An Accompaniment to Higher Mathematics

Author: George R. Exner

Publisher: Springer Science & Business Media

ISBN: 1461239982

Category: Mathematics

Page: 200

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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.
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Analysis by Its History

Author: Ernst Hairer,Gerhard Wanner

Publisher: Springer Science & Business Media

ISBN: 0387770313

Category: Mathematics

Page: 382

View: 9933

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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.
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The Nuts and Bolts of Proofs

An Introduction to Mathematical Proofs

Author: Antonella Cupillari

Publisher: Academic Press

ISBN: 0080537901

Category: Mathematics

Page: 192

View: 5847

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The Nuts and Bolts of Proof instructs students on the basic logic of mathematical proofs, showing how and why proofs of mathematical statements work. It provides them with techniques they can use to gain an inside view of the subject, reach other results, remember results more easily, or rederive them if the results are forgotten.A flow chart graphically demonstrates the basic steps in the construction of any proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems. * The "List of Symbols" has been extended. * Set Theory section has been strengthened with more examples and exercises. * Addition of "A Collection of Proofs"
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Undergraduate Algebra

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 0387220259

Category: Mathematics

Page: 389

View: 8148

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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
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Calculus of Several Variables

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 1461210682

Category: Mathematics

Page: 619

View: 2168

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This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.
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Introduction to Calculus and Classical Analysis

Author: Omar Hijab

Publisher: Springer Science & Business Media

ISBN: 0387693165

Category: Mathematics

Page: 342

View: 7074

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Intended for an honors calculus course or for an introduction to analysis, this is an ideal text for undergraduate majors since it covers rigorous analysis, computational dexterity, and a breadth of applications. The book contains many remarkable features: * complete avoidance of /epsilon-/delta arguments by using sequences instead * definition of the integral as the area under the graph, while area is defined for every subset of the plane * complete avoidance of complex numbers * heavy emphasis on computational problems * applications from many parts of analysis, e.g. convex conjugates, Cantor set, continued fractions, Bessel functions, the zeta functions, and many more * 344 problems with solutions in the back of the book.
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Computing the Continuous Discretely

Integer-point Enumeration in Polyhedra

Author: Matthias Beck,Sinai Robins

Publisher: Springer Science & Business Media

ISBN: 0387461124

Category: Mathematics

Page: 227

View: 3473

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This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. We encounter here a friendly invitation to the field of "counting integer points in polytopes", and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant.
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Introduction to Cryptography

Author: Johannes Buchmann

Publisher: Springer Verlag

ISBN: 9780387950341

Category: Computers

Page: 281

View: 5025

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A text written for students with only basic mathematical knowledge interested in the science of cryptography. Explains the basic methods, showing how to crack electronic codes, how to measure the efficiency and security of a code, and understand the basic techniques. DLC: Coding theory.
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Newsletter

Author: New Zealand Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 7918

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