Matematikens grunder

Logic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are explained in simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy. In this new edition Graham Priest expands his discussion to cover the subjects of algorithms and axioms, and proofs in mathematics.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Suguru is a logic puzzle with simple rules and challenging solutions. The task consists of a rectangular or square grid divided into regions.

The rules of Suguru are simple, each region must be filled with each of the digits from 1 to the number of cells in the region. Cells with the same digits must not be orthogonality or diagonally adjacent.

This Logic Puzzles book is packed with the following features:

- 500 Suguru (12x12) Puzzles from Easy to Hard.

- Answers to every puzzle are provided.

- Each puzzle is guaranteed to have only one solution.

Includes free bonus puzzles you can download book (Tons of Sudoku Puzzles for Adults & Seniors) Includes free bonus puzzles you can download book (Word Search With Hidden Message: 102 Puzzles for Adults and Seniors) 

We hope you enjoy this book, which would also make a great gift for any puzzle lover.

Proofs play a central role in advanced mathematics and theoretical computer science, yet many students struggle the first time they take a course in which proofs play a significant role. This bestselling text's third edition helps students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. Featuring over 150 new exercises and a new chapter on number theory, this new edition introduces students to the world of advanced mathematics through the mastery of proofs. The book begins with the basic concepts of logic and set theory to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for an analysis of techniques that can be used to build up complex proofs step by step, using detailed 'scratch work' sections to expose the machinery of proofs about numbers, sets, relations, and functions. Assuming no background beyond standard high school mathematics, this book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and, of course, mathematicians.

'Wooldridge is like the teacher you wish you'd had' GUARDIAN'This book is simply brilliant . . . I learned so much' SIR DAVID SPIEGELHALTER, UNIVERSITY OF CAMBRIDGE'Fresh, clever and playful' MATT RIDLEY, AUTHOR OF THE ORIGINS OF VIRTUE'Michael explains the complex, strategic structures of our world with masterful beauty'MILIND TAMBE, HARVARD UNIVERSITY'Effortlessly covers a broad swath of core ideas in game theory, with a sprinkle of British humour'EDITH ELKIND, NORTHWESTERN UNIVERSITY'A wonderful book' YOAV SHOHAM, STANFORD UNIVERSITY______A fascinating deep-dive into game theory, its history and its practical applications by award-winning expert on computer science and artificial intelligence.Most of us have some idea about game theory. Concepts like zero-sum games and the prisoner's dilemma crop up in films, novels and casual conversation, often as shorthand for cut-throat competition or inevitable betrayal. But game theory, the science behind these ideas, is widely misunderstood. All too often it's seen solely as the science of conflict and greed. In fact, this field has a lot to teach us about how to make a better world. It shows us just what it takes to enable cooperation and mutual benefit.This essential primer presents twenty one 'life lessons from game theory', which illustrate the key ideas in the field, and which are packed with real world examples: from overfishing in the Atlantic; to the Cuban Missile Crisis; to security measures at international airports; to advertising wars between major brands. This is a hopeful and practical book that highlights the value of game theory and provides a course correction for its integration into the real world.

Mathematician and popular science author Eugenia Cheng is on a mission to show you that mathematics can be flexible, creative, and visual. This joyful journey through the world of abstract mathematics into category theory will demystify mathematical thought processes and help you develop your own thinking, with no formal mathematical background needed. The book brings abstract mathematical ideas down to earth using examples of social justice, current events, and everyday life - from privilege to COVID-19 to driving routes. The journey begins with the ideas and workings of abstract mathematics, after which you will gently climb toward more technical material, learning everything needed to understand category theory, and then key concepts in category theory like natural transformations, duality, and even a glimpse of ongoing research in higher-dimensional category theory. For fans of How to Bake Pi, this will help you dig deeper into mathematical concepts and build your mathematical background.

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use--from our computers and cars, to home appliances. How did a system of mathematics established in the Victorian era become the basis for such incredible technological achievements a century later? In The Logician and the Engineer, Paul Nahin combines engaging problems and a colorful historical narrative to tell the remarkable story of how two men in different eras--mathematician and philosopher George Boole and electrical engineer and pioneering information theorist Claude Shannon--advanced Boolean logic and became founding fathers of the electronic communications age. Nahin takes readers from fundamental concepts to a deeper and more sophisticated understanding of modern digital machines, in order to explore computing and its possible limitations in the twenty-first century and beyond.

Explains how scientists who study complexity are convinced that certain constant processes are at work in all kinds of unrelated complex systems.

'Fascinating and immensely readable' Ian Stewart 'A charming tour through the realm of the very, very, very numerous, from the ancient world through to the distant future' Jordan Ellenberg, author of How Not to Be WrongWhat if, every time you wanted to write down 1,000,000, you had to draw a picture of a god? And what if that number were the biggest you had a symbol for? In ancient Egypt, those were the rules: anything bigger broke maths. Writing down some numbers is still beyond us today: try it with all the zeroes in a googolplex, or an outrageous alien number like FISH 7. Even harnessing every particle in the universe, you wouldn't come close. But that hasn't stopped us from hunting down these mind-bendingly big numbers and studying them.In Huge Numbers, mathematician and Numberphile presenter Richard Elwes shows how counting has shaped human thought. Whether recorded with notches carved on a tally stick, beads on an abacus, or electrical signals carrying binary code, it allows us to test the limits of mathematics over and over, breaking it down and putting it back together again.Come on a fascinating tour that spans continents and millennia, from the Mayan calendar to today's chatbots. You'll see that huge numbers are everywhere, expanding our horizons and powering our modern world.

This book stems from lectures on commutative algebra for 4th-year university students at two French universities (Paris and Rennes). At that level, students have already followed a basic course in linear algebra and are essentially fluent with the language of vector spaces over fields. The topics introduced include arithmetic of rings, modules, especially principal ideal rings and the classification of modules over such rings, Galois theory, as well as an introduction to more advanced topics such as homological algebra, tensor products, and algebraic concepts involved in algebraic geometry. More than 300 exercises will allow the reader to deepen his understanding of the subject. The book also includes 11 historical vignettes about mathematicians who contributed to commutative algebra.

Very Short Introductions: Brilliant, Sharp, Inspiring Kurt Gödel first published his celebrated theorem, showing that no axiomatization can determine the whole truth and nothing but the truth concerning arithmetic, nearly a century ago. The theorem challenged prevalent presuppositions about the nature of mathematics and was consequently of considerable mathematical interest, while also raising various deep philosophical questions. Gödel's Theorem has since established itself as a landmark intellectual achievement, having a profound impact on today's mathematical ideas. Gödel and his theorem have attracted something of a cult following, though his theorem is often misunderstood.This Very Short Introduction places the theorem in its intellectual and historical context, and explains the key concepts as well as common misunderstandings of what it actually states. A. W. Moore provides a clear statement of the theorem, presenting two proofs, each of which has something distinctive to teach about its content. Moore also discusses the most important philosophical implications of the theorem. In particular, Moore addresses the famous question of whether the theorem shows the human mind to have mathematical powers beyond those of any possible computerABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

This classic by one of the 20th century's most prominent mathematicians offers a concise introduction to set theory. Suitable for advanced undergraduates and graduate students in mathematics, it employs the language and notation of informal mathematics. Topics include the basic concepts of set theory, cardinal numbers, transfinite methods, and a good deal more in 25 brief chapters.

Test your powers of logic with 200 number puzzles from The TimesJust like a mathematical crossword, these puzzles are ideal for fans of Su Doku who relish grappling with figures. Contains four levels of difficulty, combining arithmetic with an intersecting layout: Mild, Medium, Tricky and Tough.Kakuro originated in the United States in the 1950s under the name of Cross Sums. A logic puzzle, the aim is to complete a grid using digits from 1 to 9, with the digits in each row/column adding up to the clue for that block. It’s similar to Su Doku in the sense that digits cannot be repeated in a row/column.Also known as: Croco Puzzle, Cross Sums, CrossSam, Kasan Kurosu, Kreuzsummenrätsel,Tashizan Cross, ZahlenschwedeAre you up to the challenge?

While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself.By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been contentto "assume" the real numbers. Its prerequisites are calculus and basic mathematics.Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets,  countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.

*A Financial Times and Waterstones Book of the Year 2025* Many artists are unaware of the mathematics that bubble beneath their craft, while some consciously use it for inspiration. Our instincts might tell us that these two subjects are incompatible forces with nothing in common, but what if we’re wrong? Marcus du Sautoy, acclaimed mathematician and Simonyi Professor for the Public Understanding of Science at the University of Oxford, looks to art, music, design and literature to uncover the key mathematical structures that underpin both human creativity and the natural world.Blueprints takes us from the earliest stone circles to the modernist architecture of Le Corbusier, from Bach’s circular compositions to Radiohead’s disruptive soundscapes, and from Shakespeare’s hidden numerical clues to the Dada artists who embraced randomness. Instead of polar opposites we find a complementary relationship that spans a vast historical and geographic landscape.Whether we are searching for meaning in an abstract painting or deciphering poetry, there are blueprints everywhere: prime numbers, symmetry, fractals and the weirder worlds of Hamiltonian cycles and hyperbolic geometry. Nature similarly exploits these structures to achieve the wonders of our universe.In this innovative and delightfully bold exploration of creativity, Marcus explains how we make art, why a creative mindset is vital for discovering new mathematics and how a fundamental connection to the natural world intrinsically links these two subjects.‘Blueprints is an extraordinary book which shows us how mathematics and art are connected through structures. Du Sautoy shows us how to bridge the divide of science and the humanities and proves that we can only face and solve the big challenges of the twenty-first century if we go beyond the fear of pooling knowledge’ Hans Ulrich Obrist, Artistic Director, Serpentine Galleries

Forget everything you've been taught about math. In Burn Math Class , Jason Wilkes takes the traditional approach to how we learn math,with its unwelcoming textbooks, unexplained rules, and authoritarian assertions,and sets it on fire.Focusing on how mathematics is created rather than on mathematical facts, Wilkes teaches the subject in a way that requires no memorization and no prior knowledge beyond addition and multiplication. From these simple foundations, Burn Math Class shows how mathematics can be (re)invented from scratch without preexisting textbooks and courses. We can discover math on our own through experimentation and failure, without appealing to any outside authority. When math is created free from arcane notations and pretentious jargon that hide the simplicity of mathematical concepts, it can be understood organically,and it becomes fun!Following this unconventional approach, Burn Math Class leads the reader from the basics of elementary arithmetic to various advanced" topics, such as time-dilation in special relativity, Taylor series, and calculus in infinite-dimensional spaces. Along the way, Wilkes argues that orthodox mathematics education has been teaching the subject backward: calculus belongs before many of its so-called prerequisites, and those prerequisites cannot be fully understood without calculus.Like the smartest, craziest teacher you've ever had, Wilkes guides you on an adventure in mathematical creation that will radically change the way you think about math. Revealing the beauty and simplicity of this timeless subject, Burn Math Class turns everything that seems difficult about mathematics upside down and sideways until you understand just how easy math can be.

Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of students of computer science. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and easy to understand. The uniform use of tableaux-based techniques facilitates learning advanced logical systems based on what the student has learned from elementary systems.The logical systems presented are: propositional logic, first-order logic, resolution and its application to logic programming, Hoare logic for the verification of sequential programs, and linear temporal logicfor the verification of concurrent programs.The third edition has been entirely rewritten and includes new chapters on central topics of modern computer science: SAT solvers and model checking.

This new, updated second edition of In All Likelihood explores the central role of likelihood in a wide spectrum of statistical problems, ranging from simple comparisons-such as evaluating accident rates between two groups-to sophisticated analyses involving generalized linear models and semiparametric methods. Rather than treating likelihood merely as a tool for point estimation, the book highlights its broader value as a foundational framework for constructing, understanding and computational implementation of statistical models. It emphasizes how likelihood perspectives inform model development, assessment, and inference in a cohesive and intuitive way.While grounded in essential mathematical theory, the book adopts an informal and accessible approach, using heuristic reasoning and illustrative, realistic examples to convey key ideas. It avoids overly contrived problems that yield to theoretically clean and closed-form solutions, instead embracing more realistic and complex real-world data analysis made tractable by modern computing resources. This perspective helps focus attention on the statistical reasoning behind model choice and interpretation.The text also integrates a wide range of modern topics that extend classical likelihood theory, including generalized and hierarchical generalized linear models, nonparametric smoothing techniques, robust methods, the EM algorithm, and empirical likelihood. Suitable for students, researchers, and practitioners, this book provides both foundational insights and contemporary perspectives on likelihood-based statistical modelling.

How the concept of proof has enabled the creation of mathematical knowledgeThe Story of Proof investigates the evolution of the concept of proof—one of the most significant and defining features of mathematical thought—through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge.Stillwell begins with Euclid and his influence on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as “infinitesimal algebra,” and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved.Shedding light on the workings of mathematics at its most fundamental levels, The Story of Proof offers a compelling new perspective on the field’s power and progress.

*A Financial Times and Waterstones Book of the Year 2025* Many artists are unaware of the mathematics that bubble beneath their craft, while some consciously use it for inspiration. Our instincts might tell us that these two subjects are incompatible forces with nothing in common, but what if we’re wrong? Marcus du Sautoy, acclaimed mathematician and Simonyi Professor for the Public Understanding of Science at the University of Oxford, looks to art, music, design and literature to uncover the key mathematical structures that underpin both human creativity and the natural world.Blueprints takes us from the earliest stone circles to the modernist architecture of Le Corbusier, from Bach’s circular compositions to Radiohead’s disruptive soundscapes, and from Shakespeare’s hidden numerical clues to the Dada artists who embraced randomness. Instead of polar opposites we find a complementary relationship that spans a vast historical and geographic landscape.Whether we are searching for meaning in an abstract painting or deciphering poetry, there are blueprints everywhere: prime numbers, symmetry, fractals and the weirder worlds of Hamiltonian cycles and hyperbolic geometry. Nature similarly exploits these structures to achieve the wonders of our universe.In this innovative and delightfully bold exploration of creativity, Marcus explains how we make art, why a creative mindset is vital for discovering new mathematics and how a fundamental connection to the natural world intrinsically links these two subjects.‘Blueprints is an extraordinary book which shows us how mathematics and art are connected through structures. Du Sautoy shows us how to bridge the divide of science and the humanities and proves that we can only face and solve the big challenges of the twenty-first century if we go beyond the fear of pooling knowledge’ Hans Ulrich Obrist, Artistic Director, Serpentine Galleries

A WATERSTONES BEST BOOK OF 2023A NEW SCIENTIST BEST BOOK OF 2023WINNER OF THE LA TIMES SCIENCE & TECHNOLOGY 2023 BOOK PRIZE'A generous tour of mathematics for anyone whose instincts tend less towards "Just tell me the answer" and more towards "Wait, but why?"' JORDAN ELLENBERGTo many, maths feels like an unmapped wilderness. Between abstract concepts like imaginary numbers and infinity, it can sometimes feel like a lot of maths is just made up. Why, for example, is 1 not a prime? Why do two negatives cancel each other out? Where does trigonometry come from? Is maths even real? Abstract mathematician Eugenia Cheng shows that curiosity is the best teacher. Is Maths Real? takes us on a scintillating tour of the simple questions that provoke mathematics' deepest insights. 'Intriguing...celebrates the dizziness and disorientation engendered by childlike questions that hint at the deep mysteries beneath'NEW SCIENTIST'Masterfully uncovers what's simply profound in the profoundly simple'FRANCIS SU'Discover what it feels like to be a real mathematician'DAILY TELEGRAPH

This book examines the philosophical conception of abductive reasoning as developed by Charles S. Peirce, the founder of American pragmatism. It explores the historical and systematic connections of Peirce's original ideas and debates about their interpretations. Abduction is understood in a broad sense which covers the discovery and pursuit of hypotheses and inference to the best explanation. The analysis presents fresh insights into this notion of reasoning, which derives from effects to causes or from surprising observations to explanatory theories.The author outlines some logical and AI approaches to abduction as well as studies various kinds of inverse problems in astronomy, physics, medicine, biology, and human sciences to provide examples of retroductions and abductions. The discussion covers also everyday examples with the implication of this notion in detective stories, one of Peirce’s own favorite themes.The author uses Bayesian probabilities to argue that explanatory abduction is a method of confirmation. He uses his own account of truth approximation to reformulate abduction as inference which leads to the truthlikeness of its conclusion. This allows a powerful abductive defense of scientific realism. This up-to-date survey and defense of the Peircean view of abduction may very well help researchers, students, and philosophers better understand the logic of truth-seeking.

When we learn, we change what we believe and how we interact with the world. This changes who we are as people and what we can achieve.Many people grow up being told they are ‘not a maths person’ or perhaps ‘not smart’. They come to believe their potential is limited.Now, however, the latest science has revealed that our identities are constantly in flux; when we learn new things, we can change our identities, increase our potential and broaden our capacity to receive new information.Drawing from the latest research, Professor Boaler followed thousands of school students, studied their learning practices and examined the most effective ways to transform pupils from low to high achievers. Throughout her study, Boaler has collaborated with Stanford University neuroscience experts, harnessing their expertise to reinforce her advanced understanding of learning and educational development.In Limitless Mind, Boaler presents original groundbreaking research that proves that limiting beliefs really do hold us back from fulfilling our potential and that with a few careful life hacks we can transform our potential for good.