The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination.

    The study of type systems--and of programming languages from a type-theoretic perspective--has important applications in software engineering, language design, high-performance compilers, and security.This text provides a comprehensive introduction both to type systems in computer science and to the basic theory of programming languages. The approach is pragmatic and operational; each new concept is motivated by programming examples and the more theoretical sections are driven by the needs of implementations. Each chapter is accompanied by numerous exercises and solutions, as well as a running implementation, available via the Web. Dependencies between chapters are explicitly identified, allowing readers to choose a variety of paths through the material.The core topics include the untyped lambda-calculus, simple type systems, type reconstruction, universal and existential polymorphism, subtyping, bounded quantification, recursive types, kinds, and type operators. Extended case studies develop a variety of approaches to modeling the features of object-oriented languages.

    "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems."

    Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, more. Bibliography.

    

    Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set.

    of Wisconsin-Madison) and Wichern (Texas A&M U.) present the newest edition of this college text on the statistical methods for describing and analyzing multivariate data, designed for students who have taken two or more statistics courses. The fifth edition includes the addition of seve

    It just feels that way.Certified nutritionist Leanne Ely loves delicious food and is dedicated to enticing today’s busy families back to the dinner table with home cooking that cannot be beat. In Saving Dinner the Low-Carb Way, she integrates low-carb requirements into her mélange of dining pleasures for every season–providing easy-to-follow menus and highlighting per-serving measurements of calories, fat, protein, carbohydrates, cholesterol, and sodium for each dish.Itemizing ingredients by product in convenient lists, Ely makes your grocery shopping quick and effortless. She also gives you a helping hand in the kitchen with shortcuts that take the stress out of cooking, and suggests menu variations for children and family members who choose not to go the low-carb route.The result? These dinners are not only balanced and healthy but truly varied and delectably good to eat. Main dishes like Low-Carb Beef Stroganoff, Crustless Quiche Lorraine, Crock-Pot Pork Jambalaya, Skillet Salmon with Horseradish Cream, and nearly 150 other entrees (plus recommendations for great side dishes) make dinnertime special in more ways than one.

    This well-respected text offers an accessible introduction to functional programming concepts and techniques for students of mathematics and computer science. The treatment is as nontechnical as possible, and it assumes no prior knowledge of mathematics or functional programming. Cogent examples illuminate the central ideas, and numerous exercises appear throughout the text, offering reinforcement of key concepts. All problems feature complete solutions.

    Pendel's attention. It is very interesting and throws many sidelights on the life of the White House. Pendel writes: "In 1861, or 1862, the Metropolitan Police was established by Congress at the Capital, and I made application for and received an appointment on the force. I made the first arrest, with the assistance of "Buck" Essex. The case was that of a fellow named Grady, one of the English Hill toughs. A roundsman said to us, "Boys, you take a walk down Seventh Street, and if you see anything going on, take a hand in it." Just as we got opposite the Patent Office, this Grady had assaulted, or rather was assaulting, a young fellow with a whip. I went up and grabbed him and put him under arrest, then took him to Squire Dunn's court and preferred charges against him. The Squire was busy writing for some time. When he got through he handed me the paper he was writing, and I was so green at the business I did not know what it was, so said: "What is this, Squire?" He replied, "Why, that is the paper of commitment for this fellow. Take him to jail." "On November 3, 1864, Sergeant John Cronin, Alfonso Dunn, Andrew Smith, and myself were ordered to report at the First Precinct, in the old City Hall, at one o'clock in the afternoon. We supposed we were to be detailed for detective work in New York City on account of the great riot then on there, especially as we were ordered to report in citizens' clothes, to conceal our revolvers, and to be sure to have them all clean and in good order. We arrived at the City Hall, and then were told where we were to go, which was to the President's Mansion, there to report to Marshal Lanham, at that time United States Marshal of the District of Columbia, and a bosom friend of Abraham Lincoln. "These were days that tried men's hearts, and women's, too. Men were falling at the front by hundreds, both in the Union and in the Confederate armies. There was weeping and mourning all over the land. Our nation was trembling with anxiety; we were all hoping that the great strife was over or soon to be. "Marshal Lanham took us upstairs and into the President's office, where we were introduced to him and to his two secretaries, Mr. Nicolay and Mr. Hay, the latter now being Secretary of State. We were then instructed to keep a sharp lookout in the different parts of the house, more particularly in the East Room and at the door of the President's office. " CONTENTS I — Under President Lincoln II — Under President Johnson III — Under President Grant IV — Under President Hayes V — Under President Garfield VI — Under President Arthur VII — Under President Cleveland VIII — Under President Harrison IX — Cleveland's Second Administration X— Under President McKinley XI — Furniture in Executive Mansion Originally published in 1902; reformatted for the Kindle; may contain an occasional imperfections; original spellings have been kept in place.

     -Byte, September 1995 I can't begin to tell you how many pleasurable hours of study and recreation they have afforded me! I have pored over them in cars, restaurants, at work, at home... and even at a Little League game when my son wasn't in the line-up. -Charles Long If you think you're a really good programmer... read [Knuth's] Art of Computer Programming... You should definitely send me a resume if you can read the whole thing. -Bill Gates It's always a pleasure when a problem is hard enough that you have to get the Knuths off the shelf. I find that merely opening one has a very useful terrorizing effect on computers. -Jonathan Laventhol This first volume in the series begins with basic programming concepts and techniques, then focuses more particularly on information structures-the representation of information inside a computer, the structural relationships between data elements and how to deal with them efficiently. Elementary applications are given to simulation, numerical methods, symbolic computing, software and system design. Dozens of simple and important algorithms and techniques have been added to those of the previous edition. The section on mathematical preliminaries has been extensively revised to match present trends in research. Ebook (PDF version) produced by Mathematical Sciences Publishers (MSP), http: //msp.org

    But its myriad occurrences in art, nature, and science have been a source of speculation and wonder for thousands of years. Divine Proportion draws upon both religion and science to tell the story of Phi and to explore its manifestations in such diverse places as the structure of the inner ear, the spiral of a hurricane, the majesty of the Parthenon, and the elusive perfection of the Mona Lisa. A universal key to harmony, regeneration, and balance, Phi is at the heart of a tantalizing story begun on clay tablets in ancient Babylon, and which will continue to be written for centuries to come.

    The Fuel Up section is designed for just that - it is where you will find my recipes for grab-and-go breakfasts, lunches on the run and dinners that take less than 30 minutes to satisfy you after a long day at work! However, I truly believe that when we do have the time to cook a meal, bake some bread and sit down with friends and family to share some food, we should totally embrace those moments. This is where the Power Down section comes in: for when you're not in a hurry, I have included my chosen recipes for lazy weekend brunches, family dinners, breads and teatime treats. This is a cookbook that will help you fall in love with cooking and improve your relationship with food, so that you approach it not only as a source of nutrients, but also happiness, satisfaction and health.Hazel x Includes more than 100 recipes PLUS: - 10 'no recipe recipes' for emergency snacks + meal prep hacks for maintaining a healthy lifestyle when you're busy - an introduction to Hazel's five store-cupboard saviours, including 10 ways to cook with each one - a key for special dietary requirements including vegetarian, vegan, gluten-free and low sugar - nutritional advice covering the basics of nutrition, how to meet your 5-a-day and special nutritional requirements for a plant-based diet - features on how to live well for optimum health, with information on sleep, meditation, mindfulness and mindful eating

    Rucker acquaints us with Godel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations.Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Godel's incompleteness theorems. His personal encounters with Godel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.

    In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.