An Accompaniment To Higher Mathematics

Author : George R. Exner
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461239987

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An Accompaniment to Higher Mathematics by George R. Exner Pdf

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 : Richard Earl
Publisher : Cambridge University Press
Page : 546 pages
File Size : 55,9 Mb
Release : 2017-09-07
Category : Mathematics
ISBN : 9781108327183

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Towards Higher Mathematics: A Companion by Richard Earl Pdf

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.

Author : Daniel M. Fendel,Diane Resek
Publisher : Addison Wesley
Page : 486 pages
File Size : 42,7 Mb
Release : 1990
Category : Mathematics
ISBN : UCSC:32106018326642

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Foundations of Higher Mathematics by Daniel M. Fendel,Diane Resek Pdf

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.

Author : Stella Fletcher,Patty
Publisher : Unknown
Page : 128 pages
File Size : 53,5 Mb
Release : 1992
Category : Electronic
ISBN : 0534930557

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Foundations of Higher Mathematics by Stella Fletcher,Patty Pdf

Author : Valentin Deaconu,Donald C. Pfaff
Publisher : CRC Press
Page : 218 pages
File Size : 54,7 Mb
Release : 2016-12-19
Category : Mathematics
ISBN : 9781498775267

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A Bridge to Higher Mathematics by Valentin Deaconu,Donald C. Pfaff Pdf

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.

Author : Randall Maddox
Publisher : Academic Press
Page : 324 pages
File Size : 50,7 Mb
Release : 2002
Category : Mathematics
ISBN : 9780124649767

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Mathematical Thinking and Writing by Randall Maddox Pdf

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 : Peter Hilton,Derek Holton,Jean Pedersen
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 46,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475736816

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Mathematical Vistas by Peter Hilton,Derek Holton,Jean Pedersen Pdf

This book collects nine related mathematical essays which will intrigue and inform. From the reviews: "The authors put their writing where their talents are, and students get to see just how alive mathematics is...there is much to commend the book. It contains plenty of interesting mathematics, often going in unusual directions. I like the diagrams; the authors have chosen mathematics that involves especially pretty ones." --THE MATHEMATICAL ASSOCIATION OF AMERICA

Author : Mansfield Merriman,Robert Simpson Woodward
Publisher : Unknown
Page : 618 pages
File Size : 44,5 Mb
Release : 1898
Category : Error analysis (Mathematics)
ISBN : UCAL:$B418302

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Higher Mathematics by Mansfield Merriman,Robert Simpson Woodward Pdf

Author : Stephen Fletcher Hewson
Publisher : World Scientific
Page : 672 pages
File Size : 48,8 Mb
Release : 2009
Category : Education
ISBN : 9789812834072

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A Mathematical Bridge by Stephen Fletcher Hewson Pdf

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.

Author : Bob A Dumas,John E McCarthy
Publisher : Unknown
Page : 128 pages
File Size : 55,7 Mb
Release : 2015
Category : Mathematics
ISBN : OCLC:1191907013

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Transition to Higher Mathematics by Bob A Dumas,John E McCarthy Pdf

Author : James R. Kirkwood,Raina S. Robeva
Publisher : CRC Press
Page : 258 pages
File Size : 46,9 Mb
Release : 2024-05-08
Category : Mathematics
ISBN : 9781040023600

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A Bridge to Higher Mathematics by James R. Kirkwood,Raina S. Robeva Pdf

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 feel like you love mathematics but hate proofs, this book is for you. The change from example-based courses such as Introductory Calculus to the proof-based courses in the major is often abrupt, and some students are left 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 some fundamental content and essential methods of constructing mathematical proofs in the context of four main courses required for the mathematics major – probability, linear algebra, real analysis, and abstract algebra. Following an optional foundational chapter on background material, four short chapters, each focusing on a particular course, provide a slow-paced but rigorous introduction. Students get a preview of the discipline, its focus, language, mathematical objects of interest, and methods of proof commonly used in the field. The organization of the book helps to focus on the specific methods of proof and main ideas that will be emphasized in each of the courses. The text may also be used as a review tool at the end of each 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 : Béla Bajnok
Publisher : Springer Nature
Page : 443 pages
File Size : 48,6 Mb
Release : 2020-10-27
Category : Mathematics
ISBN : 9783030561741

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An Invitation to Abstract Mathematics by Béla Bajnok Pdf

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

Author : RADEMACHER
Publisher : Birkhäuser
Page : 138 pages
File Size : 42,5 Mb
Release : 2013-09-11
Category : Mathematics
ISBN : 1489949798

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Higher Mathematics from an Elementary Point of View by RADEMACHER Pdf

Author : Peter Hilton,Derek Holton,Jean Pedersen
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461219323

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Mathematical Reflections by Peter Hilton,Derek Holton,Jean Pedersen Pdf

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 : Anonim
Publisher : Unknown
Page : 285 pages
File Size : 41,7 Mb
Release : 2022
Category : Electronic
ISBN : 9390812860

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Higher Mathematics by Anonim Pdf