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Author: C. Stanley Ogilvy Publisher: Courier Corporation ISBN: 9780486282831 Category : Science Languages : en Pages : 196
Book Description
This lively and accessible exploration of the nature of mathematics examines the role of the mathematician as well as the four major branches: number theory, algebra, geometry, and analysis.
Author: Hongwei Chen Publisher: American Mathematical Soc. ISBN: 0883859351 Category : Mathematics Languages : en Pages : 301
Book Description
Excursions in Classical Analysis will introduce students to advanced problem solving and undergraduate research in two ways: it will provide a tour of classical analysis, showcasing a wide variety of problems that are placed in historical context, and it will help students gain mastery of mathematical discovery and proof. The [Author]; presents a variety of solutions for the problems in the book. Some solutions reach back to the work of mathematicians like Leonhard Euler while others connect to other beautiful parts of mathematics. Readers will frequently see problems solved by using an idea that, at first glance, might not even seem to apply to that problem. Other solutions employ a specific technique that can be used to solve many different kinds of problems. Excursions emphasizes the rich and elegant interplay between continuous and discrete mathematics by applying induction, recursion, and combinatorics to traditional problems in classical analysis. The book will be useful in students' preparations for mathematics competitions, in undergraduate reading courses and seminars, and in analysis courses as a supplement. The book is also ideal for self study, since the chapters are independent of one another and may be read in any order.
Author: David Berlinski Publisher: Vintage ISBN: 030778973X Category : Mathematics Languages : en Pages : 353
Book Description
Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. "An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review
Author: Israel Kleiner Publisher: Springer Science & Business Media ISBN: 0817682686 Category : Mathematics Languages : en Pages : 347
Book Description
This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work. Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses.
Author: L. C. G. Rogers Publisher: Cambridge University Press ISBN: 9780521775939 Category : Mathematics Languages : en Pages : 498
Book Description
This celebrated volume gives an accessible introduction to stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes.
Author: Peter Borwein Publisher: Springer Science & Business Media ISBN: 0387216529 Category : Mathematics Languages : en Pages : 220
Book Description
This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.
Author: Richard N. Aufmann Publisher: Brooks/Cole ISBN: 9780618608539 Category : Mathematics Languages : en Pages : 0
Book Description
By presenting problem solving in purposeful and meaningful contexts,Mathematical Excursions,2/e, provides students in the Liberal Arts course with a glimpse into the nature of mathematics and how it is used to understand our world. Highlights of the book include the proven Aufmann Interactive Method and multi-part Excursion exercises that emphasize collaborative learning. An extensive technology program provides instructors and students with a comprehensive set of support tools. New!Content new to this edition includes a subsection onReading and Interpreting Graphs,a section onRight Triangle Trigonometry,and a section onStocks, Bonds, and Annuities. New!Online algebra review appendix helps students review prerequisite algebra concepts. AnExcursionactivity and correspondingExcursion Exercisesconclude each section, providing concept reinforcement and opportunities for in-class cooperative work, hands-on learning, and development of critical-thinking skills. Aufmann Interactive Method ensures that students try concepts and manipulate real-life data as they progress through the material. Every objective contains at least one set of matched-pair examples, the first of which is a completely worked-out example with an annotated solution. The second problem, calledCheck Your Progress,is for the student to try. Each problem includes a reference to afully worked-out solutionin the back of the text. A section on Problem Solving Strategies in Chapter 1 introduces students to the inductive and deductive reasoning strategies they will use throughout the text. Question/Answerfeature encourages students to pause and think about the current discussion and to answer the question. For immediate reinforcement, the Answer is provided in a footnote on the same page. Carefully developed exercise sets emphasize skill building, skill maintenance, concepts, and applications. Icons are used to identify various types of exercises, including writing, data analysis, graphing calculator, and web exercises. Extension exercises at the end of each exercise set include Critical Thinking, Cooperative Learning, and Explorations, which may require Internet or library research. Math Mattersfeature throughout the text helps to motivate students by demonstrating how and why math is applicable to contemporary, real-life situations. Variety of supporting margin notes includesTake Note,alerting students to a concept requiring special attention;Point of Interest,offering motivating contextual information;Historical Notes,providing background information or vignettes of individuals responsible for major advancements in their field; andCalculator Notes,providing point-of-use tips. Chapter-ending resources include aChapter SummarywithKey WordsandEssential Concepts; Chapter Review Exercises(answers available in a special section), and aChapter Test.
Author: Robert M. Young
Author: Robert M. Young
Author: C. Stanley Ogilvy
Author: Hongwei Chen
Author: Dan Kalman
Author: David Berlinski
Author: Israel Kleiner
Author: L. C. G. Rogers
Author: Peter Borwein
Author: Vladimir Boltyanski
Author: Richard N. Aufmann