Towards Higher Mathematics: A Companion


Author: Richard Earl
Publisher: Cambridge University Press
ISBN: 1107162386
Category: Mathematics
Page: 536
View: 1940

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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.

Towards Higher Mathematics: A Companion


Author: Richard Earl
Publisher: Cambridge University Press
ISBN: 1108326382
Category: Mathematics
Page: N.A
View: 7660

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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.

Towards Higher Mathematics: A Companion


Author: Richard Earl
Publisher: Cambridge University Press
ISBN: 9781316614839
Category: Mathematics
Page: 536
View: 960

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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.

How to Think Like a Mathematician

A Companion to Undergraduate Mathematics
Author: Kevin Houston
Publisher: Cambridge University Press
ISBN: 9781139477055
Category: Mathematics
Page: N.A
View: 7765

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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.

Concepts of Modern Mathematics


Author: Ian Stewart
Publisher: Courier Corporation
ISBN: 0486134954
Category: Mathematics
Page: 368
View: 7812

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In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.

Closing the Gap

The Quest to Understand Prime Numbers
Author: Vicky Neale
Publisher: Oxford University Press
ISBN: 0191092436
Category: Mathematics
Page: 208
View: 2740

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In 2013, a little known mathematician in his late 50s stunned the mathematical community with a breakthrough on an age-old problem about prime numbers. Since then, there has been further dramatic progress on the problem, thanks to the efforts of a large-scale online collaborative effort of a type that would have been unthinkable in mathematics a couple of decades ago, and the insight and creativity of a young mathematician at the start of his career. Prime numbers have intrigued, inspired and infuriated mathematicians for millennia. Every school student studies prime numbers and can appreciate their beauty, and yet mathematicians' difficulty with answering some seemingly simple questions about them reveals the depth and subtlety of prime numbers. Vicky Neale charts the recent progress towards proving the famous Twin Primes Conjecture, and the very different ways in which the breakthroughs have been made: a solo mathematician working in isolation and obscurity, and a large collaboration that is more public than any previous collaborative effort in mathematics and that reveals much about how mathematicians go about their work. Interleaved with this story are highlights from a significantly older tale, going back two thousand years and more, of mathematicians' efforts to comprehend the beauty and unlock the mysteries of the prime numbers.

Curvature in Mathematics and Physics


Author: Shlomo Sternberg
Publisher: Courier Corporation
ISBN: 0486292711
Category: Mathematics
Page: 416
View: 3571

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Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.

The Princeton Companion to Applied Mathematics


Author: Nicholas J. Higham
Publisher: Princeton University Press
ISBN: 1400874475
Category: Mathematics
Page: 1016
View: 4063

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This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index

Advanced Problems in Mathematics

Preparing for University
Author: Stephen Siklos
Publisher: Open Book Publishers
ISBN: 1783741449
Category: Mathematics
Page: 186
View: 1598

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This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers). STEP examinations are used by Cambridge colleges as the basis for conditional offers in mathematics and sometimes in other mathematics-related subjects. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on past papers to become accustomed to university-style mathematics. Advanced Problems in Mathematics is recommended as preparation for any undergraduate mathematics course, even for students who do not plan to take the Sixth Term Examination Paper. The questions analysed in this book are all based on recent STEP questions selected to address the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions. Each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anybody interested in advanced mathematics.

The Cambridge Companion to the Age of Justinian


Author: Michael Maas
Publisher: Cambridge University Press
ISBN: 1139826875
Category: History
Page: N.A
View: 6700

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This book introduces the Age of Justinian, the last Roman century and the first flowering of Byzantine culture. Dominated by the policies and personality of emperor Justinian I (527–565), this period of grand achievements and far-reaching failures witnessed the transformation of the Mediterranean world. In this volume, twenty specialists explore the most important aspects of the age including the mechanics and theory of empire, warfare, urbanism, and economy. It also discusses the impact of the great plague, the codification of Roman law, and the many religious upheavals taking place at the time. Consideration is given to imperial relations with the papacy, northern barbarians, the Persians, and other eastern peoples, shedding new light on a dramatic and highly significant historical period.

A First Course in Analysis


Author: John B. Conway
Publisher: Cambridge University Press
ISBN: 1107173140
Category: Mathematics
Page: 375
View: 1954

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This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the theorems of Green, Gauss, and Stokes. Minimal prerequisites are assumed, and relevant linear algebra topics are reviewed right before they are needed, making the material accessible to students from diverse backgrounds. Abstract topics are preceded by concrete examples to facilitate understanding, for example, before introducing differential forms, the text examines low-dimensional examples. The meaning and importance of results are thoroughly discussed, and numerous exercises of varying difficulty give students ample opportunity to test and improve their knowledge of this difficult yet vital subject.

The Cambridge Companion to Jane Austen


Author: Edward Copeland,Juliet McMaster
Publisher: Cambridge University Press
ISBN: 0521763088
Category: Literary Criticism
Page: 271
View: 3686

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A fully updated edition with seven brand new essays.

Mathematics for Physics

A Guided Tour for Graduate Students
Author: Michael Stone,Paul Goldbart
Publisher: Cambridge University Press
ISBN: 1139480618
Category: Science
Page: N.A
View: 3263

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An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.

Mathematics Rebooted

A Fresh Approach to Understanding
Author: Lara Alcock
Publisher: Oxford University Press
ISBN: 0192525948
Category: Mathematics
Page: 220
View: 6374

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Would you like to understand more mathematics? Many people would. Perhaps at school you liked mathematics for a while but were then put off because you missed a key idea and kept getting stuck. Perhaps you always liked mathematics but gave it up because your main interest was music or languages or science or philosophy. Or perhaps you studied mathematics to advanced levels, but have now forgotten most of what you once knew. Whichever is the case, this book is for you. It aims to build on what you know, revisiting basic ideas with a focus on meaning. Each chapter starts with an idea from school mathematics - often primary school mathematics - and gradually builds up a network of links to more advanced material. It explores fundamental ideas in depth, using insights from research in mathematics education and psychology to explain why people often get confused, and how to overcome that confusion. For nervous readers, it will build confidence by clarifying basic ideas. For more experienced readers, it will highlight new connections to more advanced material. Throughout, the book explains how mathematicians think, and how ordinary people can understand and enjoy mathematical ideas and arguments. If you would like to be better informed about the intrinsic elegance of mathematics, this engaging guide is the place to start.

Mathematical Writing


Author: Franco Vivaldi
Publisher: Springer
ISBN: 1447165276
Category: Mathematics
Page: 204
View: 3403

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This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student. The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition. Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150 of them have complete solutions, to facilitate self-study. Mathematical Writing will be of interest to all mathematics students who want to raise the quality of their coursework, reports, exams, and dissertations.

How to Integrate It

A Practical Guide to Finding Elementary Integrals
Author: Seán M. Stewart
Publisher: Cambridge University Press
ISBN: 1108311148
Category: Mathematics
Page: N.A
View: 3781

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While differentiating elementary functions is merely a skill, finding their integrals is an art. This practical introduction to the art of integration gives readers the tools and confidence to tackle common and uncommon integrals. After a review of the basic properties of the Riemann integral, each chapter is devoted to a particular technique of elementary integration. Thorough explanations and plentiful worked examples prepare the reader for the extensive exercises at the end of each chapter. These exercises increase in difficulty from warm-up problems, through drill examples, to challenging extensions which illustrate such advanced topics as the irrationality of π and e, the solution of the Basel problem, Leibniz's series and Wallis's product. The author's accessible and engaging manner will appeal to a wide audience, including students, teachers and self-learners. The book can serve as a complete introduction to finding elementary integrals, or as a supplementary text for any beginning course in calculus.

The Cambridge Companion to Vygotsky


Author: Harry Daniels,Michael Cole,James V. Wertsch
Publisher: Cambridge University Press
ISBN: 1107494834
Category: Psychology
Page: 474
View: 8740

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L. S. Vygotsky was an early-twentieth-century Russian social theorist whose writing exerts a significant influence on the development of social theory in the early-twenty-first century. His non-deterministic, non-reductionist account of the formation of mind provides current theoretical developments with a broadly drawn yet very powerful sketch of the ways in which humans shape and are shaped by social, cultural, and historical conditions. This dialectical conception of development insists on the importance of genetic or developmental analysis at several levels. The Cambridge Companion to Vygotsky is a comprehensive text that provides students, academics, and practitioners with a critical perspective on Vygotsky and his work.

The Mathematics Lover's Companion

Masterpieces for Everyone
Author: Edward R. Scheinerman
Publisher: Yale University Press
ISBN: 0300223005
Category: Mathematics
Page: 296
View: 6173

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Twenty-three mathematical masterpieces for exploration and enlightenment

Mathematics


Author: Timothy Gowers
Publisher: Sterling Publishing Company, Inc.
ISBN: 9781402768972
Category: Mathematics
Page: 180
View: 2030

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Mathematics is a subject we are all exposed to in our daily lives, but one that many of us fear. Timothy Gowers’s entertaining overview of the topic explains the differences between what we learn at school and advanced mathematics, and helps the math phobic emerge with a clearer understanding of such paradoxical-sounding concepts as “infinity,” “curved space,” and “imaginary numbers.” From basic ideas to philosophical queries to common sociological questions about the mathematical community, this book unravels the mysteries of space and numbers.

Symmetry

An Introduction to Group Theory and Its Applications
Author: R. McWeeny
Publisher: Elsevier
ISBN: 1483226247
Category: Mathematics
Page: 262
View: 2183

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Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.