This book provides students of mathematics with the minimum amount of knowledge in logic and set theory needed for a profitable continuation of their studies. There is a chapter on statement calculus, followed by eight chapters on set theory.

Throughout history, application rather than abstraction has been the prominent driving force in mathematics. From the compass and sextant to partial differential equations, mathematical advances were spurred by the desire for better navigation tools, weaponry, and construction methods. But the religious upheaval in Victorian England and the fledgling United States opened the way for the rediscovery of pure mathematics, a tradition rooted in Ancient Greece. In Equations from God, Daniel J. Cohen captures the origins of the rebirth of abstract mathematics in the intellectual quest to rise above common existence and touch the mind of the deity. Using an array of published and private sources, Cohen shows how philosophers and mathematicians seized upon the beautiful simplicity inherent in mathematical laws to reconnect with the divine and traces the route by which the divinely inspired mathematics of the Victorian era begot later secular philosophies.

Revving engines, smoking tires, and high speeds. Car racing enthusiasts and race drivers alike know the thrill of competition, the push to perform better, and the agony—and dangers—of bad decisions. But driving faster and better involves more than just high horsepower and tightly tuned engines. Physicist and amateur racer Chuck Edmondson thoroughly discusses the physics underlying car racing and explains just what’s going on during any race, why, and how a driver can improve control and ultimately win. The world of motorsports is rich with excitement and competition—and physics. Edmondson applies common mathematical theories to real-world racing situations to reveal the secrets behind successful fast driving. He explains such key concepts as how to tune your car and why it matters, how to calculate 0 to 60 mph times and quarter-mile times and why they are important, and where, when, why, and how to use kinematics in road racing. He wraps it up with insight into the impact and benefit of green technologies in racing. In each case, Edmondson’s in-depth explanations and worked equations link the physics principles to qualitative racing advice. From selecting shifting points to load transfer in car control and beyond, Fast Car Physics is the ideal source to consult before buckling up and cinching down the belts on your racing harness.

Basic concepts of number theory are discussed. Topics include set theory, mathematical induction, com-binatorics, arithmetic, real numbers, limit and convergence, and complex numbers.

As anyone from cold climates knows, frequently occurring ice and snow lead to a special appreciation of sports such as skiing, sledding, and skating. Prolific physics popularizer Mark Denny’s take on winter athletics lays out the physical principles that govern glaciated game play. After discussing the physical properties of ice and snow and how physics describes sliding friction and aerodynamic drag, Denny applies these concepts to such sports as bobsledding, snowboarding, and curling. He explains why clap skates would only hinder hockey players, how a curling rock curls, the forces that control luge speed, how steering differs in skiing and snowboarding, and much more. With characteristic accuracy and a touch of wit, Denny provides fans, competitors, and coaches with handy, applicable insight into the games they love. His separate section of technical notes offers an original and mathematically rigorous exploration of the key aspects of winter sports physics. A physics-driven exploration of sports played on ice and snow that is truly fun and informative, Gliding for Gold is the perfect primer for understanding the science behind cold weather athletics.

Why does a harpsichord sound different from a piano? For that matter, why does middle C on a piano differ from middle C on a tuning fork, a trombone, or a flute? Good Vibrations explains in clear, friendly language the out-of-sight physics responsible not only for these differences but also for the whole range of noises we call music. The physical properties and history of sound are fascinating to study. Barry Parker's tour of the physics of music details the science of how instruments, the acoustics of rooms, electronics, and humans create and alter the varied sounds we hear. Using physics as a base, Parker discusses the history of music, how sounds are made and perceived, and the various effects of acting on sounds. In the process, he demonstrates what acoustics can teach us about quantum theory and explains the relationship between harmonics and the theory of waves. Peppered throughout with anecdotes and examples illustrating key concepts, this invitingly written book provides a firm grounding in the actual and theoretical physics of music.

L'univers de l'homme moderne, si pétri de rationalisme, si environné de technologies et d'artéfacts rassurants, est néanmoins imprégné de hasard, davantage que ne l'était celui de ses ancêtres. L'auteur traite des séries de nombres aléatoires, de leurs propriétés, leur test, leur génération, leur application dans l'estimation Monte Carlo, une méthode qui utilise massivement les capacités de calcul de l'ordinateur pour trouver des solutions numériques approximatives à des problèmes complexes.

What is the maximum number of pizza slices one can get by making four straight cuts through a circular pizza? How does a computer determine the best set of pixels to represent a straight line on a computer screen? How many people at a minimum does it take to guard an art gallery? Discrete mathematics has the answer to these—and many other—questions of picking, choosing, and shuffling. T. S. Michael's gem of a book brings this vital but tough-to-teach subject to life using examples from real life and popular culture. Each chapter uses one problem—such as slicing a pizza—to detail key concepts about counting numbers and arranging finite sets. Michael takes a different perspective in tackling each of eight problems and explains them in differing degrees of generality, showing in the process how the same mathematical concepts appear in varied guises and contexts. In doing so, he imparts a broader understanding of the ideas underlying discrete mathematics and helps readers appreciate and understand mathematical thinking and discovery. This book explains the basic concepts of discrete mathematics and demonstrates how to apply them in largely nontechnical language. The explanations and formulas can be grasped with a basic understanding of linear equations.

Fruit de la collaboration des professeur Walter Hengarther de l’Université Laval, Marcel Lambert et Corina Reischer de l’Université du Québec à Trois-Rivières, Introduction à l’analyse fonctionnelle se distingue tant par l’étendue de son contenu que par l’accessibilité de sa présentation. Sans céder quoi que ce soit sur la rigueur, il est parfaitement adapté à un premier cours d’analyse fonctionnelle. Tout en étant d’abord destiné aux étudiants en mathématiques, il pourra certes être utile aux étudiants de second cycle en sciences et en génie.

Les auteurs leur proposent donc une approche pratique et empirique qui allie l’analyse statistique à l’utilisation d’un logiciel facile d’accès : SPSS. En décrivant les diverses méthodes de l’analyse multivariée, ils présentent les interrelations entre plusieurs variables d’une base de données et en généralisent les conclusions par inférence statistique du traitement informatique des données jusqu’à l’interprétation des résultats.