Towards Higher Mathematics A Companion
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Towards Higher Mathematics A Companion
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Author : Richard Earl
language : en
Publisher: Cambridge University Press
Release Date : 2017-09-07
Towards Higher Mathematics A Companion written by Richard Earl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-07 with Mathematics categories.
This book allows students to stretch their mathematical abilities and bridges the gap between school and university.
Topology
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Author : Richard Earl
language : en
Publisher: Oxford University Press, USA
Release Date : 2020-01-11
Topology written by Richard Earl and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-11 with MATHEMATICS categories.
How is a subway map different from other maps? What makes a knot knotted? What makes the M�bius strip one-sided? These are questions of topology, the mathematical study of properties preserved by twisting or stretching objects. In the 20th century topology became as broad and fundamental as algebra and geometry, with important implications for science, especially physics. In this Very Short Introduction Richard Earl gives a sense of the more visual elements of topology (looking at surfaces) as well as covering the formal definition of continuity. Considering some of the eye-opening examples that led mathematicians to recognize a need for studying topology, he pays homage to the historical people, problems, and surprises that have propelled the growth of this field. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Mathematical Analysis A Very Short Introduction
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Author : Richard Earl
language : en
Publisher: Oxford University Press
Release Date : 2023-05-23
Mathematical Analysis A Very Short Introduction written by Richard Earl and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-23 with Mathematics categories.
Very Short Introductions: Brilliant, sharp, inspiring The 17th-century calculus of Newton and Leibniz was built on shaky foundations, and it wasn't until the 18th and 19th centuries that mathematicians—especially Bolzano, Cauchy, and Weierstrass—began to establish a rigorous basis for the subject. The resulting discipline is now known to mathematicians as analysis. This book, aimed at readers with some grounding in mathematics, describes the nascent evolution of mathematical analysis, its development as a subject in its own right, and its wide-ranging applications in mathematics and science, modelling reality from acoustics to fluid dynamics, from biological systems to quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Advanced Mathematics
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Author : Stanley J. Farlow
language : en
Publisher: John Wiley & Sons
Release Date : 2019-10-02
Advanced Mathematics written by Stanley J. Farlow and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-02 with Mathematics categories.
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.
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.
Progress To Higher Mathematics
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Author : Mary Teresa Fyfe
language : en
Publisher:
Release Date : 2007
Progress To Higher Mathematics written by Mary Teresa Fyfe and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
An Accompaniment To Higher Mathematics
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Author : George R. Exner
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-06-22
An Accompaniment To Higher Mathematics written by George R. Exner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-22 with Mathematics categories.
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.
How To Think Like A Mathematician
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Author : Kevin Houston
language : en
Publisher: Cambridge University Press
Release Date : 2009-02-12
How To Think Like A Mathematician written by Kevin Houston and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-12 with Mathematics categories.
Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.
Transition To Higher Mathematics
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Author : Bob A Dumas
language : en
Publisher:
Release Date : 2015
Transition To Higher Mathematics written by Bob A Dumas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
Oxford Ib Diploma Programme Mathematics Higher Level Statistics Course Companion
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Author : Marlene Torres-Skoumal
language : en
Publisher: Oxford University Press - Children
Release Date : 2014-11-13
Oxford Ib Diploma Programme Mathematics Higher Level Statistics Course Companion written by Marlene Torres-Skoumal and has been published by Oxford University Press - Children this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-13 with Mathematics categories.
Written by experienced IB workshop leaders and curriculum developers, this book covers all the course content and essential practice needed for success in the Statistics Option for Higher Level. Enabling a truly IB approach to mathematics, real-world context is thoroughly blended with mathematical applications, supporting deep understanding and instilling confident mathematical thinking skills. Exam support is integrated, building assessment potential. Directly linked to the Oxford Higher Level Course Book, naturally extending learning Drive a truly IB approach to mathematics, helping learners connect mathematical theory with the world around them The most comprehensive, accurately matched to the most recent syllabus, written by experienced workshop leaders Build essential mathematical skills with extensive practice enabling confident skills-development Cement assessment potential, with examiner guidance and exam questions driving confidence in every topic Complete worked solutions included online