Are Numbers Real?
The Uncanny Relationships Between Maths and the Physical World
Brian Clegg explores a question fundamental to science: would numbers still exist without people to think about them, or is mathematics just a tool to help us understand the universe? Beginning with the devising of a new system to count goats, he traces the history of numbers, explaining their application to our everyday lives and asking whether the direction of contemporary physics has become too influenced by mathematics.
A Curious History
Euclid, Fibonacci, Fermat and Gauss are some of the distinguished mathematicians featured in this illustrated introduction to the history of mathematics, which ranges from prehistoric arithmetic through Renaissance accountancy to modern-day chaos theory. Key concepts, including geometry, algebra, trigonometry and calculus are discussed in non-technical, accessible language, with minimal use of symbols, jargon or complex techniques.
2,600 Years of Discovery: from Thales to Higgs
While the language of mathematics can describe physical reality in complex detail, the art of drawing can delineate with simple clarity. Aimed at the less mathematically inclined, this history of physics uses 51 seminal illustrations from 26 centuries of physics to tell, in chronological order, the stories of great scientific discoveries, from the phases of the moon and size of the Earth to the discovery of the neutron and the Higgs Boson particle.
How it Shaped Our World
In this companion guide to the Science Museum’s Winton Gallery, curator David Rooney considers the everyday practical applications of mathematics, both past and present, including mathematics in design, economics, geography, medicine, travel and war. This generously illustrated volume features many of the objects and diagrams from the gallery’s collection, among them Charles Babbage’s Difference Engine and Le Corbusier’s Le Modulor infographic, while four essays by prominent academics include two on women’s place in the history of mathematics.
Swinging and Twisting
A geometric dissection is a cutting of a geometric figure into pieces that can be arranged to form another figure. They are employed in visual demonstrations of relationships such as Pythagoras’ theorem, and as mathematical puzzles such as Loyd and Dudeney’s hinged dissection of a quadrilateral triangle to a square. For those fascinated by beautiful geometric objects, Frederickson presents his second collection of dissections, hinged rather than simply cut, and including swings and twists for 3D puzzles. Off-mint with a felt-tip mark on lower trimmed edge.
How the World Became Obsessed with Time
‘Technology is making everything faster, and because we know that things will become faster in the future, it follows that nothing is fast enough now.’ Surveying how, over the last 250 years, time has come to dominate our lives, Simon Garfield considers its practical applications rather than theoretical physics: the subjects of his ‘illuminating stories’ include – definitely not in chronological order – football, Beethoven’s Ninth, railway timetables, Roger Bannister, Swiss watchmakers, The Clock (Christian Marclay’s film) and the British Museum.
It All Adds Up
The Story of People and Mathematics
Just as non-musicians can love music, believes Launay, anyone can understand and marvel at the numbers and geometry that surround us every day. In this book he guides the reader on a journey through the history of mathematics, revealing how curiosity and serendipity have led to new discoveries, from ancient Mesopotamian frieze designs and the earliest written number symbols to the Mandelbrot set, which can be drawn only with the aid of computers.
An Expedition to the Outer Limits of Mathematics
Beginning by attempting to explain what infinity is – and why it is ‘easy to think about but hard to pin down’ – this approachable guide uses carefully chosen analogies and classic thought experiments such as Hilbert's Hotel to help illuminate complex ideas. Eugenia Cheng presents mathematics as an exciting journey of discovery, and uses practical examples to help us understand the abstract concept of infinity in the context of our daily lives.
The Humongous Book of Geometry Problems
The best way to learn about geometry is to work through lots of problems and proofs – but it can be frustrating when a textbook just gives you the answer without explaining clearly how to reach it. This collection of 1,000 problems is fully annotated with tips and step-by-step solutions to guide you through basic rules and concepts, from parallel and intersecting lines to vectors, transformations and truth tables, by way of the key theorems for circles and triangles.
At the Edge of Infinity and Beyond
Aleph-null is the cardinality, or size, of the set of natural numbers, and is a ‘countably infinite cardinal’. Remarkably, whereas 1 + 1 = 2, 1 + aleph-null = aleph-null. The authors of this advanced maths explainer utilize plain English in an attempt to understand difficult mathematical concepts, including large numbers, higher dimensions, computation and primes, fusing historical, philosophical and anecdotal aspects of each concept with the decidedly technical. Slightly off-mint.
Maths in Bite-sized Chunks
Chris Waring’s accessible guide is designed for anyone who is keen to overcome a fear of mathematics. Employing numerous examples, common-sense explanations, fascinating asides and clear diagrams, this volume breaks down seemingly inscrutable mathematical concepts into easy-to-follow steps, explaining simple arithmetic and number, ratio and proportion, algebra, geometry, statistics and probability. Reassuringly, Waring emphasises real-world applications of mathematical principles, championing the great mathematicians of history in the process.
Entropy of Hidden Markov Processes and Connections to Dynamical Systems
Papers from the Banff International Research Station Workshop
The mathematics of hidden Markov processes (HMPs) can be applied to many kinds of noise-related technologies, from speech and optical character recognition to biomolecular sequence analysis. This collection of nine papers from a 2007 workshop at the Banff International Research Station covers the entropy rate problem, or measure of randomness, of HMPs, with reference to informational theory, dynamical systems, statistical mechanics and probability theory.
The Quality of Numbers One to Thirty-one
In these essays – one for each day of the month – Held demonstrates the fascinating qualities and associations, both cultural and scientific, of the first 31 integers. His ‘excursions into the realm of number’ visit such varied calling-points as the eleven-year sunspot cycle, humans’ 23 pairs of chromosomes, Snow White’s seven dwarves and Judas’ 30 pieces of silver.
Number Treasury 3
Investigations, Facts and Conjectures About More than 100 Number Families
Written as a resource for both teachers and students, this enlarged third edition of Number Treasury is designed to guide readers through the steps that will help them to think critically, to provide explanations and to formulate conjectures about different families of positive integers. Its 137 exercises and 28 'investigations', at three levels of difficulty, cover such intriguing topics as magic squares, palindromic numbers and twin primes. Detailed solutions are provided at the back of the book.
How Smart Are You?
Test Your Math IQ
How to improve your number skills: these 50 ten-question quizzes have an IQ-style scoring system that enables you to compare your performance with the average mark. The tests cover decimals and fractions, interest and percentages, means and medians and pose a range of algebraic word problems, interspersed with brief biographies of great mathematicians from Pythagoras to Andrew Wiles, who solved Fermat’s Last Theorem in 1994. American spelling and elastic closure.
Suitable both for students beginning their study of algebra and for those who want to recollect what they once knew, these nine chapters progress from basic principles of addition and subtraction to the solution of quadratic equations. Everything is presented as painlessly as possible, with step-by-step guides to solving each kind of problem, advice on common mistakes to avoid and illustrative drawings and diagrams.
Abbo of Fleury and Ramsey
Commentary on the Calculus of Victorius of Aquitaine
This didactic work by Abbo of Fleury (c.945–1004) is a philosophical Commentary on the mathematical tables produced by Victorius of Aquitaine (fl.457) to facilitate calculations using Roman numerals and fractions. Latin texts of both Victorius and Abbo. No jacket.