An Accompaniment To Higher Mathematics

Author : George R. Exner
Publisher : Springer Science & Business Media
ISBN 13 : 1461239982
Total Pages : 212 pages
Book Rating : 4.87/5 ( download)

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Download or read book An Accompaniment to Higher Mathematics written by George R. Exner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for students preparing to engage in their first struggles to understand and write proofs and to read mathematics independently, this is well suited as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology. The book teaches in detail how to construct examples and non-examples to help understand a new theorem or definition; it shows how to discover the outline of a proof in the form of the theorem and how logical structures determine the forms that proofs may take. Throughout, the text asks the reader to pause and work on an example or a problem before continuing, and encourages the student to engage the topic at hand and to learn from failed attempts at solving problems. The book may also be used as the main text for a "transitions" course bridging the gap between calculus and higher mathematics. The whole concludes with a set of "Laboratories" in which students can practice the skills learned in the earlier chapters on set theory and function theory.

Author : George R. Exner
Publisher :
ISBN 13 :
Total Pages : 198 pages
Book Rating : 4.79/5 ( download)

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Download or read book Accompaniment to Higher Maths written by George R. Exner and published by . This book was released on 1996 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Bob A. Dumas
Publisher : McGraw-Hill Education
ISBN 13 : 9780071106474
Total Pages : 0 pages
Book Rating : 4.72/5 ( download)

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Download or read book Transition to Higher Mathematics written by Bob A. Dumas and published by McGraw-Hill Education. This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written for students who have taken calculus and want to learn what "real mathematics" is.

Author : Peter Hilton
Publisher : Springer Science & Business Media
ISBN 13 : 1461219329
Total Pages : 367 pages
Book Rating : 4.23/5 ( download)

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Download or read book Mathematical Reflections written by Peter Hilton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: A relaxed and informal presentation conveying the joy of mathematical discovery and insight. Frequent questions lead readers to see mathematics as an accessible world of thought, where understanding can turn opaque formulae into beautiful and meaningful ideas. The text presents eight topics that illustrate the unity of mathematical thought as well as the diversity of mathematical ideas. Drawn from both "pure" and "applied" mathematics, they include: spirals in nature and in mathematics; the modern topic of fractals and the ancient topic of Fibonacci numbers; Pascals Triangle and paper folding; modular arithmetic and the arithmetic of the infinite. The final chapter presents some ideas about how mathematics should be done, and hence, how it should be taught. Presenting many recent discoveries that lead to interesting open questions, the book can serve as the main text in courses dealing with contemporary mathematical topics or as enrichment for other courses. It can also be read with pleasure by anyone interested in the intellectually intriguing aspects of mathematics.

Author : James R. Kirkwood
Publisher :
ISBN 13 : 9781032623856
Total Pages : 0 pages
Book Rating : 4.53/5 ( download)

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Download or read book A Bridge to Higher Mathematics written by James R. Kirkwood and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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 : George R. Exner
Publisher : Springer Science & Business Media
ISBN 13 : 038722646X
Total Pages : 227 pages
Book Rating : 4.60/5 ( download)

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Download or read book Inside Calculus written by George R. Exner and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: The approach here relies on two beliefs. The first is that almost nobody fully understands calculus the first time around. The second is that graphing calculators can be used to simplify the theory of limits for students. This book presents the theoretical pieces of introductory calculus, using appropriate technology, in a style suitable to accompany almost any first calculus text. It offers a large range of increasingly sophisticated examples and problems to build an understanding of the notion of limit and other theoretical concepts. Aimed at students who will study fields in which the understanding of calculus as a tool is not sufficient, the text uses the "spiral approach" of teaching, returning again and again to difficult topics, anticipating such returns across the calculus courses in preparation for the first analysis course. Suitable as the "content" text for a transition to upper level mathematics course.

Author : Lindsay N. Childs
Publisher : Springer Science & Business Media
ISBN 13 : 1441987029
Total Pages : 540 pages
Book Rating : 4.20/5 ( download)

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Download or read book A Concrete Introduction to Higher Algebra written by Lindsay N. Childs and published by Springer Science & Business Media. This book was released on 2012-12-04 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: An informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials, with much emphasis placed on congruence classes leading the way to finite groups and finite fields. New examples and theory are integrated in a well-motivated fashion and made relevant by many applications -- to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises, ranging from routine examples to extensions of theory, are scattered throughout the book, with hints and answers for many of them included in an appendix.

Author : Stanley J. Farlow
Publisher : John Wiley & Sons
ISBN 13 : 1119563518
Total Pages : 480 pages
Book Rating : 4.18/5 ( download)

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Download or read book Advanced Mathematics written by Stanley J. Farlow and published by John Wiley & Sons. This book was released on 2019-10-08 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a smooth and pleasant transition from first-year calculus to upper-level mathematics courses in real analysis, abstract algebra and number theory Most universities require students majoring in mathematics to take a “transition to higher math” course that introduces mathematical proofs and more rigorous thinking. Such courses help students be prepared for higher-level mathematics course from their onset. Advanced Mathematics: A Transitional Reference provides a “crash course” in beginning pure mathematics, offering instruction on a blendof inductive and deductive reasoning. By avoiding outdated methods and countless pages of theorems and proofs, this innovative textbook prompts students to think about the ideas presented in an enjoyable, constructive setting. Clear and concise chapters cover all the essential topics students need to transition from the "rote-orientated" courses of calculus to the more rigorous "proof-orientated” advanced mathematics courses. Topics include sentential and predicate calculus, mathematical induction, sets and counting, complex numbers, point-set topology, and symmetries, abstract groups, rings, and fields. Each section contains numerous problems for students of various interests and abilities. Ideally suited for a one-semester course, this book: Introduces students to mathematical proofs and rigorous thinking Provides thoroughly class-tested material from the authors own course in transitioning to higher math Strengthens the mathematical thought process of the reader Includes informative sidebars, historical notes, and plentiful graphics Offers a companion website to access a supplemental solutions manual for instructors Advanced Mathematics: A Transitional Reference is a valuable guide for undergraduate students who have taken courses in calculus, differential equations, or linear algebra, but may not be prepared for the more advanced courses of real analysis, abstract algebra, and number theory that await them. This text is also useful for scientists, engineers, and others seeking to refresh their skills in advanced math.

Author : B. R. Hastie
Publisher : Hodder Gibson
ISBN 13 : 9780716932406
Total Pages : 96 pages
Book Rating : 4.07/5 ( download)

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Download or read book Solutions to Higher Still Higher Mathematics written by B. R. Hastie and published by Hodder Gibson. This book was released on 1999 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Maxwell Rosenlicht
Publisher : Courier Corporation
ISBN 13 : 0486134687
Total Pages : 272 pages
Book Rating : 4.80/5 ( download)

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Download or read book Introduction to Analysis written by Maxwell Rosenlicht and published by Courier Corporation. This book was released on 2012-05-04 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.