Mathematical foundations Books

Book SynopsisOne of the most illuminating, useful and exciting books ever published in the mathematical field Taking only a modicum of knowledge for granted, Lancelot Hogben leads readers of this famous book through the whole course from simple arithmetic to calculus. His illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty. Mathematics is the language of size, shape, and order – a language Hogben shows one can both master and enjoy.Trade Review'It makes alive the contents of the elements of mathematics' Albert Einstein'Deals with maths in a way that they never taught us at school' Daily Express'If only I had been brought up on this book, the sense and meaning of mathematics would have been made clear to me... The book combines utmost brilliance with extraordinarily good common sense' A. L. Rowse'A great book of first-class importance' H. G. Wells

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Book SynopsisA comprehensive guide to statistics—with information on collecting, measuring, analyzing, and presenting statistical data—continuing the popular 101 series. Data is everywhere. In the age of the internet and social media, we’re responsible for consuming, evaluating, and analyzing data on a daily basis. From understanding the percentage probability that it will rain later today, to evaluating your risk of a health problem, or the fluctuations in the stock market, statistics impact our lives in a variety of ways, and are vital to a variety of careers and fields of practice. Unfortunately, most statistics text books just make us want to take a snooze, but with Statistics 101, you’ll learn the basics of statistics in a way that is both easy-to-understand and apply. From learning the theory of probability and different kinds of distribution concepts, to identifying data patterns and graphing and presenting precise findings, this essential guide can help turn statistical math from scary and complicated, to easy and fun. Whether you are a student looking to supplement your learning, a worker hoping to better understand how statistics works for your job, or a lifelong learner looking to improve your grasp of the world, Statistics 101 has you covered.

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Book SynopsisThe Shape of Space, Third Edition maintains the standard of excellence set by the previous editions. This lighthearted textbook covers the basic geometry and topology of two- and three-dimensional spacesâstretching studentsâ minds as they learn to visualize new possibilities for the shape of our universe.Written by a master expositor, leading researcher in the field, and MacArthur Fellow, its informal exposition and engaging exercises appeal to an exceptionally broad audience, from liberal arts students to math undergraduate and graduate students looking for a clear intuitive understanding to supplement more formal texts, and even to laypeople seeking an entertaining self-study book to expand their understanding of space.Features of the Third Edition: Full-color figures throughout Picture proofs have replaced algebraic proofs Simpler handles-and-crosscaps approach to surfaces Updated discussiTable of ContentsPart I Surfaces and Three-Manifolds Flatland Gluing Vocabulary Orientability Classification of Surfaces Products Flat Manifolds Orientability vs. Two-Sidedness Part II Geometries on Surfaces The Sphere The Hyperbolic Plane Geometries on Surfaces Gauss-Bonnet Formula and Euler Number Part III Geometries on Three-Manifolds Four-Dimensional Space The Hypersphere Hyperbolic Space Geometries on Three-Manifolds I Bundles Geometries on Three-Manifolds II Part IV The Universe The Universe The History of Space Appendix A: Answers Appendix B: Bibliography Appendix C: Conway’s ZIP Proof

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Book SynopsisEmphasizes the historical development of number theory, describing methods, theorems, and proofs in the contexts in which they originated, and providing an accessible introduction to one of the subjects in mathematics. This title includes helpful hints for when students are unsure of how to get started on a given problem.Trade Review"An excellent contribution to the list of elementary number theory textbooks. Number theory, it is true, has as rich a history as any branch of mathematics, and Watkins has done terrific work in integrating the stories of the people behind this subject with the traditional topics of elementary number theory. There is more than enough material here for a one-semester course, and while this is standard for textbooks at this level, the added historical and biographical material--which cover mathematical developments and people well into the 20th century--are well worth the increased weight of the text."--Mark Bollman, MAA Reviews

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Book SynopsisJohn Mason is a Professor Emeritus at the Open University and a Senior Research Fellow at the University of Oxford. Kaye Stacey is a Foundation Professor of Mathematics Education at the Melbourne Graduate School of Education, University of MelbourneTrade Review‘Every student doing a mathematics degree should read this book.’James Blowey, Durham University ‘The ideas I encountered in Thinking Mathematically continue to influence the way in which I work today.’David J Wraith, National University of Ireland, Maynooth ‘[This book] transformed my attitude to mathematics from apathy to delight’Nichola Clarke, Oxford University 'Thinking Mathematically has always been one of my favorite books. Expanded and updated, this version is a must for my bookshelf and should be for yours too.'Alan Schoenfeld, University ofCalifornia, BerkeleyTable of Contents1. Everyone can start 2. Phases of work 3. Responses to being STUCK 4. ATTACK: conjecturing 5. ATTACK: justifying and convincing 6. Still STUCK? 7. Developing an internal monitor 8. On becoming your own questioner 9. Developing mathematical thinking 10. Something to think about 11. Thinking mathematically in curriculum topics Bibliography &nb

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Book SynopsisWinner, Euler Book Prize, awarded by the Mathematical Association of America. With over 200 full color photographs, this non-traditional, tactile introduction to non-Euclidean geometries also covers early development of geometry and connections between geometry, art, nature, and sciences. For the crafter or would-be crafter, there are detailed instructions for how to crochet various geometric models and how to use them in explorations. New to the 2nd Edition; Daina Taimina discusses her own adventures with the hyperbolic planes as well as the experiences of some of her readers. Includes recent applications of hyperbolic geometry such as medicine, architecture, fashion & quantum computing.Trade Review"This beautifully and profusely illustrated second edition of "Crocheting Adventures with Hyperbolic Planes" is a unique and extraordinary instructional manual and guide that is unreservedly recommended for personal, professional, community, and academic library"—James A. Cox, Editor-in-Chief, Midwest Book Review"This book shows just how fun deep mathematics can be and reveals the importance of thinking of mathematics with your hands, eyes and body — not just the brain. More importantly, it shows how good mathematics needs input from all sorts of people and cultures, in particular here the geometry essential to fibre arts."—Professor Edmund Harris, University of Arkansas, co-author of Patterns/Visions of the Universe with Alex Bellos"This is a lovely introduction to hyperbolic geometry and how to represent it in a tactile, playful way. The book takes you through a wonderful history of both the maths and the art, exploring how we have perceived the world around us over the centuries and how this applies today. You get to explore the concepts with your own hands and really see how it all works. As both a mathematician and a crocheter I’m itching to make my own hyperbolic planes and use them in all sorts of places!"—Samantha Durbin, The Royal Institution of Great BritainThis is the second edition of the book Crocheting Adventures with Hyperbolic Planes, which won the 2012 Euler Book Prize[. . . . ]This book presents an amazing hybrid approach to two seemingly different audiences: mathematicians and fiber artists.For the mathematician, the book presents a tactile approach to the very theoretical concepts in hyperbolic geometry, providing clear directions on how to construct objects in hyperbolic geometry. This book is a great introduction to hyperbolic geometry for anyone wanting to know about the subject and would be a great asset to any undergraduate math student studying non-Euclidean geometries.For the fiber artist interested in crochet, the book does a great job of explaining very advanced mathematics in an inviting and understanding way, encouraging artists to pursue more mathematics to incorporate into their creative works. It also provides insight into the creative process of developing mathematics, showing that mathematicians and artists both use very creative processes.This book is extremely well-written and organized. [. . . .] The book also weaves together the history and development of non-Euclidean geometries and their connections to many different areas such as art, biology and nature, physics, computer science, music, chemistry, and architecture. Each chapter has a clear purpose, and the imagery really complements the writing. At the end of the book, there is a section on how to make models. For the artist interested in crochet, the directions are a little bit more mathematical, but they are presented clearly. It will definitely be quite different than any pattern you have read before! For the mathematician who would like to have some tactile hyperbolic models, there are directions for making models out of paper as well. This book is more than just a great introduction to hyperbolic geometry, it is a great book to showcase the work of mathematicians and the process of discovering mathematics. As mathematicians, we often only present our finished and most-polished versions of our work, and we don’t let many people see the process by which this polished mathematics was developed.This book gives the reader insight into that process and illuminates the creativity involved in the development of mathematics.—Rachelle Bouchat, MAA Reviews October 2019Praise for previous edition"2012 Euler Book Prize Winner ...elegant, novel approach... that is perfectly capable of standing on its mathematical feet as a clear, rigorous, and beautifully illustrated introduction to hyperbolic geometry. It is truly a book where art, craft, science, and mathematics come together in perfect harmony."—MAA, December 2011"This book is richly illustrated with photographs and colored illustrations and it has been produced on high-quality paper. It would be a useful addition to the library of a school or university."—Gazette-Australia, May 2011"Daina's crochet models break through the austere, formal stereotype of mathematics and present a path to a whole-brain understanding of a beautiful cluster of simple and significant ideas. The book helps to change the way of thinking about mathematics - an art of human understanding!"—Corina Mohorianu, Zentralblatt MATH, September 2009"The models illustrated in this book are prime examples of art influencing mathematics. Daina provides the necessary instructions for even novices to crochet and create hyperbolic models of their own."—Swami Swaminathan, Canadian Mathematical Society Notes, October 2009"It lays out the fundamental knowledge for appreciation of tactile hyperbolic manifolds cautiously and accessibly. ... an enjoyable read for a general audience."—David Jacob Wildstrom, Mathematical Reviews, December 2009Table of ContentsForeword by William Thurston. Introduction. What Is the Hyperbolic Plane? Can We Crochet It?. What Can You Learn from Your Model?. Four Strands in the History of Geometry. Tidbits from the History of Crochet. What is Non-Euclidean Geometry?. Pseudosphere. Metamorphoses of the Hyperbolic Plane. Other Surfaces with Negative Curvature. Looking for Applications of Hyperbolic Geometry. Hyperbolic Crochet goes Viral. Appendix: How to Make Models.

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Book SynopsisTrade Review"[Stillwell] writes clearly and engagingly... [Elements of Mathematics] can appeal to various constituencies at different levels of mathematical sophistication."--Mark Hunacek, MAA Reviews "A great exploration of elementary mathematics, its limitations, how infinity complicates things, and how various branches of mathematics fit together."--Antonio Cangiano, Math-Blog "Stillwell is ... One of the better current mathematical authors: he writes clearly and engagingly, and makes more of an effort than most to provide historical detail and a sense of how various mathematical ideas tie in with one another... The features we have learned to expect from Stillwell (including, but not limited to, excellent writing) are present in [Elements of Mathematics] as well."--MAA Reviews "An accessible read... Stillwell breaks down the basics, providing both historical and practical perspectives from arithmetic to infinity."--Gemma Tarlach, Discover "[A] sophisticated treatment of topics usually described as elementary."--John Allen Paulos "[Elements of Mathematics] is quite a tour de force, organized by areas of mathematics--arithmetic, computation, algebra, geometry, calculus, and so on--and in each area Stillwell manages to distill down the big ideas and the connections with other areas. He is a master expositor, and the text manages to be engaging and accessible without watering down the mathematics. I definitely learned new things from the book!"--Brent Yorgey, Math Less Traveled blog "From a lifetime of teaching, Stillwell has distilled some nice examples from the entire gamut of elementary mathematics."--Mathematical Reviews Clippings "[A] wonderful book... I think that [Elements of Mathematics] will itself become a modern classic and a reference work for anyone trying to learn basic topics in any of the major fields of mathematics."--Victor Katz, Bulletin of the American Mathematical Society "Elements of Mathematicsis a fine ... overview of the field of mathematics... The writing is clear, succinct, organized, and the diagrams [and] illustrations excellent... While some of the discussion is introductory or elementary, it always leads to deeper, more challenging ideas... [T]his will make a fine basic addition to most mathematicians' bookshelves."--Math Tango "Stillwell uses his broad and impressive command of mathematics to transport a reader through each topic and to a higher level of understanding and questioning."--Convergence "[A] wonderful book ... I think that [Elements of Mathematics] will itself become a modern classic and a reference work for anyone trying to learn basic topics in any of the major fields of mathematics."--Victor Katz, Bulletin of the American Mathematical Society "[Elements of Mathematics] is a book that everybody should read. You will be the better for it."--Reuben Hersh, American Mathematical MonthlyTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. xi*1. Elementary Topics, pg. 1*2. Arithmetic, pg. 35*3. Computation, pg. 73*4. Algebra, pg. 106*5. Geometry, pg. 148*6. Calculus, pg. 193*7. Combinatorics, pg. 243*8. Probability, pg. 279*9. Logic, pg. 298*10. Some Advanced Mathematics, pg. 336*Bibliography, pg. 395*Index, pg. 405

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Book SynopsisDesign Techniques for Origami Tessellations is both a collection of origami tessellations and a manual to design them.This book begins by explaining general design methods, the history and definitions of origami tessellations, and the geometric features of flat origami, before moving on to introduce a brand-new design method: the twist-based design method. This method generates base parts that connect twist patterns (that can be folded with a twist) without using a lattice. Therefore, it can generate base parts such as regular pentagons, which cannot be generated with more conventional methods, and can generate new origami tessellations connected to them.Features: No proofs or formulas in the text and minimal jargon. Suitable for readers with a roughly middle school to high school level of mathematical background. Web application implementing the method described in this book is available, allowing the readers to design tTable of Contents0. Origami and Traditional Tessellation Patterns. 0.1. Background of Origami Tessellations. 0.2 Crease Patterns. 0.3 Basic Geometry of Flat-Foldable Crease Patterns. 0.4 Folded State of Crease Patterns. 0.5 Patterns for Twist-Folding. 0.6 Tessellations. 0.7. Tips for Making Beautiful Folds. 1.Folding on Square Grid. 1.1. Square Twist-Patterns. 1.2. Isosceles Right Triangle Twist Pattern. 1.3. Checker Base. 1.4. Changing folded shape. 1.5. Crease patterns as connectable tile. Appendix 1: Pixel Arts Composed of Origami Tessellation. 2. Folding on Equilateral Triangle Grid. 2.1. Equilateral Triangle Twist-Patterns. 2.2. Regular Hexagon Twist-Patterns. 2.3. Right Triangle Twist-Patterns. Column 1: Grid and Twist Pattern. 3. Connecting Triangle Twist Patterns. 3.1. Creating Triangle Twist Patterns. 3.2. Connecting Triangle Twist Patterns. 3.3. Design for Regular Polygon Patterns. Column 02: How to use Triangle Twist Pattern Maker. Appendix 2: Changing Length of Pleat Base. 4.Connecting of Different Base Parts. 4.1. Connectable Side of Boundary. 4.2. Regular Tessellations. 4.3. Tessellation with Equilateral Polygons. 4.4. Combining Crease Patterns Having Different Guide Sides. Appendix 3: Condition that Boundaries are Folded into Similar Shape. 5. Generating Aesthetic Origami Tessellations. 5.1. Origami Tessellations Regarding as Positive-Negative Pattern. 5.2. Parallel Moving Faces by Flat Folding. 5.3. Design for Origami Tessellations Regarding as Positive-Negative Pattern. Appendix 4: Deformation of crease pattern using pleat bases. 6. Folding Bellows. 6.1. Folding Parallel Lines. 6.2. Bent Bellows. 6.3. Periodic Bellows. 6.4. Bending Irregular Bellows. Column 03: Origami Tessellation Design Software “Tess”. 7. Application of Twist Pattern Design Method. 7.1. Reconstructing Guide from Given Origami Tessellation. 7.2. Fractal Origami Tessellations and Guides. 7.3. Guide with Gaps. Column 4: Connecting 3D Origami Arts and Origami Tessellations.

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Book SynopsisPrimary Maths for Scotland Textbook 1C is the third of 3 first level textbooks. These engaging and pedagogically rigorous books are the first maths textbooks for Scotland completely aligned to the benchmarks and written specifically to support Scottish children in mastering mathematics at their own pace.Primary Maths for Scotland Textbook 1C is the third of 3 first level textbooks. The books are clear and simple with a focus on developing conceptual understanding alongside procedural fluency. They cover the entire first level mathematics Curriculum for Excellence in an easy-to-use set of textbooks which can fit in with teacher's existing planning, resources and scheme of work.- Packed with problem-solving, investigations and challenging problems- Diagnostic check lists at the start of each unit ensure that pupils possess the required pre-requisite knowledge to engage on the unit of work- Worked examples and non-examples help pupils fully understand mathematical concepts- Includes intel

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Book SynopsisPrimary Maths for Scotland Textbook 2A is the first of 3 second level textbooks. These engaging and pedagogically rigorous books are the first maths textbooks for Scotland completely aligned to the benchmarks and written specifically to support Scottish children in mastering mathematics at their own pace.Primary Maths for Scotland Textbook 2A is the first of 3 second level textbooks. The books are clear and simple with a focus on developing conceptual understanding alongside procedural fluency. They cover the entire second level mathematics Curriculum for Excellence in an easy-to-use set of textbooks which can fit in with teacher's existing planning, resources and scheme of work.- Packed with problem-solving, investigations and challenging problems- Diagnostic check lists at the start of each unit ensure that pupils possess the required pre-requisite knowledge to engage on the unit of work- Worked examples and non-examples help pupils fully understand mathematical concepts- Includes in

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Book Synopsis Larry Goldstein has received several distinguished teaching awards, given more than fifty Conference and Colloquium talks & addresses, and written more than fifty books in math and computer programming.  He received his PhD at Princeton and his BA and MA at the University of Pennsylvania. He also teaches part time at Drexel University.   David Schneider, who is known widely for his tutorial software, holds a BA degree from Oberlin College and a PhD from MIT.  He is currently an emeritus professor of mathematics at the University of Maryland. He has authored eight widely used math texts, fourteen highly acclaimed computer books, and three widely used mathematical software packages. He has also produced instructional videotapes at both the University of Maryland and the BBC. Table of Contents 1. Linear Equations and Straight Lines 2. Matrices 3. Linear Programming, A Geometric Approach 4. The Simplex Method 5. Sets and Counting 6. Probability 7. Probability and Statistics 8. Markov Processes 9. The Theory of Games 10. The Mathematics of Finance 11. Logic Appendix A. Areas Under the Standard Normal Curve Appendix B. The TI-83/84 Plus Graphing Calculators Appendix C. Spreadsheet Fundamentals Appendix D. Wolfram Alpha Answers to Odd-Numbered Exercises Index

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Book Synopsis Larry Goldstein has received several distinguished teaching awards, given more than fifty Conference and Colloquium talks & addresses, and written more than fifty books in math and computer programming.  He received his PhD at Princeton and his BA and MA at the University of Pennsylvania. He also teaches part time at Drexel University.   David Schneider, who is known widely for his tutorial software, holds a BA degree from Oberlin College and a PhD from MIT.  He is currently an emeritus professor of mathematics at the University of Maryland. He has authored eight widely used math texts, fourteen highly acclaimed computer books, and three widely used mathematical software packages. He has also produced instructional videotapes at both the University of Maryland and the BBC. Table of Contents 1. Linear Equations and Straight Lines 2. Matrices 3. Linear Programming, A Geometric Approach 4. The Simplex Method 5. Sets and Counting 6. Probability 7. Probability and Statistics 8. Markov Processes 9. The Theory of Games 10. The Mathematics of Finance 11. Logic Appendix A. Areas Under the Standard Normal Curve Appendix B. The TI-83/84 Plus Graphing Calculators Appendix C. Spreadsheet Fundamentals Appendix D. Wolfram Alpha Answers to Odd-Numbered Exercises Index

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Book SynopsisThe maths needed to succeed in AS and A Level Psychology is harder now than ever before. Suitable for all awarding bodies, this practical handbook covers all of the maths skills needed for the AS and A Level Psychology specifications. Worked examples, practice questions, ''remember points'' and ''stretch yourself'' questions give students the key knowledge and then the opportunity to practise and build confidence.

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Book SynopsisProvides authoritative exposition, comprehensive survey, and fundamental research exploring the underlying unifying themes in the various areas of application of logic in artificial intelligence and computer science. The book assumes as background some mathematical sophistication.Trade ReviewReview of the first three volumes: `.. an essential acquisition for any library covering theoretical computer science and highly desirable for any researcher in the field.' Times Higher Education SupplementReview of the first three volumes: `... the first three volumes... represent a detailed and comprehensive exposition of the theoretical and computational features of a wide variety of classical and non-classical logics.' `... can be unreservedly recommended to AI practitioners with proficiency in logic and commitment to its role in the development of AI systems.' The Computer JournalTable of ContentsList of contributors ; 1.1 The role(s) of logic in artificial intelligence ; 1.2 First order logic ; 1.3 Methods and calculi for deduction ; 1.4 Deduction systems based on resolution ; 1.5 Equational reasoning and term rewriting systems ; 1.6 Basic modal logic ; 1.7 Logical features of Horn clauses ; Author index ; Subject index

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Book SynopsisMathematics for the Imagination provides an accessible and entertaining investigation into mathematical problems in the world around us. From world navigation, family trees, and calendars to patterns, tessellations, and number tricks, this informative and fun new book helps you to understand the maths behind real-life questions and rediscover your arithmetical mind.Trade ReviewEveryone can find something interesting. * Zentralblatt Math *Table of ContentsPREFACE ; 1. World Travel ; 2. The Travelling World ; 3. The Geometric Picture ; 4. The World of Archimedes ; 5. Reflections and Curves ; 6. Covering the World ; 7. Possible and Impossible Constructions ; 8. For Conoisseurs ; FURTHER READING ; INDEX

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Book SynopsisPropositiones ad acuendos juvenes (Problems to Sharpen the Young) is a ninth-century book written by medieval teacher and scholar Alcuin of York. Today, it has become one of the foundational texts in what is commonly called recreational mathematics. The book has been translated in many languages and analysed from various mathematical angles and perspectives, from contemporary arithmetic and geometry to the nature of sequences. It is not only a collection of ingenious and challenging puzzles, but the core ideas collected in this book have become major themes and branches of mathematics.Here, Marcel Danesi revisits all fifty-three problems in Alcuin''s original text, providing detailed solutions and analyses. Alcuin''s Recreational Mathematics examines the problems in the Propositiones in easy-to-follow language, extracting from them the notions and techniques that today constitute basic mathematics. Each chapter discusses Alcuin''s problems more broadly, and ends with ten exploratory puzzles based on Alcuin''s original problems and related themes. Answers and detailed solutions are included at the back.Alcuin''s Recreational Mathematics demonstrates how Alcuin''s Propositiones puts basic mathematical thinking on display via ingenious problems that often require outside-of-the-box thinking, constituting an original and imaginative investigation of mathematics in its essence.

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Book SynopsisMadulo goes to spend her school holiday with her cousin Serowe. She doesn''t expect it to be too exciting, but thanks to an unfriendly bus driver, a teenage boy, an expedition with her friends, a frightening encounter with thieves and a certificate for bravery, the holiday turns out to be the adventure of a lifetime.

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The origami introduced in this book is based on simple techniques. Some were previously known by origami artists and some were discovered by the author. Curved-Folding Origami Design shows a way to explore new area of origami composed of curved folds. Each technique is introduced in a step-by-step fashion, followed by some beautiful artwork examples. A commentary explaining the theory behind the technique is placed at the end of each chapter.Features Explains the techniques for designing curved-folding origami in seven chapters Contains many illustrations and photos (over 140 figures), with simple instructions Contains photos of 24 beautiful origami artworks, as well as their crease patterns Some basic theories behind the techniques are introduced

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Book SynopsisPraise for the First EditionLuck, Logic, and White Lies teaches readers of all backgrounds about the insight mathematical knowledge can bring and is highly recommended reading among avid game players, both to better understand the game itself and to improve one's skills. Midwest Book ReviewThe best book I''ve found for someone new to game math is Luck, Logic and White Lies by Jörg Bewersdorff. It introduces the reader to a vast mathematical literature, and does so in an enormously clear manner. . . Alfred Wallace, Musings, Ramblings, and Things Left UnsaidThe aim is to introduce the mathematics that will allow analysis of the problem or game. This is done in gentle stages, from chapter to chapter, so as to reach as broad an audience as possible . . . Anyone who likes games and has a taste for analytical thinking will enjoy this book. Peter Fillmore, CMS NotesLuck, Logic, and Trade Review"The book presents mathematical explanation of problems related to playing games of chance, combinatorial and strategic games, with descriptions of their historical perspectives and recreational aspects. [. . .] The author notes that people play games investigating the unknown outcomes, in amusement and hope of winning in conditions of uncertainty caused by three possible mechanisms: chance, a large number of combinations of various moves, and different states of information among the individual players. Respectively, the games can be divided to three classes: games of chance (e.g., dice, cards, roulette) where the random processes dominate the players decisions; combinatorial games (chess, go) where the uncertainty rests on the multiplicity of possible moves; and strategic games (rock-paper-scissors) where the players’ uncertainty arises from imperfect information. Many games have mixed features (backgammon, poker, skat), and the degree of influence of the three main causes of uncertainty defines specifics of each game. The book introduces mathematical methods developed for description and solutions of games: the games of chance can be analyzed with the help of probability theory, the combinatorial games are considered by variety of methods used in particular problems, and the strategic games are studied by the game theory models for decision-making in the interactive optimizing economic processes. The book is organized in four parts containing 51 chapters on various topics.[. . .] All topics are illustrated by multiple figures and numerical tables. [. . .] It can be useful to instructors, students, and readers wishing to extend understanding of the games’ intrinsic features needed to improve ability to win in actual playing."- Stan Lipovetsky, Technometrics"As the title indicates, Bewersdorff’s book is intended to span the mathematics of games in general – not only games of chance but also including strategic and skill games. The author covers all the big categories of games – casino, tournament, and house or social games. In fact, the skill-strategic dimension of the games balanced with the chance-uncertainty dimension is the central element around which the author presents games as an important field of application of mathematics; he takes them as a good opportunity to advocate for the beauty and power of mathematics. To that point, the book is written so as to be both popular and scholarly, and these attributes are not at all inconsistent with each other for such a general topic, content, and style. [. . .] The book leaves the impression of its author’s being a skilled advocate of the unlimited power of mathematics, shown through the examples of games. Not only is mathematics able to describe the games and the way we play them, but it is entitled to address fundamental questions beyond the problem-solving aspects of games and gaming. It is mainly game theory and probability theory that grant mathematics such a virtue. [. . .] Although the chapters can mostly be read independent of each other, and the mathematical content is not systematized throughout the book, the mathematically-inclined reader can put things together to have an objective overview of one of the most interesting fields in application of mathematics – games – which themselves shaped the development of mathematics."– International Gambling Studies"The author provides a great deal of insight into a wide variety of games, all inspected from a mathematical point of view. He develops the prerequisites mathematically, so that someone with a good high-school background in mathematics and a willingness to learn will be able to build up the necessary tools for successful play. Moreover, the author’s arguments are often very detailed, so that even a novice can easily follow them. The numerous diagrams also help.I find Bewersdorff's writing to be clear and detailed. He has taken care in the presentation of the ideas. The book, the size of which has now grown to 568 pages, provides a great deal of information, and the reader can easily pick and choose topics of interest without having to absorb the entire treatise. The level of Mathematical skill needed, however, does vary greatly from chapter to chapter. When necessary, the reader can make use of previous chapters to develop the required background to proceed. To the prospective reader, good luck, and may your play be a winning one!"– The Mathematical IntelligencerThis book, successor to the first edition (2005) and translated from the 7th German edition, treats games of chance (“luck”), combinatorial games (“logic”), and games of strategy (bluff, or “white lies”). The first part develops succinctly the needed theory of probability and investigates the nature of randomness. The second part explores minimax optimization, Grundy values, Conway’s theory of games, and complexity theory. The third part is based on the fact that in a symmetric two-person zero-sum game, the players are guaranteed optimal mixed strategies; for some games, finding such strategies can be done by linear programming. This edition adds a fourth part that investigates measuring the proportion of skill in a game, with particular application to poker. The reader needs to be comfortable with algebra and summation signs, and infinite series make appearances; end-of-chapter notes and footnotes contribute further mathematical depth.– Mathematics Magazine, MAA"Exceptionally well written, organized and presented, Luck, Logic, and White Lies: The Mathematics of Games is a unique and unreservedly recommended addition to professional, community, college, and university library Game Theory & Mathematics collections."– Midwest Books Review"A great variety of games are analyzed in an accessible way. The treatment of blackjack, in particular, is superb."– Stewart Ethier, Professor Emeritus, University of Utah and author of The Doctrine of Chances: Probabilistic Aspects of Gambling "People play games for fun and for profit. To become better at a game, you need to study it. In Luck, Logic and White Lies, Jörg Bewersdorff takes you, almost imperceptibly, from the history of numerous concrete games to their mathematical analysis. This touches upon a wide range of techniques, not only in mathematics, but also in computing and psychology. If you get the hang of it, you can apply these techniques to other areas of life, such as business, economics, biology, and sociology."– Tom Verhoeff, Dept. Math & CS, Eindhoven University of TechnologyPraise for the First Edition"Luck, Logic, and White Lies teaches readers of all backgrounds about the insight mathematical knowledge can bring and is highly recommended reading among avid game players, both to better understand the game itself and to improve one's skills."– Midwest Book Review"The best book I've found for someone new to game math is Luck, Logic and White Lies by Jörg Bewersdorff. It introduces the reader to a vast mathematical literature, and does so in an enormously clear manner. . ."– Alfred Wallace, Musings, Ramblings, and Things Left Unsaid"The aim is to introduce the mathematics that will allow analysis of the problem or game. This is done in gentle stages, from chapter to chapter, so as to reach as broad an audience as possible [. . .] Anyone who likes games and has a taste for analytical thinking will enjoy this book."– Peter Fillmore, CMS NotesTable of ContentsI. Games of Chance. 1. Dice and Probability. 2. Waiting for a Double. 3. Tips on Playing the Lottery: More Equal Than Equal? 4. A Fair Division: But How? 5. The Red and the Black: The Law of Large Numbers. 6. Asymmetric Dice: Are They Worth Anything? 7. Probability and Geometry. 8. Chance and Mathematical Certainty: Are They Reconcilable? 9. In Quest of the Equiprobable. 10. Winning the Game: Probability and Value. 11. Which Die Is Best? 12. A Die Is Tested. 13. The Normal Distribution: A Race to the Finish! 14. And Not Only at Roulette: The Poisson Distribution. 15. When Formulas Become Too Complex: The Monte Carlo Method. 16. Markov Chains and the Game Monopoly. 17 Blackjack: A Las Vegas Fairy Tale. II. Combinatorial Games. 18. Which Move Is Best? 19. Chances of Winning and Symmetry. 20. A Game for Three. 21. Nim: The Easy Winner! 22. Lasker Nim: Winning Along a Secret Path. 23. Black-and-White Nim: To Each His (or Her) Own. 24. A Game with Dominoes: Have We Run Out of Space Yet? 25. Go: A Classical Game with a Modern Theory. 26. Misere Games: Loser Wins! 27. The Computer as Game Partner. 28. Can Winning Prospects Always Be Determined? 29. Games and Complexity: When Calculations Take Too Long. 30. A Good Memory and Luck: And Nothing Else? 31. Backgammon: To Double or Not to Double? 32. Mastermind: Playing It Safe. III. Strategic Games. 33. Rock–Paper–Scissors: The Enemy's Unknown Plan. 34. Minimax Versus Psychology: Even in Poker? 35. Bluffing in Poker: Can It Be Done Without Psychology? 36. Symmetric Games: Disadvantages Are Avoidable, but How? 37. Minimax and Linear Optimization: As Simple as Can Be. 38. Play It Again, Sam: Does Experience Make Us Wiser? 39. Le Her: Should I Exchange? 40. Deciding at Random: But How? 41. Optimal Play: Planning Efficiently. 42. Baccarat: Draw from a Five? 43. Three-Person Poker: Is It a Matter of Trust? 44 QUAAK! Child's Play? 45 Mastermind: Color Codes and Minimax. 46. A Car, Two Goats–and a Quizmaster. IV. Epilogue: Chance, Skill, and Symmetry. 47. A Player's Inuence and Its Limits. 48. Games of Chance and Games of Skill. 49. In Quest of a Measure. 50. Measuring the Proportion of Skill. 51. Poker: The Hotly Debated Issue.

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Book SynopsisKnot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject. Ed Witten, Recipient of the Fields MedalI spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It's a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field. Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deeTrade Review"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject."– Ed Witten, Recipient of the Fields Medal"I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis "An encyclopedia is expected to be comprehensive, and to include independent expository articles on many topics. The Encyclopedia of Knot Theory is all this. This book will be an excellent introduction to topics in the field of knot theory for advanced undergraduates, graduate students, and researchers interested in knots from many directions."– MAA Reviews"Knot theory is an area of mathematics that requires no introduction, and while this massive tome is certainly no introductory text, it does give a panoramic — and, well, encyclopaedic — view of this vast subject.[. . . ] A book with such an ambitious remit is bound to contain omissions and oddities. [. . .] But this is a small point compared to what has been achieved by this encyclopaedia, which would make a fine addition to any personal or departmental library, or to a departmental coffee table."– London Mathematical SocietyThe Encyclopedia of Knot Theory is close to 1000 pages, and every section, article, paragraph, and sentence inspires the reader to want to learn more knot theory. A wonderful attribute of this text is the reference section at the end of each article as opposed to the end of the book. This allows readers to highlight different sources that will allow them to dive deeper into the topic of that section. [. . .] And while it is nearly impossible to include discussions of every branch of the knot theorytree, the editors made a great choice to focus on current topics showing how the area is still a living subject. [. . .] As a knot theory enthusiast, I truly enjoyed reading about topics I was more familiar with while also exploring topics that were new to me. As an educator, I am excited to share this book with my students and encourage them to read more articles on the topics. Some of the articles in the book include thoughtful open questions for researchers in the field to enjoy, while also providing background for anyone new to knot theory research to use as a foundation. All in all, I loved this text.– American Mathematical MonthlyTable of ContentsI Introduction and History of Knots. 1. Introduction to Knots. II Standard and Nonstandard Representations of Knots. 2. Link Diagrams. 3. Gauss Diagrams. 4. DT Codes. 5. Knot Mosaics. 6. Arc Presentations of Knots and Links. 7. Diagrammatic Representations of Knots and Links as Closed Braids. 8. Knots in Flows. 9. Multi-Crossing Number of Knots and Links. 10. Complementary Regions of Knot and Link Diagrams. 11. Knot Tabulation. III Tangles. 12. What Is a Tangle? 13. Rational and Non-Rational Tangles. 14. Persistent Invariants of Tangles. IV Types of Knots. 15. Torus Knots. 16. Rational Knots and Their Generalizations. 17. Arborescent Knots and Links. 18. Satellite Knots. 19. Hyperbolic Knots and Links. 20. Alternating Knots. 21. Periodic Knots. V Knots and Surfaces. 22. Seifert Surfaces and Genus. 23. Non-Orientable Spanning Surfaces for Knots. 24. State Surfaces of Links. 25. Turaev Surfaces. VI Invariants Defined in Terms of Min and Max. 26. Crossing Numbers. 27. The Bridge Number of a Knot. 28. Alternating Distances of Knots. 29. Superinvariants of Knots and Links. VII Other Knotlike Objects. 30. Virtual Knot Theory. 31. Virtual Knots and Surfaces. 32. Virtual Knots and Parity. 33. Forbidden Moves,Welded Knots and Virtual Unknotting. 34. Virtual Strings and Free Knots. 35. Abstract and Twisted Links. 36. What Is a Knotoid? 37. What Is a Braidoid? 38. What Is a Singular Knot? 39. Pseudoknots and Singular Knots. 40. An Introduction to the World of Legendrian and Transverse Knots 41. Classical Invariants of Legendrian and Transverse Knots. 42. Ruling and Augmentation Invariants of Legendrian Knots. VIII Higher Dimensional Knot Theory. 43. Broken Surface Diagrams and Roseman Moves. 44. Movies and Movie Moves. 45. Surface Braids and Braid Charts. 46. Marked Graph Diagrams and Yoshikawa Moves. 47. Knot Groups. 48. Concordance Groups. IX Spatial Graph Theory. 49. Spatial Graphs. 50. A Brief Survey on Intrinsically Knotted and Linked Graphs. 51. Chirality in Graphs. 52. Symmetries of Graphs Embedded in Sᶟ and Other 3-Manifolds. 53. Invariants of Spatial Graphs. 54. Legendrian Spatial Graphs. 55. Linear Embeddings of Spatial Graphs. 56. Abstractly Planar Spatial Graphs. X Quantum Link Invariants. 57. Quantum Link Invariants. 58. Satellite and Quantum Invariants. 59. Quantum Link Invariants: From QYBE and Braided Tensor Categories. 60. Knot Theory and Statistical Mechanics. XI Polynomial Invariants. 61. What Is the Kauffman Bracket? 62. Span of the Kauffman Bracket and the Tait Conjectures. 63. Skein Modules of 3-Manifold. 64. The Conway Polynomial. 65. Twisted Alexander Polynomials. 66. The HOMFLYPT Polynomial. 67. The Kauffman Polynomials. 68. Kauffman Polynomial on Graphs. 69. Kauffman Bracket Skein Modules of 3-Manifolds. XII Homological Invariants. 70. Khovanov Link Homology. 71. A Short Survey on Knot Floer Homolog. 72. An Introduction to Grid Homology. 73. Categorification. 74. Khovanov Homology and the Jones Polynomial. 75. Virtual Khovanov Homology. XIII Algebraic and Combinatorial Invariants. 76. Knot Colorings. 77. Quandle Cocycle Invariants. 78. Kei and Symmetric Quandles. 79. Racks, Biquandles and Biracks. 80. Quantum Invariants via Hopf Algebras and Solutions to the Yang-Baxter Equation. 81. The Temperley-Lieb Algebra and Planar Algebras. 82. Vassiliev/Finite Type Invariants. 83. Linking Number and Milnor Invariants. XIV Physical Knot Theory. 84. Stick Number for Knots and Links. 85. Random Knots. 86. Open Knots. 87. Random and Polygonal Spatial Graphs. 88. Folded Ribbon Knots in the Plane. XV Knots and Science. 89. DNA Knots and Links. 90. Protein Knots, Links, and Non-Planar Graphs. 91. Synthetic Molecular Knots and Links.

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Book SynopsisThe goal for this textbook is to complement the inquiry-based learning movement. According to the author, concepts and ideas will stick with the reader more when they are motivated in an interesting way. Topics are presented mathematically as questions about the games themselves are posed.Table of Contents1. Mathematics and Probability. 1.1. Introduction. 1.2. About Mathematics. 1.3. Probability. 1.4. Candy (Yum)! 1.5. Exercises. 2. Roulette and Craps: Expected Value. 2.1. Roulette. 2.2. Summations. 2.3. Craps. 2.4. Exercises. 3. Counting: Poker Hands. 3.1. Cards and Counting. 3.2. Seven Card Pokers. 3.3. Texas Hold'Em. 3.4. Exercises. 4. More Dice: Counting and Combinations, and Statistics. 4.1. Liar's Dice. 4.2. Arkham Horror. 4.3. Yahtzee. 4.4. Exercises. 5. Game Theory: Poker Bluffing and Other Games. 5.1. Bluffing. 5.2. Game Theory Basics. 5.3. Non-Zero Sum Games. 5.4. Three-Player Game Theory. 5.5. Exercises. 6. Probability/Stochastic Matrices: Board Game Movement. 6.1. Board Game Movement. 6.2. Pay Day (The Board Game). 6.3. Monopoly. 6.4. Spread, Revisited. 6.5. Exercises. 7. Sports Mathematics: Probability Meets Athletics. 7.1. Sports Betting. 7.2. Game Theory and Sports. 7.3. Probability Matrices and Sports. 7.4. Winning a Tennis Tournament. 7.5. Repeated Play: Best of Seven. 7.6. Exercises 8. Blackjack: Previous Methods Revisited. 8.1. Blackjack. 8.2. Blackjack Variants. 8.3. Exercises. 9. A Mix of Other Games. 9.1. The Lottery. 9.2. Bingo. 9.3. Uno. 9.4. Baccarat. 9.5. Farkle. 9.6. Scrabble. 9.7. Backgammon. 9.8. Memory. 9.9. Zombie Dice. 9.10. Exercises. 10. Betting Systems: Can You Beat the System? 10.1. Betting Systems. 10.2. Gambler's Ruin. 10.3. Exercises. 11. Potpourri: Assorted Adventures in Probability. 11.1. True Randomness? 11.2. Three Dice "Craps". 11.3. Counting "Fibonacci" Coins "Circularly". 11.4. Compositions and Probabilities. 11.5. Sicherman Dice. 11.6. Traveling Salesmen. 11.7. Random Walks and Generating Functions. 11.8. More Probability! Appendices. Index.

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1 The Axiom of Extension.- 2 The Axiom of Specification.- 3 Unordered Pairs.- 4 Unions and Intersections.- 5 Complements and Powers.- 6 Ordered Pairs.- 7 Relations.- 8 Functions.- 9 Families.- 10 Inverses and Composites.- 11 Numbers.- 12 The Peano Axioms.- 13 Arithmetic.- 14 Order.- 15 The Axiom of Choice.- 16 Zorn's Lemma.- 17 Well Ordering.- 18 Transfinite Recursion.- 19 Ordinal Numbers.- 20 Sets of Ordinal Numbers.- 21 Ordinal Arithmetic.- 22 The Schröder-Bernstein Theorem.- 23 Countable Sets.- 24 Cardinal Arithmetic.- 25 Cardinal Numbers.

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Book Synopsis1 Naive Set Theory.- 1.1 What is a Set?.- 1.2 Operations on Sets.- 1.3 Notation for Sets.- 1.4 Sets of Sets.- 1.5 Relations.- 1.6 Functions.- 1.7 Well-Or der ings and Ordinals.- 1.8 Problems.- 2 The ZermeloFraenkel Axioms.- 2.1 The Language of Set Theory.- 2.2 The Cumulative Hierarchy of Sets.- 2.3 The ZermeloFraenkel Axioms.- 2.4 Classes.- 2.5 Set Theory as an Axiomatic Theory.- 2.6 The Recursion Principle.- 2.7 The Axiom of Choice.- 2.8 Problems.- 3 Ordinal and Cardinal Numbers.- 3.1 Ordinal Numbers.- 3.2 Addition of Ordinals.- 3.3 Multiplication of Ordinals.- 3.4 Sequences of Ordinals.- 3.5 Ordinal Exponentiation.- 3.6 Cardinality, Cardinal Numbers.- 3.7 Arithmetic of Cardinal Numbers.- 3.8 Regular and Singular Cardinals.- 3.9 Cardinal Exponentiation.- 3.10 Inaccessible Cardinals.- 3.11 Problems.- 4 Topics in Pure Set Theory.- 4.1 The Borel Hierarchy.- 4.2 Closed Unbounded Sets.- 4.3 Stationary Sets and Regressive Functions.- 4.4 Trees.- 4.5 Extensions of Lebesgue Measure.- 4.6 A ReTable of ContentsPreface; 1. Naïve Set Theory; 2. The Zermelo-Fraenkel Axioms; 3. Ordinal and Cardinal Numbers; 4. Topics in Pure Set Theory; 5. The Axiom of Constructibility; 6. Independence Proofs in Set Theory; 7. Non-Well-Founded Set Theory; Bibliography; Glossary of Symbols; Index

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Book SynopsisA.- I Introduction.- II Syntax of First-Order Languages.- III Semantics of First-Order Languages.- IV A Sequent Calculus.- V The Completeness Theorem.- VI The Löwenheim-Skolem and the Compactness Theorem.- VII The Scope of First-Order Logic.- VIII Syntactic Interpretations and Normal Forms.- B.- IX Extensions of First-Order Logic.- X Limitations of the Formal Method.- XI Free Models and Logic Programming.- XII An Algebraic Characterization of Elementary Equivalence.- XIII Lindström's Theorems.- References.- Symbol Index.Trade Review“…the book remains my text of choice for this type of material, and I highly recommend it to anyone teaching a first logic course at this level.” – Journal of Symbolic LogicTable of ContentsPreface; Part A: 1. Introduction; 2. Syntax of First-Order Languages; 3. Semantics of first-Order Languages; 4. A Sequent Calculus; 5. The Completeness Theorem; 6. The Lowenheim-Skolem and the Compactness Theorem; 7. The Scope of First-Order Logic; 8. Syntactic Interpretations and Normal Forms; Part B: 9. Extensions of First-Order Logic; 10. Limitations of the Formal Method; 11. Free Models and Logic Programming; 12. An Algebraic Characterization of Elementary Equivalence; 13. Lindstroem's Theorems; References; Symbol Index; Subject Index

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Book SynopsisSheaves also appear in logic as carriers for models of set theory. Beginning with several examples, it explains the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.Trade ReviewFrom the reviews: "A beautifully written book, a long and well motivated book packed with well chosen clearly explained examples. … authors have a rare gift for conveying an insider’s view of the subject from the start. This book is written in the best Mac Lane style, very clear and very well organized. … it gives very explicit descriptions of many advanced topics--you can learn a great deal from this book that, before it was published, you could only learn by knowing researchers in the field." (Wordtrade, 2008)Table of ContentsPreface; Prologue; Categorical Preliminaries; 1. Categories of Functors; 2. Sheaves of Sets; 3. Grothendieck Topologies and Sheaves; 4. First Properties of Elementary Topoi; 5. Basic Constructions of Topoi; 6. Topoi and Logic; 7. Geometric Morphisms; 8. Classifying Topoi; 9. Localic Topoi; 10. Geometric Logic and Classifying Topoi; Appendix: Sites for Topoi; Epilogue; Bibliography; Index of Notations; Index

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Book SynopsisThe later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.Table of Contents1 Introduction.- 2 Definitions and First Properties of Computation.- 3 Computation over a Ring.- 4 Decision Problems and Complexity over a Ring.- 5 The Class NP and NP-Complete Problems.- 6 Integer Machines.- 7 Algebraic Settings for the Problem “P ? NP?”.- 8 Newton’s Method.- 9 Fundamental Theorem of Algebra: Complexity Aspects.- 10 Bézout’s Theorem.- 11 Condition Numbers and the Loss of Precision of Linear Equations.- 12 The Condition Number for Nonlinear Problems.- 13 The Condition Number in ?(H(d).- 14 Complexity and the Condition Number.- 15 Linear Programming.- 16 Deterministic Lower Bounds.- 17 Probabilistic Machines.- 18 Parallel Computations.- 19 Some Separations of Complexity Classes.- 20 Weak Machines.- 21 Additive Machines.- 22 Nonuniform Complexity Classes.- 23 Descriptive Complexity.- References.

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Book SynopsisAssumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structuresTrade ReviewFrom the reviews: MATHEMATICAL REVIEWS "This is an extremely fine graduate level textbook on model theory. There is a careful selection of topics…There is a strong focus on the meaning of model-theoretic concepts in mathematically interesting examples. The exercises touch on a wealth of beautiful topics." "This is an extremely fine graduate level textbook on model theory. There is a careful selection of topics, with a route leading to a substantial treatment of Hrushovski’s proof of the Mordell-Lang conjecture for function fields. … The exercises touch on a wealth of beautiful topics. … There is additional basic background in two appendices (on set theory and on real algebra)." (Dugald Macpherson, Mathematical Reviews, 2003 e) "Model theory is the branch of mathematical logic that examines what it means for a first-order sentence … to be true in a particular structure … . This is a text for graduate students, mainly aimed at those specializing in logic, but also of interest for mathematicians outside logic who want to know what model theory can offer them in their own disciplines. … it is one which makes a good case for model theory as much more than a tool for specialist logicians." (Gerry Leversha, The Mathematical Gazette, Vol. 88 (513), 2004) "The author’s intended audience for this high level introduction to model theory is graduate students contemplating research in model theory, graduate students in logic, and mathematicians who are not logicians but who are in areas where model theory has interesting applications. … The text is noteworthy for its wealth of examples and its desire to bring the student to the point where the frontiers of research are visible. … this book should be on the shelf of anybody with an interest in model theory." (J. M. Plotkin, Zentralblatt Math, Vol. 1003 (03), 2003)Table of ContentsIntroduction * Structures and Theories * Basic Techniques * Algebraic Examples * Realizing and Omitting Types * Indiscernibles * w-stable theoryes * w-stable groups * Geometry of strongly minmal sets * Appendix A: Set Theory * Appendix B: Real Algebra * References * Index

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Book SynopsisDiscrete optimization models are used to tackle a wide variety of problems in many fields, including operations research, management science, engineering, and mathematics. Written by two internationally recognized integer programming experts, this book presents the mathematical foundations, theory, and algorithms of discrete optimization methods.Table of ContentsFOUNDATIONS. The Scope of Integer and Combinatorial Optimization. Linear Programming. Graphs and Networks. Polyhedral Theory. Computational Complexity. Polynomial-Time Algorithms for Linear Programming. Integer Lattices. GENERAL INTEGER PROGRAMMING. The Theory of Valid Inequalities. Strong Valid Inequalities and Facets for Structured Integer Programs. Duality and Relaxation. General Algorithms. Special-Purpose Algorithms. Applications of Special- Purpose Algorithms. COMBINATORIAL OPTIMIZATION. Integral Polyhedra. Matching. Matroid and Submodular Function Optimization. References. Indexes.

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Book SynopsisPraise for William Dunham s Journey Through Genius The Great Theorems of Mathematics Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions and proofs, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments.Table of ContentsPreface v Acknowledgements ix Chapter 1 Hippocrates' Quadrature of the Lune (ca 440 BC) 1 Chapter 2 Euclid's Proof of the Pythagorean Theorem (ca 300 BC) 27 Chapter 3 Euclid and the Infinitude of Primes (ca 300 BC) 61 Chapter 4 Archimedes' Determination of Circular Area (ca 225 BC) 84 Chapter 5 Heron's Formula for Triangular Area (ca AD 75) 113 Chapter 6 Cardano and the Solution of the Cubic (1545) 133 Chapter 7 A Gem from Isaac Newton (Late 1660s) 155 Chapter 8 The Bernoullis and the Harmonic Series (1689) 184 Chapter 9 The Extraordinary Sums of Leonhard Euler (1734) 207 Chapter 10 A Sampler of Euler's Number Theory (1736) 223 Chapter 11 The Non-Denumerability of the Continuum (1874) 245 Chapter 12 Cantor and the Transfinite Realm (1891) 267 Afterword 285 Chapter Notes 287 References 291 Index 295

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Book SynopsisThis adaptation of an earlier work by the authors is a graduate text and professional reference on the fundamentals of graph theory. It covers the theory of graphs, its applications to computer networks and the theory of graph algorithms. Also includes exercises and an updated bibliography.Table of ContentsBasic Concepts. Trees, Cutsets, and Circuits. Eulerian and Hamiltonian Graphs. Graphs and Vector Spaces. Directed Graphs. Matrices of a Graph. Planarity and Duality. Connectivity and Matching. Covering and Coloring. Matroids. Graph Algorithms. Flows in Networks. Indexes.

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Book SynopsisWritten for engineering students, this textbook on numerical methods stresses the typical methods that engineers use in daily practice. A chapter on design introduces problems which bring relevance to the use of this tool in engineering situations.Table of ContentsFOUNDATIONS. Systems of Linear Algebraic Equations. Nonlinear Algebraic Equations. DATA ANALYSIS. Statistics and Least-Squares Approximation. Curve Fitting. NUMERICAL CALCULUS. Differentiation and Integration. Ordinary Differential Equations. ADVANCED TOPICS. Matrix Eigenproblems. Introduction to Partial Differential Equations. Design and Optimization. Appendices. References. Bibliography. Answers to Selected Problems. Index.

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Book SynopsisThe Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The second introduces important classes of categories that have played a fundamental role in the subject's development and applications.Table of ContentsPreface; Introduction to the handbook; 1. Abelian categories; 2. Regular categories; 3. Algebraic theories; 4. Monads; 5. Accessible categories; 6. Enriched category theory; 7. Topological categories; 8. Fibred categories; Bibliography; Index.

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Book SynopsisFirst up-to-date treatment of the categorical view of sets with extra algebraic structure (data types), with applications in analysis, topology and number theory, geometry, and mathematical physics. A stimulating read for graduate students and researchers in category theory, general algebra, theoretical computer science and algebraic topology.Trade Review'The book is very well written and made as self-contained as it is reasonable for the intended audience of graduate students and researchers.' Zentralblatt MATHTable of ContentsForeword F. W. Lawvere; Introduction; Preliminaries; Part I. Abstract Algebraic Categories: 1. Algebraic theories and algebraic categories; 2. Sifted and filtered colimits; 3. Reflexive coequalizers; 4. Algebraic categories as free completions; 5. Properties of algebras; 6. A characterization of algebraic categories; 7. From filtered to sifted; 8. Canonical theories; 9. Algebraic functors; 10. Birkhoff's variety theorem; Part II. Concrete Algebraic Categories: 11. One-sorted algebraic categories; 12. Algebras for an endofunctor; 13. Equational categories of Σ-algebras; 14. S-sorted algebraic categories; Part III. Selected Topics: 15. Morita equivalence; 16. Free exact categories; 17. Exact completion and reflexive-coequalizer completion; 18. Finitary localizations of algebraic categories; A. Monads; B. Abelian categories; C. More about dualities for one-sorted algebraic categories; Summary; Bibliography; Index.

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Book SynopsisAll students taking laboratory courses within the physical sciences and engineering will benefit from this book, whilst researchers will find it an invaluable reference. This concise, practical guide brings the reader up-to-speed on the proper handling and presentation of scientific data and its inaccuracies. It covers all the vital topics with practical guidelines, computer programs (in Python), and recipes for handling experimental errors and reporting experimental data. In addition to the essentials, it also provides further background material for advanced readers who want to understand how the methods work. Plenty of examples, exercises and solutions are provided to aid and test understanding, whilst useful data, tables and formulas are compiled in a handy section for easy reference.Trade Review"Overall, this would be a nice text or reference to accompany a short course in statistics for undergraduate science or engineering..also useful for researchers desiring a primer or review...Recommended." - CHOICETable of ContentsPart I. Data and Error Analysis: 1. Introduction; 2. The presentation of physical quantities with their inaccuracies; 3. Errors: classification and propagation; 4. Probability distributions; 5. Processing of experimental data; 6. Graphical handling of data with errors; 7. Fitting functions to data; 8. Back to Bayes: knowledge as a probability distribution; Answers to exercises; Part II. Appendices: A1. Combining uncertainties; A2. Systematic deviations due to random errors; A3. Characteristic function; A4. From binomial to normal distributions; A5. Central limit theorem; A6. Estimation of the varience; A7. Standard deviation of the mean; A8. Weight factors when variances are not equal; A9. Least squares fitting; Part III. Python Codes; Part IV. Scientific Data: Chi-squared distribution; F-distribution; Normal distribution; Physical constants; Probability distributions; Student's t-distribution; Units.

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