Author : Ulrich Daepp
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 18,35 MB
Release : 2006-04-18
Category : Mathematics
ISBN : 0387215603
This book, based on Pólya's method of problem solving, aids students in their transition to higher-level mathematics. It begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and ends by providing projects for independent study. Students will follow Pólya's four step process: learn to understand the problem; devise a plan to solve the problem; carry out that plan; and look back and check what the results told them.
Author : Ulrich Daepp
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 11,44 MB
Release : 2011-06-23
Category : Mathematics
ISBN : 1441994793
This book, which is based on Pólya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics. The book begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and ends with suggested projects for independent study. Students will follow Pólya's four step approach: analyzing the problem, devising a plan to solve the problem, carrying out that plan, and then determining the implication of the result. In addition to the Pólya approach to proofs, this book places special emphasis on reading proofs carefully and writing them well. The authors have included a wide variety of problems, examples, illustrations and exercises, some with hints and solutions, designed specifically to improve the student's ability to read and write proofs. Historical connections are made throughout the text, and students are encouraged to use the rather extensive bibliography to begin making connections of their own. While standard texts in this area prepare students for future courses in algebra, this book also includes chapters on sequences, convergence, and metric spaces for those wanting to bridge the gap between the standard course in calculus and one in analysis.
Author : Daniel J. Velleman
Publisher : Cambridge University Press
Page : 401 pages
File Size : 14,17 MB
Release : 2006-01-16
Category : Mathematics
ISBN : 0521861241
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
Author : Theodore A. Sundstrom
Publisher : Prentice Hall
Page : 0 pages
File Size : 12,78 MB
Release : 2007
Category : Logic, Symbolic and mathematical
ISBN : 9780131877184
Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom
Author : Martin Aigner
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 20,68 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 3662223430
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author : Richard H. Hammack
Publisher :
Page : 314 pages
File Size : 40,36 MB
Release : 2016-01-01
Category : Mathematics
ISBN : 9780989472111
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
Author : Ethan D. Bloch
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 39,94 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461221307
The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.
Author : Larry Gerstein
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 36,19 MB
Release : 2013-11-21
Category : Science
ISBN : 1468467085
This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper division instructors feel the need to start their courses with the rudiments of logic, set theory, equivalence relations, and other basic mathematical raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried the students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a nontrivial level if they are to achieve the sophisticated blend of knowledge, disci pline, and creativity that we call "mathematical maturity. " I don't believe that "theorem-proving" can be taught any more than "question-answering" can be taught. Nevertheless, I have found that it is possible to guide stu dents gently into the process of mathematical proof in such a way that they become comfortable with the experience and begin asking them selves questions that will lead them in the right direction.
Author : Carol Jago
Publisher : Bedford/St. Martin's
Page : 1568 pages
File Size : 38,29 MB
Release : 2010-06-11
Category : Literary Collections
ISBN : 9780312388065
From Carol Jago and the authors of The Language of Composition comes the first textbook designed specifically for the AP* Literature and Composition course. Arranged thematically to foster critical thinking, Literature & Composition: Reading • Writing • Thinking offers a wide variety of classic and contemporary literature, plus all of the support students need to analyze it carefully and thoughtfully. The book is divided into two parts: the first part of the text teaches students the skills they need for success in an AP Literature course, and the second part is a collection of thematic chapters of literature with extensive apparatus and special features to help students read, analyze, and respond to literature at the college level. Only Literature & Composition has been built from the ground up to give AP students and teachers the materials and support they need to enjoy a successful and challenging AP Literature course. Use the navigation menu on the left to learn more about the selections and features in Literature & Composition: Reading • Writing • Thinking. *AP and Advanced Placement Program are registered trademarks of the College Entrance Examination Board, which was not involved in the publication of and does not endorse this product.
Author : Donald Estep
Publisher : Springer Science & Business Media
Page : 621 pages
File Size : 18,46 MB
Release : 2006-04-06
Category : Mathematics
ISBN : 0387226443
This text places the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer.
