An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

‘Another terrific book by Rob Eastaway’ SIMON SINGH ‘A delightfully accessible guide to how to play with numbers’ HANNAH FRY

How many licks to the center of a Tootsie Pop? How many people are having sex at this moment? How long would it take a monkey on a typewriter to produce the plays of Shakespeare? For all those questions that keep you up at night, here's the way to answer them. And the beauty of it is that it's all approximate! Using Enrico Fermi's theory of approximation, Santos brings the world of numbers into perspective. For puzzle junkies and trivia fanatics, these 70 word puzzles will show the reader how to take a bit of information, add what they already know, and extrapolate an answer. Santos has done the impossible: make math and the multiple possibilities of numbers fun and informative. Can you really cry a river? Is it possible to dig your way out of jail with just a teaspoon and before your life sentence is up? Taking an academic subject and using it as the prism to view everyday off-the-wall questions as math problems to be solved is a natural step for the lovers of sudoku, cryptograms, word puzzles, and other thought-provoking games.

Simple and effective techniques for quickly estimating virtually anything Guesstimation 2.0 reveals the simple and effective techniques needed to estimate virtually anything—quickly—and illustrates them using an eclectic array of problems. A stimulating follow-up to Guesstimation, this is the must-have book for anyone preparing for a job interview in technology or finance, where more and more leading businesses test applicants using estimation questions just like these. The ability to guesstimate on your feet is an essential skill to have in today's world, whether you're trying to distinguish between a billion-dollar subsidy and a trillion-dollar stimulus, a megawatt wind turbine and a gigawatt nuclear plant, or parts-per-million and parts-per-billion contaminants. Lawrence Weinstein begins with a concise tutorial on how to solve these kinds of order of magnitude problems, and then invites readers to have a go themselves. The book features dozens of problems along with helpful hints and easy-to-understand solutions. It also includes appendixes containing useful formulas and more. Guesstimation 2.0 shows how to estimate everything from how closely you can orbit a neutron star without being pulled apart by gravity, to the fuel used to transport your food from the farm to the store, to the total length of all toilet paper used in the United States. It also enables readers to answer, once and for all, the most asked environmental question of our day: paper or plastic?

How many socks make a pair? The answer is not always two. And behind this question lies a world of maths that can be surprising, amusing and even beautiful. Using playing cards, a newspaper, the back of an envelope, a Sudoku, some pennies and of course a pair of socks, Rob Eastaway shows how maths can demonstrate its secret beauties in even the most mundane of everyday objects. If you already like maths you’ll discover plenty of new surprises. And if you’ve never picked up a maths book in your life, this one will change your view of the subject forever.

From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

If you're a little worried about what the future holds, you might be stock-piling cans of beans or building an underground bunker. But the real key to surviving in an unpredictable world is understanding the natural forces and relationships that rule everything we do. An Equation for Every Occasiontackles some frankly ridiculous scenarios with essential bullet-proof equations that you'll probably never be able to apply in real life. Whether you paid much attention to the mathematics you were taught at school or not, the inescapable truth is that real life is full of equations and a lot of our everyday decisions are calculated - we just don't always realise it. And that's ok - you absentmindedly use differentiation when you're driving your car and it gets you from A to B. You unthinkingly apply basic geometry when you're crossing the road between traffic and you will pretty much always make it to the other side safely. But what if you were plummeting to your death in a plane with no engine and you needed to know what size parachute to make from your cabinmate's sari in order to jump and survive? These entirely plausible real-life situations clearly require a little more thought. From how to work out the best guard configuration to protect a world-famous painting in the Louvre from being stolen to successfully piloting a space shuttle back to earth from the ISS to saving the planet from total blackout during an energy crisis, Chris Waring demonstrates the mind-bending and humanity-saving beauty of equations.

This book will help those wishing to teach a course in technical writing, or who wish to write themselves.

Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.

This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.