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Their mission: to unlock the deep mysteries of Time and Space Discover why you can't break the ultimate speed barrier, how to become older than your mother, how to put on weight without getting fat, and how to live forever without even knowing it. A selection of mathematical puzzles, stories, tricks and short articles - great to read all in one go, or to dip into. The content varies between simple logic puzzles to introductions to more advanced topics such as the Four Colour Theorem, which tells us that we can colour in any map using only four colours, so that no bordering countries have the same colour.

A collection of strange mathematical facts and stories. This anthology covers a whole range of ages, maths and mathematicians, and includes probability paradoxes, jumbled Shakespearean sonnets, record-breaking monkeys and typewriters, and theories of big game hunting.

Also featured are stories of people who looked for logical loopholes in the American Constitution or calmed their nerves with algebra. This collection by best-selling author David Wells, a Cambridge math scholar and teacher, includes more than puzzles, from the "mind sharpeners" of a medieval monk to the eitheenth-century Ladies' Diary, the Hindu Bhakshali manuscript, and riddles and popular rhymes.

None require any mathematics beyond the most elementary algebra and geometry - and few require even that. Complete answers appear at the end. Famed puzzle expert Martin Gardner explains the mathematics behind a multitude of mystifying tricks: card tricks, stage "mind reading," coin and match tricks, counting out games, geometric dissections, etc. Each of these are actually demonstrations of probability, sets, number theory, topology and other braches of mathematics. No skill at sleight of hand is needed to perform the more than tricks described in this book because mathematics guarantees their success.

Can maths be creative? This book sets out to prove that it can, through a selection of short articles on surprising maths in everyday life. Through lots of intriguing problems, involving card tricks, polar bears and, of course, socks, Rob Eastaway shows shows how maths can demonstrate its secret beauties in even the most mundane of everyday objects.

With a foreword by Tim Rice, this book will change the way you see the world. Why is it better to buy a lottery ticket on a Friday? Why are showers always too hot or too cold? And what's the connection between a rugby player taking a conversion and a tourist trying to get the best photograph of Nelson's Column?

These and many other fascinating questions are answered in this entertaining and highly informative book, which is ideal for anyone wanting to remind themselves - or discover for the first time - that maths is relevant to almost everything we do. Dating, cooking, travelling by car, gambling and even life-saving techniques have links with intriguing mathematical problems, as you will find explained here. Whether you have a PhD in astrophysics or haven't touched a maths problem since your school days, this book will give you a fresh understanding of the world around you.

In , Edwin A. Now, Ian Stewart has written a fascinating, modern sequel to Abbott's book. Through larger-than-life characters and an inspired story line, "Flatterland" explores our present understanding of the shape and origins of the universe, the nature of space, time, and matter, as well as modern geometries and their applications. Ever since the Sphinx asked his legendary riddle of Oedipus, riddles, conundrums, and puzzles of all sizes have kept humankind perplexed and amused.

Each chapter introduces the basic puzzle, discusses the mathematics behind it, and includes exercises and answers plus additional puzzles similar to the one under discussion. Here is a veritable kaleidoscope of puzzling labyrinths, maps, bridges, and optical illusions that will keep aficionados entertained for hours.

An exploration of surprising ways maths occurs in our everyday lives, centred around five famous unsolved problems in mathematics. Topics include how to detect an art forgery, winning strategies in Monopoly, and how to crack a code. Sprinkled with games and links to interactive online content so you can try out some of the ideas for yourself! This is the complete guide to exploring the fascinating world of maths you were never told about at school.

See a Problem?

Stand-up comedian and mathematician Matt Parker uses bizarre Klein Bottles, unimaginably small pizza slices, knots no one can untie and computers built from dominoes to reveal some of the most exotic and fascinating ideas in mathematics. Starting with simple numbers and algebra, this book goes on to deal with inconceivably big numbers in more dimensions than you ever knew existed.

And always with something for you to make or do along the way. In this book are twenty more curious puzzles and fantastical mathematical stories from one of the world's most popular and accessible writers on mathematics. This is a strange world of never-ending chess games, empires on the moon, furious fireflies, and, of course, disputes over how best to cut a cake.

Each chapter - with titles such as, "How to Play Poker By Post" and "Repealing the Law of Averages" - presents a fascinating mathematical puzzle that is challenging, fun, and introduces the reader to a significant mathematical problem in an engaging and witty way.

Illustrated with clever and quirky cartoons, each tale will delight those who love puzzles and mathematical conundrums. The appeal of games and puzzles is timeless and universal. In this book, David Wells explores the fascinating connections between games and mathematics, proving that mathematics is not just about tedious calculation but imagination, insight and intuition.

Ramanujan and me

The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. This thought-provoking book is perfect for anyone with a thirst for mathematics and its hidden beauty; a good high school grounding in mathematics is all the background that is required, and the puzzles and games will suit pupils from 14 years.

Collected over several years by Peter Winkler, dozens of elegant, intriguing challenges are presented in this book. The answers are easy to explain, but without this book, devilishly hard to find. Creative reasoning is the key to these puzzles. No involved computation or higher mathematics is necessary, but your ability to construct a mathematical proof will be severly tested - even if you are a professional mathematician. For the truly adventurous, there is even a chapter on unsolved puzzles. Beautifully crafted and immensely enjoyable, the problems in this book require minimal technical knowledge, being accessible to young secondary school pupils.

However, there is an astonishing range in difficulty; while some of the problems are fairly straightforward, others are significantly tougher, with a great deal of ingenuity and clarity of thought needed to make progress. Whether you are a student preparing for a maths competition, an educational establishment seeking to supplement your problem solving resources, or an individual looking for a different sort of challenge, Elastic Numbers is a unique collection, and will push you to the very edge of your abilities.

Thinking Mathematically is perfect for anyone who wants to develop their powers to think mathematically, whether at school, at university or just out of interest. This book is invaluable for anyone who wishes to promote mathematical thinking in others or for anyone who has always wondered what lies at the core of mathematics. Thinking Mathematically reveals the processes at the heart of mathematics and demonstrates how to encourage and develop them.

Extremely practical, it involves the reader in questions so that subsequent discussions speak to immediate experience. This book tells the story of one of the biggest adventures in mathematics: the search for symmetry. This is the story of how humankind has come to its understanding of the bizarre world of symmetry - a subject of fundamental significance to the way we interpret the world around us. Our eyes and minds are drawn to symmetrical objects, from the sphere to the swastika, from the pyramid to the pentagon. When do the hands of a clock coincide?

How likely is it that two children in the same class will share a birthday? How do we calculate the volume of a doughnut? Mathematics for the Curious provides anyone interested in mathematics with a simple and entertaining account of what it can do. Author Peter Higgins gives clear explanations of the more mysterious features of childhood mathematics as well as novelties and connections that prove that mathematics can be enjoyable and full of surprises.

Topics include: the truth about fractions, ten questions and their answers, and the golden ratio. Higgins poses entertaining puzzles and questions tempting the reader to ponder math problems with imagination instead of dread. Mathematics for the Curious is an accessible introduction to basic mathematics for beginning students and a lively refresher for adults. Mathematics for the Imagination provides an accessible and entertaining investigation into mathematical problems in the world around us.

The 10 best mathematicians

From world navigation, family trees, and calendars to patterns, tessellations, and number tricks, this informative and fun book helps you to understand the maths behind real-life questions and rediscover your arithmetical mind. This is a highly involving book which encourages the reader to enter into the spirit of mathematical exploration. A stimulating account of development of basic mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations and non-Euclidean geometries.

Also describes how maths is used in optics, astronomy, motion under the law of gravitation, acoustics, electromagnetism, and other aspects of physics. In this book, Professor Ogilvy demonstrates the mathematical challenege and satisfaction to be had from geometry, the only requirement being two simple implements straight-edge and compass and a little thought. Topics including harmonic division and Apollonian circles, inversive geometry, the hexlet, conic sections, projective geometry, the Golden Section and angle trisection are addressed in a way that brings out the true intellectual excitement inherent in each.

Also included are some unsolved problems of modern geometry. This book offers a fascinating glimpse into the world of mathematics and mathematicians. It is designed for the reader who has no advanced mathematical background of special aptitude, but who wants to acquaint him or herself with the intellectually stimulating and aesthetically satisfying aspects of the subject. After illuminating the role of the mathematician and dispelling several popular misconceptions about the nature of mathematics, Professor Ogilvy takes you on a lively tour of the four basic branches of the subject: number theory, algebra, geometry and analysis.

Focusing on the interesting, and even amusing, aspects of mathematics, he points out the interconnections between the branches and presents mathematics as a vital subject whose frontiers are continually expanding. Many illustrations and examples illuminate classic aspects of the subject as well as recent advances.

This delightful volume, by two well-known mathematicians, invites readers to join a challenging expedition into the mystery and magic of number theory. No special training is needed - just high school mathematics, a fondness for figures and an inquisitive mind. Beginning with familiar notions, the authors skillfully transport the reader to higher realms of mathematics, developing the necessary concepts along the way. Included are thorough discussions of prime numbers, number patterns, irrationals and iterations and calculating prodigies, among other topics.

Which famous proof did Archimedes inscribe on his tombstone? How and why do knots make perfect pentagons? Have you ever seen a proof so completely that it is just obvious? In this delicious little book, top down-under mathemagician Dr. Polster presents many of the most visually intuitive and exciting proofs from the dusty annuals of mathematical history. You can test your ability to follow the logic, leap into mathemagnosis and experience eureka-moment after eureka-moment. A perennial bestseller by eminent mathematician G.

The Mathematician as a Type

Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out - from building a bridge to winning a game of anagrams.

Aryabhatta - The Genius Indian Mathematician - The OpenBook

Generations of readers have relished Polya's deft - indeed, brilliant - instructions on stripping away irrelevancies and going straight to the heart of the problem. Maths is everywhere, often where we don't even realise. Award-winning professor Steven Strogatz acts as our guide as he takes us on a tour of numbers that - unbeknownst to the unitiated - connect pop culture, literature, art, philosophy, current affairs, business and even every day life. In The Joy of X, Strogatz explains the great ideas of maths - from negative numbers to calculus, fat tails to infinity - with clarity, wit and insight.

The Man Who Knew Infinity: a mathematician's life comes to the movies

He is the maths teacher you never had and this book is perfect for the smart and curious, the expert and the beginner. In so doing, the common less efficient approach is first mentioned and then the effective strategy is shown.


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Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics. David Acheson's extraordinary little book makes mathematics accessible to everyone. From very simple beginnings he takes us on a thrilling journey to some deep mathematical ideas. On the way, via Kepler and Newton, he explains what calculus really means, gives a brief history of pi, and even takes us to chaos theory and imaginary numbers.

Every short chapter is carefully crafted to ensure that no one will get lost on the journey. Packed with puzzles and illustrated by world famous cartoonists, this is one of the most readable and imaginative books on mathematics ever written. The purpose of this book is to introduce the basic ideas of mathematical proof to students.

The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the classic proofs.

Written for beginners and scholars, for students and teachers, for philosophers and engineers, this book is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving.

With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Containing a large and varied set of problems, this rich resource will allow students to stretch their mathematical abilities beyond the school syllabus, and bridge the gap to university-level mathematics.

Many proofs are provided to better equip students for the transition to university. The author covers substantial extension material using the language of sixth-form mathematics, thus enabling students to understand the more complex material. There are over carefully graded exercises, with hints included in the text, and solutions available online. Historical and contextual asides highlight each area of mathematics and show how it has developed over time. This book unlocks the secrets of maths - revealing it to be our lost, native language, as much a part of us as the words we use every day.

The Man Who Invented Pi

Number and form are the essence of our world: from the patterns of the stars to the pulses of the market, from the beats of our hearts to catching a ball or tying our shoelaces. Drawing on science, literature, history and philosophy, this book makes the rich patterns of maths brilliantly clear. In this book, Anany and Maria Levitin use many classic brainteasers as well as newer examples from job interviews with major corporations to show readers how to apply analytical thinking to solve puzzles requiring well-defined procedures. The book's unique collection of puzzles is supplemented with carefully developed tutorials on algorithm design strategies and analysis techniques intended to walk the reader step-by-step through the various approaches to algorithmic problem solving.

Mastery of these strategies - exhaustive search, backtracking, and divide-and-conquer, among others - will aid the reader in solving not only the puzzles contained in this book, but also others encountered in interviews, puzzle collections, and throughout everyday life. Each of the puzzles contains hints and solutions, along with commentary on the puzzle's origins and solution methods. Readers with only middle school mathematics will develop their algorithmic problem-solving skills through puzzles at the elementary level, while seasoned puzzle solvers will enjoy the challenge of thinking through more difficult puzzles.

This book introduces and develops some of the important and beautiful elementary mathematics needed for rational analysis of various gambling and game activities. Most of the standard casino games roulette, craps, blackjack, keno , some social games backgammon, poker, bridge and various other activities state lotteries, horse racing are treated in ways that bring out their mathematical aspects. The mathematics developed ranges from the predictable concepts of probability, expectation, and binomial coefficients to some less well-known ideas of elementary game theory.

Game-related exercises are included and solutions to some appear at the end of the book. Every year, thousands of students go to university to study mathematics. Many of these students are extremely intelligent and hardworking, but even the best will, at some point, struggle with the demands of making the transition to advanced mathematics. The mathematics shifts in focus from calculation to proof, so students are expected to interact with it in different ways.

These changes need not be mysterious - mathematics education research has revealed many insights into the adjustments that are necessary - but they are not obvious and they do need explaining. This book translates these research-based insights into practical advice for a student audience. It covers every aspect of studying for a mathematics degree, from the most abstract intellectual challenges to the everyday business of interacting with lecturers and making good use of study time.

Looking for a head start in your undergraduate degree in mathematics? This friendly companion will ease your transition to real mathematical thinking. First use of proof by mathematical induction, including to prove the binomial theorem. Ibn al-Haytham Alhazen. Omar Khayyam. Generalized Indian methods for extracting square and cube roots to include fourth, fifth and higher roots, noted existence of different sorts of cubic equations.

Bhaskara II. Established that dividing by zero yields infinity, found solutions to quadratic, cubic and quartic equations including negative and irrational solutions and to second order Diophantine equations, introduced some preliminary concepts of calculus. Leonardo of Pisa Fibonacci. Fibonacci Sequence of numbers, advocacy of the use of the Hindu-Arabic numeral system in Europe, Fibonacci's identity product of two sums of two squares is itself a sum of two squares.

Nasir al-Din al-Tusi. Developed field of spherical trigonometry, formulated law of sines for plane triangles. Qin Jiushao. Solutions to quadratic, cubic and higher power equations using a method of repeated approximations. Yang Hui. Kamal al-Din al-Farisi. Applied theory of conic sections to solve optical problems, explored amicable numbers, factorization and combinatorial methods. Nicole Oresme. System of rectangular coordinates, such as for a time-speed-distance graph, first to use fractional exponents, also worked on infinite series.

Luca Pacioli. Influential book on arithmetic, geometry and book-keeping, also introduced standard symbols for plus and minus. Gerolamo Cardano. Lodovico Ferrari. Devised formula for solution of quartic equations. John Napier. Marin Mersenne. Clearing house for mathematical thought during 17th Century, Mersenne primes prime numbers that are one less than a power of 2. Girard Desargues. Development of Cartesian coordinates and analytic geometry synthesis of geometry and algebra , also credited with the first use of superscripts for powers or exponents.

Bonaventura Cavalieri. Pierre de Fermat. Discovered many new numbers patterns and theorems including Little Theorem, Two-Square Thereom and Last Theorem , greatly extending knowlege of number theory, also contributed to probability theory. John Wallis. Blaise Pascal. Isaac Newton. Development of infinitesimal calculus differentiation and integration , laid ground work for almost all of classical mechanics, generalized binomial theorem, infinite power series.


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Gottfried Leibniz. Independently developed infinitesimal calculus his calculus notation is still used , also practical calculating machine using binary system forerunner of the computer , solved linear equations using a matrix. Jacob Bernoulli. Helped to consolidate infinitesimal calculus, developed a technique for solving separable differential equations, added a theory of permutations and combinations to probability theory, Bernoulli Numbers sequence, transcendental curves. Johann Bernoulli. Abraham de Moivre.

De Moivre's formula, development of analytic geometry, first statement of the formula for the normal distribution curve, probability theory. Christian Goldbach. Goldbach Conjecture, Goldbach-Euler Theorem on perfect powers. Leonhard Euler. Made important contributions in almost all fields and found unexpected links between different fields, proved numerous theorems, pioneered new methods, standardized mathematical notation and wrote many influential textbooks. Johann Lambert. Joseph Louis Lagrange. Gaspard Monge. Inventor of descriptive geometry, orthographic projection.

Pierre-Simon Laplace. Celestial mechanics translated geometric study of classical mechanics to one based on calculus, Bayesian interpretation of probability, belief in scientific determinism. Adrien-Marie Legendre. Abstract algebra, mathematical analysis, least squares method for curve-fitting and linear regression, quadratic reciprocity law, prime number theorem, elliptic functions. Joseph Fourier. Studied periodic functions and infinite sums in which the terms are trigonometric functions Fourier series. Carl Friedrich Gauss.

Pattern in occurrence of prime numbers, construction of heptadecagon, Fundamental Theorem of Algebra, exposition of complex numbers, least squares approximation method, Gaussian distribution, Gaussian function, Gaussian error curve, non-Euclidean geometry, Gaussian curvature. Augustin-Louis Cauchy. Early pioneer of mathematical analysis, reformulated and proved theorems of calculus in a rigorous manner, Cauchy's theorem a fundamental theorem of group theory.

George Peacock. Inventor of symbolic algebra early attempt to place algebra on a strictly logical basis. Charles Babbage. Designed a "difference engine" that could automatically perform computations based on instructions stored on cards or tape, forerunner of programmable computer. Nikolai Lobachevsky.

Developed theory of hyperbolic geometry and curved spaces independendly of Bolyai. Niels Henrik Abel. Proved impossibility of solving quintic equations, group theory, abelian groups, abelian categories, abelian variety.

Explored hyperbolic geometry and curved spaces independently of Lobachevsky. Carl Jacobi. Important contributions to analysis, theory of periodic and elliptic functions, determinants and matrices. William Hamilton. Theory of quaternions first example of a non-commutative algebra. Proved that there is no general algebraic method for solving polynomial equations of degree greater than four, laid groundwork for abstract algebra, Galois theory, group theory, ring theory, etc. George Boole.

Karl Weierstrass. Discovered a continuous function with no derivative, advancements in calculus of variations, reformulated calculus in a more rigorous fashion, pioneer in development of mathematical analysis. Arthur Cayley. Pioneer of modern group theory, matrix algebra, theory of higher singularities, theory of invariants, higher dimensional geometry, extended Hamilton's quaternions to create octonions. Bernhard Riemann. Non-Euclidean elliptic geometry, Riemann surfaces, Riemannian geometry differential geometry in multiple dimensions , complex manifold theory, zeta function, Riemann Hypothesis.

Richard Dedekind. Defined some important concepts of set theory such as similar sets and infinite sets, proposed Dedekind cut now a standard definition of the real numbers. John Venn.