christine has had an immense impact across the length and breadth of the country, transforming the lives of thousands of animals and the people who rely on them for their livelihood.

During this remarkable journey she has had to constantly balance her determination to make a difference with her loyalty to her husband and two sons.

Christine's Ark is an inspiring and poignant story of India, its animals and its people, and of one woman's unwavering struggle to change the world for the better.

The official book behind the Academy Award-winning film The Imitation Game, starring Benedict Cumberbatch and Keira Knightley

It is only a slight exaggeration to say that the British mathematician Alan Turing (1912-1954) saved the Allies from the Nazis, invented the computer and artificial intelligence, and anticipated gay liberation by decades--all before his suicide at age forty-one. This New York Times–bestselling biography of the founder of computer science, with a new preface by the author that addresses Turing's royal pardon in 2013, is the definitive account of an extraordinary mind and life.

Capturing both the inner and outer drama of Turing’s life, Andrew Hodges tells how Turing’s revolutionary idea of 1936--the concept of a universal machine--laid the foundation for the modern computer and how Turing brought the idea to practical realization in 1945 with his electronic design. The book also tells how this work was directly related to Turing’s leading role in breaking the German Enigma ciphers during World War II, a scientific triumph that was critical to Allied victory in the Atlantic. At the same time, this is the tragic account of a man who, despite his wartime service, was eventually arrested, stripped of his security clearance, and forced to undergo a humiliating treatment program--all for trying to live honestly in a society that defined homosexuality as a crime.

The inspiration for a major motion picture starring Benedict Cumberbatch and Keira Knightley, Alan Turing: The Enigma is a gripping story of mathematics, computers, cryptography, and homosexual persecution.

The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it.

Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?

How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.

Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

This textbook provides a comprehensive introduction to forecasting methods and presents enough information about each method for readers to use them sensibly.

Everything you need to pass the exam and get the college credit you deserve.

CLEP* is the most popular credit-by-examination program in the country, accepted by more than 2,900 colleges and universities. For over 15 years, REA has helped students pass the CLEP* exam and earn college credit while reducing their tuition costs.

Our CLEP* test preps are perfect for adults returning to college (or attending for the first time), military service members, high-school graduates looking to earn college credit, or home-schooled students with knowledge that can translate into college credit.

There are many different ways to prepare for the CLEP*. What's best for you depends on how much time you have to study and how comfortable you are with the subject matter. Our test prep for CLEP* College Algebra and the free online tools that come with it, will allow you to create a personalized CLEP* study plan that can be customized to fit you: your schedule, your learning style, and your current level of knowledge.

Here's how it works:

Diagnostic exam at the REA Study Center focuses your study

Our online diagnostic exam pinpoints your strengths and shows you exactly where you need to focus your study. Armed with this information, you can personalize your prep and review where you need it the most.

Most complete subject review for CLEP* College Algebra

Our targeted review covers all the material you'll be expected to know for the exam and includes a glossary of must-know terms.

Two full-length practice exams

The online REA Study Center gives you two full-length practice tests and the most powerful scoring analysis and diagnostic tools available today. Instant score reports help you zero in on the CLEP* College Algebra topics that give you trouble now and show you how to arrive at the correct answer-so you'll be prepared on test day.

The antidote to fuzzy thinking, with furry animals!

Have you read (or stumbled into) one too many irrational online debates? Ali Almossawi certainly had, so he wrote An Illustrated Book of Bad Arguments! This handy guide is here to bring the internet age a much-needed dose of old-school logic (really old-school, a la Aristotle).

Here are cogent explanations of the straw man fallacy, the slippery slope argument, the ad hominem attack, and other common attempts at reasoning that actually fall short—plus a beautifully drawn menagerie of animals who (adorably) commit every logical faux pas. Rabbit thinks a strange light in the sky must be a UFO because no one can prove otherwise (the appeal to ignorance). And Lion doesn’t believe that gas emissions harm the planet because, if that were true, he wouldn’t like the result (the argument from consequences).

Once you learn to recognize these abuses of reason, they start to crop up everywhere from congressional debate to YouTube comments—which makes this geek-chic book a must for anyone in the habit of holding opinions.

Logic For Dummies tracks an introductory logic course at the college level. Concrete, real-world examples help you understand each concept you encounter, while fully worked out proofs and fun logic problems encourage you students to apply what you’ve learned.

A New York Times Notable Book.

The Babylonians invented it, the Greeks banned it, the Hindus worshiped it, and the Church used it to fend off heretics. Now it threatens the foundations of modern physics. For centuries the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything.

In Zero, Science Journalist Charles Seife follows this innocent-looking number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe, its rise and transcendence in the West, and its ever-present threat to modern physics. Here are the legendary thinkers—from Pythagoras to Newton to Heisenberg, from the Kabalists to today's astrophysicists—who have tried to understand it and whose clashes shook the foundations of philosophy, science, mathematics, and religion. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything.

Logically Fallacious is one of the most comprehensive collections of logical fallacies with all original examples and easy to understand descriptions, perfect for educators, debaters, or anyone who wants to be improve his or her reasoning skills.

"Expose an irrational belief, keep a person rational for a day. Expose irrational thinking, keep a person rational for a lifetime." - Bo Bennett

An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

If you want to find out how to use Python to start answering critical questions of your data, pick up Python Machine Learning – whether you want to get started from scratch or want to extend your data science knowledge, this is an essential and unmissable resource.

What You Will LearnExplore how to use different machine learning models to ask different questions of your dataLearn how to build neural networks using Keras and TheanoFind out how to write clean and elegant Python code that will optimize the strength of your algorithmsDiscover how to embed your machine learning model in a web application for increased accessibilityPredict continuous target outcomes using regression analysisUncover hidden patterns and structures in data with clusteringOrganize data using effective pre-processing techniquesGet to grips with sentiment analysis to delve deeper into textual and social media dataIn DetailMachine learning and predictive analytics are transforming the way businesses and other organizations operate. Being able to understand trends and patterns in complex data is critical to success, becoming one of the key strategies for unlocking growth in a challenging contemporary marketplace. Python can help you deliver key insights into your data – its unique capabilities as a language let you build sophisticated algorithms and statistical models that can reveal new perspectives and answer key questions that are vital for success.

Python Machine Learning gives you access to the world of predictive analytics and demonstrates why Python is one of the world's leading data science languages. If you want to ask better questions of data, or need to improve and extend the capabilities of your machine learning systems, this practical data science book is invaluable. Covering a wide range of powerful Python libraries, including scikit-learn, Theano, and Keras, and featuring guidance and tips on everything from sentiment analysis to neural networks, you'll soon be able to answer some of the most important questions facing you and your organization.

Style and approachPython Machine Learning connects the fundamental theoretical principles behind machine learning to their practical application in a way that focuses you on asking and answering the right questions. It walks you through the key elements of Python and its powerful machine learning libraries, while demonstrating how to get to grips with a range of statistical models.

Instructors will find the latest edition pitched at a suitable level of difficulty and will appreciate its gradual increase in the level of sophistication as the student progresses through the book. Rather than inserting superficial applications at the expense of important mathematical concepts, the Beachy and Blair solid, well-organized treatment motivates the subject with concrete problems from areas that students have previously encountered, namely, the integers and polynomials over the real numbers.

Supplementary material for instructors and students available on the books Web site: www.math.niu.edu/~beachy/abstract_algebra/

Two of the authors co-wrote The Elements of Statistical Learning (Hastie, Tibshirani and Friedman, 2nd edition 2009), a popular reference book for statistics and machine learning researchers. An Introduction to Statistical Learning covers many of the same topics, but at a level accessible to a much broader audience. This book is targeted at statisticians and non-statisticians alike who wish to use cutting-edge statistical learning techniques to analyze their data. The text assumes only a previous course in linear regression and no knowledge of matrix algebra.

This story is at the same time a historical novel and an accessible explication of some of the biggest ideas of mathematics and modern philosophy. With rich characterizations and expressive, atmospheric artwork, the book spins the pursuit of these ideas into a highly satisfying tale.

Probing and ingeniously layered, the book throws light on Russell's inner struggles while setting them in the context of the timeless questions he spent his life trying to answer. At its heart, Logicomix is a story about the conflict between an ideal rationality and the unchanging, flawed fabric of reality.

Combining stories of great writers and philosophers with quotations and riddles, this completely original text for first courses in mathematical logic examines problems related to proofs, propositional logic and first-order logic, undecidability, and other topics. 2013 edition.

Updated for R 2.14 and 2.15, this second edition includes new and expanded chapters on R performance, the ggplot2 data visualization package, and parallel R computing with Hadoop.

Get started quickly with an R tutorial and hundreds of examplesExplore R syntax, objects, and other language detailsFind thousands of user-contributed R packages online, including BioconductorLearn how to use R to prepare data for analysisVisualize your data with R’s graphics, lattice, and ggplot2 packagesUse R to calculate statistical fests, fit models, and compute probability distributionsSpeed up intensive computations by writing parallel R programs for HadoopGet a complete desktop reference to RContents include: Sets and Relations — Cantor's concept of a set, etc.

Natural Number Sequence — Zorn's Lemma, etc.

Extension of Natural Numbers to Real Numbers

Logic — the Statement and Predicate Calculus, etc.

Informal Axiomatic Mathematics

Boolean AlgebraInformal Axiomatic Set TheorySeveral Algebraic Theories — Rings, Integral Domains, Fields, etc.

First-Order Theories — Metamathematics, etc.

Symbolic logic does not figure significantly until the final chapter. The main theme of the book is mathematics as a system seen through the elaboration of real numbers; set theory and logic are seen s efficient tools in constructing axioms necessary to the system.

Mathematics students at the undergraduate level, and those who seek a rigorous but not unnecessarily technical introduction to mathematical concepts, will welcome the return to print of this most lucid work.

"Professor Stoll . . . has given us one of the best introductory texts we have seen." — Cosmos.

"In the reviewer's opinion, this is an excellent book, and in addition to its use as a textbook (it contains a wealth of exercises and examples) can be recommended to all who wish an introduction to mathematical logic less technical than standard treatises (to which it can also serve as preliminary reading)." — Mathematical Reviews.

The selection of topics conveys not only their role in this historical development of mathematics but also their value as bases for understanding the changing nature of mathematics. Among the topics covered in this wide-ranging text are: mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, the real numbers system, sets, logic and philosophy and more. The emphasis on axiomatic procedures provides important background for studying and applying more advanced topics, while the inclusion of the historical roots of both algebra and geometry provides essential information for prospective teachers of school mathematics.

The readable style and sets of challenging exercises from the popular earlier editions have been continued and extended in the present edition, making this a very welcome and useful version of a classic treatment of the foundations of mathematics. "A truly satisfying book." — Dr. Bruce E. Meserve, Professor Emeritus, University of Vermont.

The two-part selection of puzzles and paradoxes begins with examinations of the nature of infinity and some curious systems related to Gödel's theorem. The first three chapters of Part II contain generalized Gödel theorems. Symbolic logic is deferred until the last three chapters, which give explanations and examples of first-order arithmetic, Peano arithmetic, and a complete proof of Gödel's celebrated result involving statements that cannot be proved or disproved. The book also includes a lively look at decision theory, better known as recursion theory, which plays a vital role in computer science.

R is both an object-oriented language and a functional language that is easy to learn, easy to use, and completely free. A large community of dedicated R users and programmers provides an excellent source of R code, functions, and data sets. R is also becoming adopted into commercial tools such as Oracle Database. Your investment in learning R is sure to pay off in the long term as R continues to grow into the go to language for statistical exploration and research.

Covers the freely-available R language for statistics Shows the use of R in specific uses case such as simulations, discrete probability solutions, one-way ANOVA analysis, and more Takes a hands-on and example-based approach incorporating best practices with clear explanations of the statistics being done

The present volume reprints the first English translation of Giidel'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.

This book will help you:

Become a contributor on a data science team Deploy a structured lifecycle approach to data analytics problems Apply appropriate analytic techniques and tools to analyzing big data Learn how to tell a compelling story with data to drive business action Prepare for EMC Proven Professional Data Science CertificationCorresponding data sets are available at www.wiley.com/go/9781118876138.

Get started discovering, analyzing, visualizing, and presenting data in a meaningful way today!

Chances are you already use Excel to perform some fairly routine calculations. Now the Excel Scientific and Engineering Cookbook shows you how to leverage Excel to perform more complex calculations, too, calculations that once fell in the domain of specialized tools. It does so by putting a smorgasbord of data analysis techniques right at your fingertips. The book shows how to perform these useful tasks and others:

Use Excel and VBA in generalImport data from a variety of sourcesAnalyze dataPerform calculationsVisualize the results for interpretation and presentationUse Excel to solve specific science and engineering problemsWherever possible, the Excel Scientific and Engineering Cookbook draws on real-world examples from a range of scientific disciplines such as biology, chemistry, and physics. This way, you'll be better prepared to solve the problems you face in your everyday scientific or engineering tasks.

High on practicality and low on theory, this quick, look-up reference provides instant solutions, or "recipes," to problems both basic and advanced. And like other books in O'Reilly's popular Cookbook format, each recipe also includes a discussion on how and why it works. As a result, you can take comfort in knowing that complete, practical answers are a mere page-flip away.

Beginning with a survey of set theory and its role in mathematics, the text proceeds to definitions and examples of categories and explains the use of arrows in place of set-membership. The introduction to topos structure covers topos logic, algebra of subobjects, and intuitionism and its logic, advancing to the concept of functors, set concepts and validity, and elementary truth. Explorations of categorial set theory, local truth, and adjointness and quantifiers conclude with a study of logical geometry.