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Author : Bob A Dumas,John E McCarthy
Publisher : Unknown
Page : 128 pages
File Size : 40,5 Mb
Release : 2015
Category : Mathematics
ISBN : OCLC:1191907013
Author : Bob A. Dumas,John Edward McCarthy
Publisher : McGraw-Hill Education
Page : 0 pages
File Size : 52,7 Mb
Release : 2007
Category : Logic, Symbolic and mathematical
ISBN : 0071106472
This book is written for students who have taken calculus and want to learn what "real mathematics" is.
Author : Gary Chartrand,Albert D. Polimeni,Ping Zhang
Publisher : Addison-Wesley Longman
Page : 392 pages
File Size : 44,6 Mb
Release : 2008
Category : Proof theory
ISBN : UCSC:32106019008397
Mathematical Proofs: A Transition to Advanced Mathematics, Second Edition, prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets.
Author : Gary Chartrand,Albert D. Polimeni,Ping Zhang
Publisher : Pearson Higher Ed
Page : 422 pages
File Size : 55,6 Mb
Release : 2013-10-03
Category : Mathematics
ISBN : 9781292052342
Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.
Author : Michael J. Cullinane
Publisher : Jones & Bartlett Publishers
Page : 367 pages
File Size : 52,6 Mb
Release : 2013
Category : Mathematics
ISBN : 9781449627782
Developed for the "transition" course for mathematics majors moving beyond the primarily procedural methods of their calculus courses toward a more abstract and conceptual environment found in more advanced courses, A Transition to Mathematics with Proofs emphasizes mathematical rigor and helps students learn how to develop and write mathematical proofs. The author takes great care to develop a text that is accessible and readable for students at all levels. It addresses standard topics such as set theory, number system, logic, relations, functions, and induction in at a pace appropriate for a wide range of readers. Throughout early chapters students gradually become aware of the need for rigor, proof, and precision, and mathematical ideas are motivated through examples.
Author : Randall Maddox
Publisher : Academic Press
Page : 324 pages
File Size : 49,5 Mb
Release : 2002
Category : Mathematics
ISBN : 9780124649767
The ability to construct proofs is one of the most challenging aspects of the world of mathematics. It is, essentially, the defining moment for those testing the waters in a mathematical career. Instead of being submerged to the point of drowning, readers of Mathematical Thinking and Writing are given guidance and support while learning the language of proof construction and critical analysis. Randall Maddox guides the reader with a warm, conversational style, through the task of gaining a thorough understanding of the proof process, and encourages inexperienced mathematicians to step up and learn how to think like a mathematician. A student's skills in critical analysis will develop and become more polished than previously conceived. Most significantly, Dr. Maddox has the unique approach of using analogy within his book to clarify abstract ideas and clearly demonstrate methods of mathematical precision.
Author : Larry Gerstein
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 53,8 Mb
Release : 2013-11-21
Category : Science
ISBN : 9781468467086
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 : Neil R. Nicholson
Publisher : CRC Press
Page : 450 pages
File Size : 54,9 Mb
Release : 2019-03-21
Category : Mathematics
ISBN : 9780429522000
A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively. The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof. Features: The text is aimed at transition courses preparing students to take analysis Promotes creativity, intuition, and accuracy in exposition The language of proof is established in the first two chapters, which cover logic and set theory Includes chapters on cardinality and introductory topology
Author : Larry J. Gerstein
Publisher : Springer Science & Business Media
Page : 401 pages
File Size : 46,5 Mb
Release : 2012-06-05
Category : Mathematics
ISBN : 9781461442653
As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuition and rigor—and the flexible thinking—required to prove a nontrivial result. In short, this book seeks to enhance the mathematical maturity of the reader. The new material in this second edition includes a section on graph theory, several new sections on number theory (including primitive roots, with an application to card-shuffling), and a brief introduction to the complex numbers (including a section on the arithmetic of the Gaussian integers). Solutions for even numbered exercises are available on springer.com for instructors adopting the text for a course.
Author : Wendell Motter
Publisher : Unknown
Page : 107 pages
File Size : 47,9 Mb
Release : 2019-07-19
Category : Electronic
ISBN : 1081357789
This textbook prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in courses called transition courses, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as the real number system, logic, set theory, mathematical induction, relations, functions, and continuity. It is also a good reference text that students can use when writing or reading proofs in their more advanced courses.
Author : Charles Roberts
Publisher : CRC Press
Page : 434 pages
File Size : 45,6 Mb
Release : 2009-06-24
Category : Mathematics
ISBN : 9781420069563
Shows How to Read & Write Mathematical ProofsIdeal Foundation for More Advanced Mathematics CoursesIntroduction to Mathematical Proofs: A Transition facilitates a smooth transition from courses designed to develop computational skills and problem solving abilities to courses that emphasize theorem proving. It helps students develop the skills n
Author : Daniel J. Velleman
Publisher : Cambridge University Press
Page : 401 pages
File Size : 50,8 Mb
Release : 2006-01-16
Category : Mathematics
ISBN : 9780521861243
This new edition of Daniel J. Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.
Author : James R. Kirkwood,Raina S. Robeva
Publisher : Unknown
Page : 0 pages
File Size : 51,5 Mb
Release : 2024
Category : Mathematics
ISBN : 1032623853
"The goal of this unique text is to provide an "experience" that would facilitate a better transition for mathematics majors to the advanced proof-based courses required for their major. If you "love mathematics, but I hate proofs" this book is for you. Example-based courses such as introductory Calculus transition somewhat abruptly, and without a warning label, to proof-based courses, and may leave students with the unpleasant feeling that a subject they loved has turned into material they find hard to understand. The book exposes students and readers to the fundamental nature and principles of constructing mathematical proofs and in the context of main courses required for the major, e.g., probability, linear algebra, real analysis, and abstract algebra. Four short chapters, each chapter focusing on a particular course, provide a short but rigorous introduction. Students then get a preview of the discipline, its focus, language, mathematical objects of interests, and common methods of proof presented in those courses. Because which ideas apply to which future courses may not be obvious in many transition courses, this structure addresses this need. The book may also be used as a review tool at the end of course and for readers who want to learn the language and scope of the broad disciplines of linear algebra, abstract algebra, real analysis, and probability, before transitioning to these courses"--
Author : Bettina Richmond,Thomas Richmond
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 46,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847893
As the title indicates, this book is intended for courses aimed at bridging the gap between lower-level mathematics and advanced mathematics. The text provides a careful introduction to techniques for writing proofs and a logical development of topics based on intuitive understanding of concepts. The authors utilize a clear writing style and a wealth of examples to develop an understanding of discrete mathematics and critical thinking skills. While including many traditional topics, the text offers innovative material throughout. Surprising results are used to motivate the reader. The last three chapters address topics such as continued fractions, infinite arithmetic, and the interplay among Fibonacci numbers, Pascal's triangle, and the golden ratio, and may be used for independent reading assignments. The treatment of sequences may be used to introduce epsilon-delta proofs. The selection of topics provides flexibility for the instructor in a course designed to spark the interest of students through exciting material while preparing them for subsequent proof-based courses.
Author : Daniel W. Cunningham
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 55,6 Mb
Release : 2012-09-19
Category : Mathematics
ISBN : 9781461436317
The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs.