A Bridge To Higher Mathematics
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Bridge To Higher Mathematics
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Author : Sam Vandervelde
language : en
Publisher: Lulu.com
Release Date : 2010
Bridge To Higher Mathematics written by Sam Vandervelde and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Education categories.
This engaging math textbook is designed to equip students who have completed a standard high school math curriculum with the tools and techniques that they will need to succeed in upper level math courses. Topics covered include logic and set theory, proof techniques, number theory, counting, induction, relations, functions, and cardinality.
A Bridge To Higher Mathematics
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Author : James R. Kirkwood
language : en
Publisher: CRC Press
Release Date : 2024-05-08
A Bridge To Higher Mathematics written by James R. Kirkwood and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-08 with Mathematics categories.
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.
A Bridge To Higher Mathematics
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Author : Valentin Deaconu
language : en
Publisher: CRC Press
Release Date : 2016-12-19
A Bridge To Higher Mathematics written by Valentin Deaconu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-19 with Mathematics categories.
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.
A Gateway To Higher Mathematics
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Author : Jason H. Goodfriend
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2005
A Gateway To Higher Mathematics written by Jason H. Goodfriend and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computers categories.
A Gateway to Higher Mathematics integrates the process of teaching students how to do proofs into the framework of displaying the development of the real number system. The text eases the students into learning how to construct proofs, while preparing students how to cope with the type of proofs encountered in the higher-level courses of abstract algebra, analysis, and number theory. After using this text, the students will not only know how to read and construct proofs, they will understand much about the basic building blocks of mathematics. The text is designed so that the professor can choose the topics to be emphasized, while leaving the remainder as a reference for the students.
A Bridge To Advanced Mathematics
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Author : Dennis Sentilles
language : en
Publisher: Courier Corporation
Release Date : 2013-05-20
A Bridge To Advanced Mathematics written by Dennis Sentilles and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-20 with Mathematics categories.
This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.
A Bridge To Advanced Mathematics
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Author : Sebastian M. Cioabă
language : en
Publisher: American Mathematical Society
Release Date : 2022-12-21
A Bridge To Advanced Mathematics written by Sebastian M. Cioabă and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-21 with Mathematics categories.
Most introduction to proofs textbooks focus on the structure of rigorous mathematical language and only use mathematical topics incidentally as illustrations and exercises. In contrast, this book gives students practice in proof writing while simultaneously providing a rigorous introduction to number systems and their properties. Understanding the properties of these systems is necessary throughout higher mathematics. The book is an ideal introduction to mathematical reasoning and proof techniques, building on familiar content to ensure comprehension of more advanced topics in abstract algebra and real analysis with over 700 exercises as well as many examples throughout. Readers will learn and practice writing proofs related to new abstract concepts while learning new mathematical content. The first task is analogous to practicing soccer while the second is akin to playing soccer in a real match. The authors believe that all students should practice and play mathematics. The book is written for students who already have some familiarity with formal proof writing but would like to have some extra preparation before taking higher mathematics courses like abstract algebra and real analysis.
Mathematical Bridge A An Intuitive Journey In Higher Mathematics 2nd Edition
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Author : Stephen Fletcher Hewson
language : en
Publisher: World Scientific Publishing Company
Release Date : 2009-01-20
Mathematical Bridge A An Intuitive Journey In Higher Mathematics 2nd Edition written by Stephen Fletcher Hewson and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-20 with Mathematics categories.
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.
A Bridge To Advanced Mathematics
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Author : Dennis Sentilles
language : en
Publisher: Courier Corporation
Release Date : 2011-01-01
A Bridge To Advanced Mathematics written by Dennis Sentilles and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.
"This helpful "bridge" book offers students the foundations they need to understand advanced mathematics, spanning the gap between practically oriented and theoretically orientated courses. Part 1 provides the most basic tools, examples, and motivation for the manner, method, and material of higher mathematics. Part 2 covers sets, relations, functions, infinite sets, and mathematical proofs and reasoning. 1975 edition"--Provided by publisher.
Crossing The Bridge To Higher Mathematics
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Author : M. Padraig M. M. McLoughlin
language : en
Publisher:
Release Date : 2008
Crossing The Bridge To Higher Mathematics written by M. Padraig M. M. McLoughlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
The author of this paper submits that a mathematics student needs to learn to conjecture and prove or disprove said conjecture. Ergo, the purpose of the paper is to submit the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method in a Bridge to Higher Mathematics course to teach students how to do, critique, or analyse proofs, counterexamples, examples, or counter-arguments. Furthermore, the author of this paper opines that set theory should be the core of the course with logic and predicate calculus as antecedents to the set theory, and number theory, cardinal and ordinal theory, or beginning topology of the reals as consequents of set theory. The author of this paper has experienced teaching such a course for approximately fifteen years; mostly teaching the course at a historically black college. The paper is organised such that in the first part of the paper justification for use of a modified Moore approach--both pedagogical and practical justification are submitted. In the second part of the paper the author submits the model for the Bridge course and focuses on what is effective for the students, what seems not useful to the students, and why; hence, explaining what practices were refined retained, modified, or deleted over the fifteen years. In the third part of the paper explanation is presented as to why the course was designed the way it was (content), how the course was revised or altered over the years and how it worked or did not for the faculty and students. The final part of the paper discusses the successes and lack thereof of how the methods and materials in the Bridge course established an atmosphere that created for some students an easier transition to advanced mathematics classes, assisted in forging a long-term undergraduate research component in the major, and encouraged some faculty to direct undergraduates in meaningful mathematics research. Qualitative and quantitative data are included to support what were or were not successes. So, this paper proposes a pedagogical approach to mathematics education that centres on exploration, discovery, conjecture, hypothesis, thesis, and synthesis such that the experience of doing a mathematical argument, creating a mathematical model, or synthesising ideas is reason enough for the exercise--and the joy of mathematics is something that needs to be instilled and encouraged in students by having them do proofs, counterexamples, examples, and counter-arguments in a Bridge course to prepare the student for work in advanced mathematics. (Contains 43 footnotes.).
A Mathematical Bridge
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Author : Stephen Fletcher Hewson
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2009-01
A Mathematical Bridge written by Stephen Fletcher Hewson and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01 with Education categories.
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.