В книге представлены задачи-головоломки, игры-головоломки и игровые творческие задания как для школьников, так и для их родителей, которые заинтересованы в том, чтобы их ребенок учился проводить свой досуг рационально и не без пользы для себя.

This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

The number of models available in neural network literature is quite large. Very often the treatment is mathematical and complex. This book provides illustrative examples in C++ that the reader can use as a basis for further experimentation. A key to learning about neural networks to appreciate their inner workings is to experiment. Neural networks, in the end, are fun to learn about and discover. Although the language for description used is C++, you will not find extensive class libraries in this book. With the exception of the backpropagation simulator, you will find fairly simple example programs for many different neural network architectures and paradigms. Since backpropagation is widely used and also easy to tame, a simulator is provided with the capacity to handle large input data sets. You use the simulator in one of the chapters in this book to solve a financial forecasting problem. You will find ample room to expand and experiment with the code presented in this book.

Just when we thought we knew everything about Lewis Carroll, here comes a highly original biography that will appeal to Alice fans everywhere. Fascinated by the inner life of Charles Lutwidge Dodson, Robin Wilson, a Carroll scholar and a noted mathematics professor, has produced this revelatory book—filled with more than one hundred striking and often playful illustrations—that examines the many inspirations and sources for Carroll's fantastical writings, mathematical and otherwise. As Wilson demonstrates, Carroll—who published serious, if occasionally eccentric, works in the fields of geometry, logic, and algebra—made significant contributions to subjects as varied as voting patterns and the design of tennis tournaments, in the process creating imaginative recreational puzzles based on mathematical ideas. In the tradition of Sylvia Nasar's A Beautiful Mind and Andrew Hodges's Alan Turing, this is an engaging look at the incredible genius of one of mathematics' and literature's most enigmatic minds. 100 illustrations

The LSAT's logic games section is anything but fun and games. These questions, which describe some situation involving six or seven people and then ask you, "If Chris is first in line, then who must be third?" or "If Anna sees the doctor on Monday, who sees the doctor on Tuesday?" strike terror into the hearts of many LSAT-takers. But if you're one of them, don't despair--you've found the expert help you're looking for. This unique guide has been prepared by experts you know you can trust: a team of Harvard Law School students who all scored in the 99th percentile on the LSAT! They'll show you how to handle every kind of logic game, how to diagram logical relationships, and how to use targeted logic tools to answer questions quickly and easily. Sequencing games, grouping games, mapping games--whatever the game type, you'll learn the techniques you need to solve most complex logic problem and find the correct answers.

With an emphasis on the philosophy,this text examines formal ways of representing uncertainty (presented in terms of definitions and theorems) and considers various logics for reasoning about it.

The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define--and why so many questions still surround them. That definition seems so simple: they are numbers that cannot be expressed as a ratio of two integers, or that have decimal expansions that are neither infinite nor recurring. But, as The Irrationals shows, these are the real "complex" numbers, and they have an equally complex and intriguing history, from Euclid's famous proof that the square root of 2 is irrational to Roger Apéry's proof of the irrationality of a number called Zeta(3), one of the greatest results of the twentieth century. In between, Havil explains other important results, such as the irrationality of e and pi. He also discusses the distinction between "ordinary" irrationals and transcendentals, as well as the appealing question of whether the decimal expansion of irrationals is "random". Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.

This book provides a detailed description of the general principles and strategies for solving chemical synthesis problems of complex organic molecules. It is the only book to deal systematically with the fundamental principles of synthetic problem solving.

Construct effective arguments with UNDERSTANDING ARGUMENTS: AN INTRODUCTION TO INFORMAL LOGIC, 8th Edition. Primarily an introduction to informal logic, this text provides a guide to understanding and constructing arguments in the context of academic studies and subsequent professional careers. Exercises, discussion questions, and readings help clarify difficult concepts and make the material meaningful and useful.

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Эта книга посвящена основам (азам) физики — науки о природе (по-гречески фисис (ϕυσις) — природа). В XXI веке основой физики является так называемая стандартная модель элементарных частиц, из которых по законам теории относительности и квантовой теории построено всё сущее. К сожалению, существующие введения в эти науки из-за их математической сложности недоступны не только школьникам, но и большинству преподавателей физики. Эта маленькая книжечка — попытка максимально просто и кратко изложить основы теории относительности (с её главной константой c) и квантовой механики (с её главной константой h). Я отчётливо понимаю,что не могу написать её так, чтобы она была понятна человеку, не знающему физики. Поэтому книжка адресована прежде всего профессиональным физикам (особенно молодым) в надежде на то, что кто-то из них использует изложенные в ней идеи при написании простых курсов современной физики и научно-популярных книг и статей. В отличие от научно-популярных книг, эта книга широко использует математические формулы. Но в отличие от формул в университетских учебниках, формулы, отобранные для этой книги, настолько просты, что для их понимания достаточно знания элементарной математики в объёме средней школы. Поэтому я уверен, что многие страницы книги будут понятны даже подросткам и помогут тем из них, кто интересуется физикой, постепенно расширять свой научный кругозор. Для этого книга снабжена подробным указателем.

Брошюра представляет собой развернутое изложение обзорного доклада, прочитанного первым из авторов — крупным специалистом по математической логике. В исключительно сжатой, но доступной и четкой форме авторам удалось изложить важнейшие современные аксиоматические обоснования теории абстрактных множеств. Эта отрасль весьма слабо представлена в советской математической литературе, а между тем современное бурное развитие исследований по основаниям математики и по математической логике тесно связано с ней. Брошюра будет полезна всем математикам, а также представителям других специальностей, интересующихся приложениями математической логики.

В книге рассмотрены, главным образом, три круга вопросов: проблемы полноты и функционально замкнутых классов, проблеммы синтеза и оценки сложности схем, теория вероятностей на конечных булевых алгебрах.