Search Results for "understanding-analysis-undergraduate-texts-in-mathematics"

Understanding Analysis

Understanding Analysis

  • Author: Stephen Abbott
  • Publisher: Springer Science & Business Media
  • ISBN: 0387215069
  • Category: Mathematics
  • Page: 260
  • View: 3427
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This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.

Analysis by Its History

Analysis by Its History

  • Author: Ernst Hairer,Gerhard Wanner
  • Publisher: Springer Science & Business Media
  • ISBN: 0387770313
  • Category: Mathematics
  • Page: 382
  • View: 2651
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This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.

A Problem Book in Real Analysis

A Problem Book in Real Analysis

  • Author: Asuman G. Aksoy,Mohamed A. Khamsi
  • Publisher: Springer Science & Business Media
  • ISBN: 1441912967
  • Category: Mathematics
  • Page: 254
  • View: 8032
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Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.

Real Mathematical Analysis

Real Mathematical Analysis

  • Author: Charles C. Pugh
  • Publisher: Springer Science & Business Media
  • ISBN: 9780387952970
  • Category: Mathematics
  • Page: 440
  • View: 8792
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Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.

Undergraduate Algebra

Undergraduate Algebra

  • Author: Serge Lang
  • Publisher: Springer Science & Business Media
  • ISBN: 0387220259
  • Category: Mathematics
  • Page: 389
  • View: 3625
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The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group

Elementary Analysis

Elementary Analysis

The Theory of Calculus

  • Author: Kenneth A. Ross
  • Publisher: Springer Science & Business Media
  • ISBN: 1461462711
  • Category: Mathematics
  • Page: 412
  • View: 2262
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For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging. The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions.

Newsletter

Newsletter

  • Author: New Zealand Mathematical Society
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 5439
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Real and Functional Analysis

Real and Functional Analysis

  • Author: Serge Lang
  • Publisher: Springer Science & Business Media
  • ISBN: 1461208971
  • Category: Mathematics
  • Page: 580
  • View: 9731
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This book is meant as a text for a first-year graduate course in analysis. In a sense, it covers the same topics as elementary calculus but treats them in a manner suitable for people who will be using it in further mathematical investigations. The organization avoids long chains of logical interdependence, so that chapters are mostly independent. This allows a course to omit material from some chapters without compromising the exposition of material from later chapters.

The Real Numbers and Real Analysis

The Real Numbers and Real Analysis

  • Author: Ethan D. Bloch
  • Publisher: Springer Science & Business Media
  • ISBN: 0387721762
  • Category: Mathematics
  • Page: 554
  • View: 8823
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This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.