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A Course in Advanced Calculus

A Course in Advanced Calculus
Author: Robert S. Borden
Publisher: Courier Corporation
Total Pages: 421
Release: 2012-09-11
Genre: Mathematics
ISBN: 0486150380

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This remarkable undergraduate-level text offers a study in calculus that simultaneously unifies the concepts of integration in Euclidean space while at the same time giving students an overview of other areas intimately related to mathematical analysis. The author achieves this ambitious undertaking by shifting easily from one related subject to another. Thus, discussions of topology, linear algebra, and inequalities yield to examinations of innerproduct spaces, Fourier series, and the secret of Pythagoras. Beginning with a look at sets and structures, the text advances to such topics as limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, and more. Carefully chosen problems appear at the end of each chapter, and this new edition features an additional appendix of tips and solutions for selected problems.


A Mathematics Course for Political and Social Research

A Mathematics Course for Political and Social Research
Author: Will H. Moore
Publisher: Princeton University Press
Total Pages: 450
Release: 2013-08-11
Genre: Political Science
ISBN: 0691159173

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Political science and sociology increasingly rely on mathematical modeling and sophisticated data analysis, and many graduate programs in these fields now require students to take a "math camp" or a semester-long or yearlong course to acquire the necessary skills. Available textbooks are written for mathematics or economics majors, and fail to convey to students of political science and sociology the reasons for learning often-abstract mathematical concepts. A Mathematics Course for Political and Social Research fills this gap, providing both a primer for math novices in the social sciences and a handy reference for seasoned researchers. The book begins with the fundamental building blocks of mathematics and basic algebra, then goes on to cover essential subjects such as calculus in one and more than one variable, including optimization, constrained optimization, and implicit functions; linear algebra, including Markov chains and eigenvectors; and probability. It describes the intermediate steps most other textbooks leave out, features numerous exercises throughout, and grounds all concepts by illustrating their use and importance in political science and sociology. Uniquely designed and ideal for students and researchers in political science and sociology Uses practical examples from political science and sociology Features "Why Do I Care?" sections that explain why concepts are useful Includes numerous exercises Complete online solutions manual (available only to professors, email david.siegel at duke.edu, subject line "Solution Set") Selected solutions available online to students


A Course of Modern Analysis

A Course of Modern Analysis
Author: E.T. Whittaker
Publisher: Courier Dover Publications
Total Pages: 624
Release: 2020-07-15
Genre: Mathematics
ISBN: 048684286X

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Historic text by two great mathematicians consists of two parts, The Processes of Analysis and The Transcendental Functions. Geared toward students of analysis and historians of mathematics. 1920 third edition.


A Course of Pure Mathematics

A Course of Pure Mathematics
Author: G. H. Hardy
Publisher: Cambridge University Press
Total Pages: 21
Release: 2008-03-13
Genre: Mathematics
ISBN: 1139643517

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There are few textbooks of mathematics as well-known as Hardy's Pure Mathematics. Since its publication in 1908, this classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of the missionary with the rigour of the purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit. Celebrating 100 years in print with Cambridge, this edition includes a Foreword by T. W. Körner, describing the huge influence the book has had on the teaching and development of mathematics worldwide. Hardy's presentation of mathematical analysis is as valid today as when first written: students will find that his economical and energetic style of presentation is one that modern authors rarely come close to.


A Course in Pure Mathematics

A Course in Pure Mathematics
Author: Margaret Gow
Publisher: Elsevier
Total Pages: 636
Release: 1960
Genre: Mathematics
ISBN: 9780340052174

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For students reading Mathematics, either as part of a general degree or as an ancilliary course for an Honours degree, the subject should be presented in as straightforward a manners as is consistent with a moderate standard of rigour. This course in algebra, co-ordinate geometry and calculus is designed to fulfil these requirements for students at Universities, Polytechnics and Colleges of Technology. The book contains 350 worked examples and 1550 practice examples selected mainly from university examination papers. The practice examples have been carefully graded and some hints are given with the answers so that the book may be used for private study as well as for class work.


A Course on Group Theory

A Course on Group Theory
Author: John S. Rose
Publisher: Courier Corporation
Total Pages: 322
Release: 2013-05-27
Genre: Mathematics
ISBN: 0486170667

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Text for advanced courses in group theory focuses on finite groups, with emphasis on group actions. Explores normal and arithmetical structures of groups as well as applications. 679 exercises. 1978 edition.


A Foundation Course in Mathematics

A Foundation Course in Mathematics
Author: Ajit Kumar
Publisher:
Total Pages: 148
Release: 2018-04-30
Genre: Mathematics
ISBN: 9781783323586

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Written in a conversational style to impart critical and analytical thinking which will be beneficial for students of any discipline. It also gives emphasis on problem solving and proof writing skills, key aspects of learning mathematics.


A First Course in Applied Mathematics

A First Course in Applied Mathematics
Author: Jorge Rebaza
Publisher: John Wiley & Sons
Total Pages: 458
Release: 2012-04-24
Genre: Mathematics
ISBN: 1118277155

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Explore real-world applications of selected mathematical theory, concepts, and methods Exploring related methods that can be utilized in various fields of practice from science and engineering to business, A First Course in Applied Mathematics details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems. Written at a level that is accessible to readers from a wide range of scientific and engineering fields, the book masterfully blends standard topics with modern areas of application and provides the needed foundation for transitioning to more advanced subjects. The author utilizes MATLAB® to showcase the presented theory and illustrate interesting real-world applications to Google's web page ranking algorithm, image compression, cryptography, chaos, and waste management systems. Additional topics covered include: Linear algebra Ranking web pages Matrix factorizations Least squares Image compression Ordinary differential equations Dynamical systems Mathematical models Throughout the book, theoretical and applications-oriented problems and exercises allow readers to test their comprehension of the presented material. An accompanying website features related MATLAB® code and additional resources. A First Course in Applied Mathematics is an ideal book for mathematics, computer science, and engineering courses at the upper-undergraduate level. The book also serves as a valuable reference for practitioners working with mathematical modeling, computational methods, and the applications of mathematics in their everyday work.


A Course in Convexity

A Course in Convexity
Author: Alexander Barvinok
Publisher: American Mathematical Soc.
Total Pages: 378
Release: 2002-11-19
Genre: Mathematics
ISBN: 0821829688

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Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. The book will benefit both teacher and student: It is easy to understand, entertaining to the reader, and includes many exercises that vary in degree of difficulty. Overall, the author demonstrates the power of a few simple unifying principles in a variety of pure and applied problems. The prerequisites are minimal amounts of linear algebra, analysis, and elementary topology, plus basic computational skills. Portions of the book could be used by advanced undergraduates. As a whole, it is designed for graduate students interested in mathematical methods, computer science, electrical engineering, and operations research. The book will also be of interest to research mathematicians, who will find some results that are recent, some that are new, and many known results that are discussed from a new perspective.


A Transition to Advanced Mathematics

A Transition to Advanced Mathematics
Author: William Johnston
Publisher: Oxford University Press
Total Pages: 766
Release: 2009-07-27
Genre: Mathematics
ISBN: 0199718660

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A Transition to Advanced Mathematics: A Survey Course promotes the goals of a "bridge'' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-level mathematics courses (where they will have to prove theorems and grapple with mathematical abstractions). The text simultaneously promotes the goals of a ``survey'' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics, including Logic, Abstract Algebra, Number Theory, Real Analysis, Statistics, Graph Theory, and Complex Analysis. The main objective is "to bring about a deep change in the mathematical character of students -- how they think and their fundamental perspectives on the world of mathematics." This text promotes three major mathematical traits in a meaningful, transformative way: to develop an ability to communicate with precise language, to use mathematically sound reasoning, and to ask probing questions about mathematics. In short, we hope that working through A Transition to Advanced Mathematics encourages students to become mathematicians in the fullest sense of the word. A Transition to Advanced Mathematics has a number of distinctive features that enable this transformational experience. Embedded Questions and Reading Questions illustrate and explain fundamental concepts, allowing students to test their understanding of ideas independent of the exercise sets. The text has extensive, diverse Exercises Sets; with an average of 70 exercises at the end of section, as well as almost 3,000 distinct exercises. In addition, every chapter includes a section that explores an application of the theoretical ideas being studied. We have also interwoven embedded reflections on the history, culture, and philosophy of mathematics throughout the text.