An Accompaniment To Higher Mathematics

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An Accompaniment to Higher Mathematics

Author : George R. Exner
Publisher : Springer Science & Business Media
ISBN 13 : 1461239982
Total Pages : 212 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis An Accompaniment to Higher Mathematics by : George R. Exner

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.

Transition to Higher Mathematics: Structure and Proof

Author : Bob Dumas
Publisher : McGraw-Hill Science/Engineering/Math
ISBN 13 : 9780073533537
Total Pages : 0 pages
Book Rating : 4.5/5 (335 download)

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Book Synopsis Transition to Higher Mathematics: Structure and Proof by : Bob Dumas

Download or read book Transition to Higher Mathematics: Structure and Proof written by Bob Dumas and published by McGraw-Hill Science/Engineering/Math. This book was released on 2006-04-20 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is intended for the Foundations of Higher Math bridge course taken by prospective math majors following completion of the mainstream Calculus sequence, and is designed to help students develop the abstract mathematical thinking skills necessary for success in later upper-level majors math courses. As lower-level courses such as Calculus rely more exclusively on computational problems to service students in the sciences and engineering, math majors increasingly need clearer guidance and more rigorous practice in proof technique to adequately prepare themselves for the advanced math curriculum. With their friendly writing style Bob Dumas and John McCarthy teach students how to organize and structure their mathematical thoughts, how to read and manipulate abstract definitions, and how to prove or refute proofs by effectively evaluating them. Its wealth of exercises give students the practice they need, and its rich array of topics give instructors the flexibility they desire to cater coverage to the needs of their school’s majors curriculum. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

Foundations of Higher Mathematics

Author : Stella Fletcher
Publisher :
ISBN 13 : 9780534930554
Total Pages : pages
Book Rating : 4.9/5 (35 download)

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Book Synopsis Foundations of Higher Mathematics by : Stella Fletcher

Download or read book Foundations of Higher Mathematics written by Stella Fletcher and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Foundations of Higher Mathematics

Author : Daniel M. Fendel
Publisher : Addison Wesley
ISBN 13 :
Total Pages : 486 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis Foundations of Higher Mathematics by : Daniel M. Fendel

Download or read book Foundations of Higher Mathematics written by Daniel M. Fendel and published by Addison Wesley. This book was released on 1990 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Higher Mathematics: Exploration and Proof is the ideal text to bridge the crucial gap between the standard calculus sequence and upper division mathematics courses. The book takes a fresh approach to the subject: it asks students to explore mathematical principles on their own and challenges them to think like mathematicians. Two unique features-an exploration approach to mathematics and an intuitive and integrated presentation of logic based on predicate calculus-distinguish the book from the competition. Both features enable students to own the mathematics they're working on. As a result, your students develop a stronger motivation to tackle upper-level courses and gain a deeper understanding of concepts presented.

A Bridge to Higher Mathematics

Author : Valentin Deaconu
Publisher : CRC Press
ISBN 13 : 1498775268
Total Pages : 218 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis A Bridge to Higher Mathematics by : Valentin Deaconu

Download or read book A Bridge to Higher Mathematics written by Valentin Deaconu and published by CRC Press. This book was released on 2016-12-19 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Bridge to Higher Mathematics is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought. The only way to understand mathematics is by doing mathematics. The reader will learn the language of axioms and theorems and will write convincing and cogent proofs using quantifiers. Students will solve many puzzles and encounter some mysteries and challenging problems. The emphasis is on proof. To progress towards mathematical maturity, it is necessary to be trained in two aspects: the ability to read and understand a proof and the ability to write a proof. The journey begins with elements of logic and techniques of proof, then with elementary set theory, relations and functions. Peano axioms for positive integers and for natural numbers follow, in particular mathematical and other forms of induction. Next is the construction of integers including some elementary number theory. The notions of finite and infinite sets, cardinality of counting techniques and combinatorics illustrate more techniques of proof. For more advanced readers, the text concludes with sets of rational numbers, the set of reals and the set of complex numbers. Topics, like Zorn’s lemma and the axiom of choice are included. More challenging problems are marked with a star. All these materials are optional, depending on the instructor and the goals of the course.

Mathematical Thinking and Writing

Author : Randall Maddox
Publisher : Academic Press
ISBN 13 : 0124649769
Total Pages : 324 pages
Book Rating : 4.1/5 (246 download)

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Book Synopsis Mathematical Thinking and Writing by : Randall Maddox

Download or read book Mathematical Thinking and Writing written by Randall Maddox and published by Academic Press. This book was released on 2002 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Reflections

Author : Peter Hilton
Publisher : Springer Science & Business Media
ISBN 13 : 1461219329
Total Pages : 367 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Mathematical Reflections by : Peter Hilton

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.

Towards Higher Mathematics: A Companion

Author : Richard Earl
Publisher : Cambridge University Press
ISBN 13 : 1108327184
Total Pages : 546 pages
Book Rating : 4.1/5 (83 download)

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Book Synopsis Towards Higher Mathematics: A Companion by : Richard Earl

Download or read book Towards Higher Mathematics: A Companion written by Richard Earl and published by Cambridge University Press. This book was released on 2017-09-07 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing a large and varied set of problems, this rich resource will allow students to stretch their mathematical abilities beyond the school syllabus, and bridge the gap to university-level mathematics. Many proofs are provided to better equip students for the transition to university. The author covers substantial extension material using the language of sixth form mathematics, thus enabling students to understand the more complex material. Exercises are carefully chosen to introduce students to some central ideas, without building up large amounts of abstract technology. There are over 1500 carefully graded exercises, with hints included in the text, and solutions available online. Historical and contextual asides highlight each area of mathematics and show how it has developed over time.

Higher Mathematics from an Elementary Point of View

Author : RADEMACHER
Publisher : Birkhäuser
ISBN 13 : 9781489949790
Total Pages : 138 pages
Book Rating : 4.9/5 (497 download)

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Book Synopsis Higher Mathematics from an Elementary Point of View by : RADEMACHER

Download or read book Higher Mathematics from an Elementary Point of View written by RADEMACHER and published by Birkhäuser. This book was released on 2013-09-11 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Invitation to Abstract Mathematics

Author : Béla Bajnok
Publisher : Springer Nature
ISBN 13 : 3030561747
Total Pages : 443 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis An Invitation to Abstract Mathematics by : Béla Bajnok

Download or read book An Invitation to Abstract Mathematics written by Béla Bajnok and published by Springer Nature. This book was released on 2020-10-27 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts. From reviews of the first edition: Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously enthusiastic.... The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH

A Bridge to Higher Mathematics

Author : James R. Kirkwood
Publisher :
ISBN 13 : 9781032623856
Total Pages : 0 pages
Book Rating : 4.6/5 (238 download)

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Book Synopsis A Bridge to Higher Mathematics by : James R. Kirkwood

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"--

A Concrete Introduction to Higher Algebra

Author : Lindsay N. Childs
Publisher : Springer Science & Business Media
ISBN 13 : 1441987029
Total Pages : 540 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis A Concrete Introduction to Higher Algebra by : Lindsay N. Childs

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.

Higher Mathematics

Author : Mansfield Merriman
Publisher :
ISBN 13 :
Total Pages : 618 pages
Book Rating : 4.:/5 (4 download)

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Book Synopsis Higher Mathematics by : Mansfield Merriman

Download or read book Higher Mathematics written by Mansfield Merriman and published by . This book was released on 1898 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Higher Mathematics from an Elementary Point of View

Author : RADEMACHER
Publisher : Birkhäuser
ISBN 13 : 9781489949776
Total Pages : 0 pages
Book Rating : 4.9/5 (497 download)

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Book Synopsis Higher Mathematics from an Elementary Point of View by : RADEMACHER

Download or read book Higher Mathematics from an Elementary Point of View written by RADEMACHER and published by Birkhäuser. This book was released on 2014-05-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Higher Mathematics

Author :
Publisher :
ISBN 13 : 9789390812868
Total Pages : 285 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Higher Mathematics by :

Download or read book Higher Mathematics written by and published by . This book was released on 2022 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Mathematical Bridge

Author : Stephen Fletcher Hewson
Publisher : World Scientific
ISBN 13 : 9812834079
Total Pages : 672 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis A Mathematical Bridge by : Stephen Fletcher Hewson

Download or read book A Mathematical Bridge written by Stephen Fletcher Hewson and published by World Scientific. This book was released on 2009 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although higher mathematics is beautiful, natural and interconnected, to the uninitiated it can feel like an arbitrary mass of disconnected technical definitions, symbols, theorems and methods. An intellectual gulf needs to be crossed before a true, deep appreciation of mathematics can develop. This book bridges this mathematical gap. It focuses on the process of discovery as much as the content, leading the reader to a clear, intuitive understanding of how and why mathematics exists in the way it does.The narrative does not evolve along traditional subject lines: each topic develops from its simplest, intuitive starting point; complexity develops naturally via questions and extensions. Throughout, the book includes levels of explanation, discussion and passion rarely seen in traditional textbooks. The choice of material is similarly rich, ranging from number theory and the nature of mathematical thought to quantum mechanics and the history of mathematics. It rounds off with a selection of thought-provoking and stimulating exercises for the reader.

Heinemann Higher Mathematics Student Book -

Author : David Clarke
Publisher : Pearson Education Ltd
ISBN 13 : 9780435516222
Total Pages : 452 pages
Book Rating : 4.5/5 (162 download)

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Book Synopsis Heinemann Higher Mathematics Student Book - by : David Clarke

Download or read book Heinemann Higher Mathematics Student Book - written by David Clarke and published by Pearson Education Ltd. This book was released on 2008-08-11 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers coverage of the higher course. This series includes multiple-choice questions that offer support for the multiple-choice paper. It contains worked examples and exam questions that help consolidate learning and provide exam preparation.