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We are what we eat, as the saying goes, but we are also how we eat, and when, and where. Our eating habits reveal as much about our society as the food on our plates, and our national identity is written in the eating schedules we follow and the customs we observe at the table and on the go. In Three Squares, food historian Abigail Carroll upends the popular understanding of our most cherished mealtime traditions, revealing that our eating habits have never been stable—far from it, in fact. The eating patterns and ideals we’ve inherited are relatively recent inventions, the products of complex social and economic forces, as well as the efforts of ambitious inventors, scientists and health gurus. Whether we’re pouring ourselves a bowl of cereal, grabbing a quick sandwich, or congregating for a family dinner, our mealtime habits are living artifacts of our collective history—and represent only the latest stage in the evolution of the American meal. Our early meals, Carroll explains, were rustic affairs, often eaten hastily, without utensils, and standing up. Only in the nineteenth century, when the Industrial Revolution upset work schedules and drastically reduced the amount of time Americans could spend on the midday meal, did the shape of our modern “three squares” emerge: quick, simple, and cold breakfasts and lunches and larger, sit-down dinners. Since evening was the only part of the day when families could come together, dinner became a ritual—as American as apple pie. But with the rise of processed foods, snacking has become faster, cheaper, and easier than ever, and many fear for the fate of the cherished family meal as a result. The story of how the simple gruel of our forefathers gave way to snack fixes and fast food, Three Squares also explains how Americans’ eating habits may change in the years to come. Only by understanding the history of the American meal can we can help determine its future.
Number theory is one of the oldest branches of mathematics that is primarily concerned with positive integers. While it has long been studied for its beauty and elegance as a branch of pure mathematics, it has seen a resurgence in recent years with the advent of the digital world for its modern applications in both computer science and cryptography. Number Theory: Step by Step is an undergraduate-level introduction to number theory that assumes no prior knowledge, but works to gradually increase the reader's confidence and ability to tackle more difficult material. The strength of the text is in its large number of examples and the step-by-step explanation of each topic as it is introduced to help aid understanding the abstract mathematics of number theory. It is compiled in such a way that allows self-study, with explicit solutions to all the set of problems freely available online via the companion website. Punctuating the text are short and engaging historical profiles that add context for the topics covered and provide a dynamic background for the subject matter.
In recent decades it has become obvious that mathematics has always been a worldwide activity. But this is the first book to provide a substantial collection of English translations of key mathematical texts from the five most important ancient and medieval non-Western mathematical cultures, and to put them into full historical and mathematical context. The Mathematics of Egypt, Mesopotamia, China, India, and Islam gives English readers a firsthand understanding and appreciation of these cultures' important contributions to world mathematics. The five section authors--Annette Imhausen (Egypt), Eleanor Robson (Mesopotamia), Joseph Dauben (China), Kim Plofker (India), and J. Lennart Berggren (Islam)--are experts in their fields. Each author has selected key texts and in many cases provided new translations. The authors have also written substantial section introductions that give an overview of each mathematical culture and explanatory notes that put each selection into context. This authoritative commentary allows readers to understand the sometimes unfamiliar mathematics of these civilizations and the purpose and significance of each text. Addressing a critical gap in the mathematics literature in English, this book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom.
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
An introductory textbook with a unique historical approach to teaching number theory The natural numbers have been studied for thousands of years, yet most undergraduate textbooks present number theory as a long list of theorems with little mention of how these results were discovered or why they are important. This book emphasizes 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 most fascinating subjects in mathematics. Written in an informal style by an award-winning teacher, Number Theory covers prime numbers, Fibonacci numbers, and a host of other essential topics in number theory, while also telling the stories of the great mathematicians behind these developments, including Euclid, Carl Friedrich Gauss, and Sophie Germain. This one-of-a-kind introductory textbook features an extensive set of problems that enable students to actively reinforce and extend their understanding of the material, as well as fully worked solutions for many of these problems. It also includes helpful hints for when students are unsure of how to get started on a given problem. Uses a unique historical approach to teaching number theory Features numerous problems, helpful hints, and fully worked solutions Discusses fun topics like Pythagorean tuning in music, Sudoku puzzles, and arithmetic progressions of primes Includes an introduction to Sage, an easy-to-learn yet powerful open-source mathematics software package Ideal for undergraduate mathematics majors as well as non-math majors Digital solutions manual (available only to professors)
Since the publication of the first edition of this work, considerable progress has been made in many of the questions examined. This edition has been updated and enlarged, and the bibliography has been revised.The variety of topics covered here includes divisibility, diophantine equations, prime numbers (especially Mersenne and Fermat primes), the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, decomposition of integers into sums of powers, some other problems of the additive theory of numbers and the theory of Gaussian integers.
From the dream team of Jon Klassen and Mac Barnett comes the second instalment in the exciting new shape trilogy. Every day, Square brings a block out of his cave and pushes it up a steep hill. This is his work. When Circle floats by, she declares Square a genius, a sculptor! “This is a wonderful statue,” she says. “It looks just like you!” But now Circle wants a sculpture of her own, a circle! Will the genius manage to create one? Even accidentally?