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 national identity as the food on our plates, as food historian Abigail Carroll vividly demonstrates in Three Squares. Reaching back to colonial America, when settlers enjoyed a single, midday meal, Carroll shows how later generations of Americans abandoned this utilitarian habit for more civilized, circumscribed rituals, trading in rustic pottages and puddings for complex roasts, sides, desserts, and—increasingly—processed foods. These new foodstuffs became the staples of breakfast and lunch in the late nineteenth century, and even brought with them a new eating tradition: snacking, which effectively transformed the American meal into one never-ending opportunity for indulgence. Revealing how the simple gruel of our forefathers gave way to cheese puffs and moon pies, Three Squares fascinatingly traces the rise and fall of the American meal.
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.
Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.
Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's elementary methods with the analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representations of an integer n as the sum of s squares of integers for any s and n. It is also the first book to give a proof of Szemeredi's theorem, and is the first number theory book to discuss how the modern theory of modular forms complements and clarifies the classical fundamental results about sums of squares. The book presents several existing, yet still interesting and instructive, examples of modular forms. Two chapters develop useful properties of the Bernoulli numbers and illustrate arithmetic progressions, proving the theorems of van der Waerden, Roth, and Szemeredi. The book also explains applications of the theory to three problems that lie outside of number theory in the areas of cryptanalysis, microwave radiation, and diamond cutting. The text is complemented by the inclusion of over one hundred exercises to test the reader's understanding.
Classic 2-part work now available in a single volume. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes problems and solutions. 1956 edition.
Author: Paul Sloane,Emily Cox,Henry Hook,Henry Rathvon
Pubpsher: Sterling Publishing Company, Inc.
Category: Games & Activities
Think ordinary conundrums are just too humdrum? Do you finish crossword puzzles in ink and in no time flat? Then get ready for a serious test of your skills, with the ultimate in mental challenges. We've got crosswords of course; more than 50 tough, "regular" ones. But you'll also enjoy dozens and dozens more of different varieties, including devilish "Crushwords" where you have to put more than one letter in each square, and mind-blowing math and logic teasers known as pixel puzzles, where if your answers are correct you'll create a picture of success! And if that isn't enough, you'll also find word puzzles that demand "lateral thinking," and may well be the truest test of your abilities.
Bradford Hill has defined a clinical trial as "A carefully and ethically designed experiment with the aim of answering some precisely framed question" . This definition specifies a careful design and requires the provision of adequate controls. Random allocation of treatments to subjects is important to ensure is entitled that the treated and control groups are similar. Therefore this book Randomised Controlled Clinical Trials. We can define a randomised controlled trial by rewriting Bradford Hill's definition as follows, "A carefully and ethi cally designed experiment which includes the provision of adequate and ap propriate controls by a process of randomisation, so that precisely framed questions can be answered. " I am a firm advocate ofRandomised Controlled Clinical Trials but intend to give a balanced view of the advantages and disadvantages of these ethical experiments. This book is directed primarily at the medical research worker, although certain chapters may find a wider application. When discussing a randomised controlled trial, it is neither practicable nor desirable to divorce theory from practice, however the first ten chapters con centrate mainly on theory, and the remainder focus on practice. The segment on trial design is followed by sections on writing the protocol, designing the forms, conducting the trial, and analysing the results. This book is meant to serve both as a reference manual and a practical guide to the design and performance of a trial.