An Introduction to Wavelets Through Linear Algebra

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Author: M.W. Frazier

Publisher: Springer

ISBN: 3642855709

Category: Mathematics

Page: 503

View: 646

Mathematics majors at Michigan State University take a "Capstone" course near the end of their undergraduate careers. The content of this course varies with each offering. Its purpose is to bring together different topics from the undergraduate curriculum and introduce students to a developing area in mathematics. This text was originally written for a Capstone course. Basic wavelet theory is a natural topic for such a course. By name, wavelets date back only to the 1980s. On the boundary between mathematics and engineering, wavelet theory shows students that mathematics research is still thriving, with important applications in areas such as image compression and the numerical solution of differential equations. The author believes that the essentials of wavelet theory are sufficiently elementary to be taught successfully to advanced undergraduates. This text is intended for undergraduates, so only a basic background in linear algebra and analysis is assumed. We do not require familiarity with complex numbers and the roots of unity.

Analysis by Its History

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Author: Ernst Hairer,Gerhard Wanner

Publisher: Springer Science & Business Media

ISBN: 0387770313

Category: Mathematics

Page: 382

View: 2114

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.

Undergraduate Algebra

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Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 1475768982

Category: Mathematics

Page: 371

View: 3597

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

Calculus of Several Variables

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Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 1461210682

Category: Mathematics

Page: 619

View: 414

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.

An Introduction to Wavelet Analysis

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Author: David F. Walnut

Publisher: Springer Science & Business Media

ISBN: 1461200016

Category: Computers

Page: 452

View: 5972

This book provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and analysis of wavelet bases. It motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, then shows how a more abstract approach allows readers to generalize and improve upon the Haar series. It then presents a number of variations and extensions of Haar construction.

Introduction to Calculus and Classical Analysis

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Author: Omar Hijab

Publisher: Springer Science & Business Media

ISBN: 0387693165

Category: Mathematics

Page: 342

View: 748

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.

Computing the Continuous Discretely

Integer-point Enumeration in Polyhedra

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Author: Matthias Beck,Sinai Robins

Publisher: Springer Science & Business Media

ISBN: 0387461124

Category: Mathematics

Page: 227

View: 7385

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.

An Introduction to Difference Equations

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Author: Saber Elaydi

Publisher: Springer Verlag

ISBN: 9780387988306

Category: Mathematics

Page: 427

View: 826

This book integrates both classical and modern treatments of difference equations. It contains the most updated material as well as a large set of applications to a variety of disciplines. Scientists and engineers who are interested in discrete mathematical models will find it useful as a reference. The presentation is also simple enough for use by advanced undergraduates. This second edition includes new sections on applications to mathematical biology, Birkhoff's theory, continued fractions and orthogonal polynomials, and many revised exercises.

Introduction to Cryptography

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Author: Johannes Buchmann

Publisher: Springer Verlag

ISBN: 9780387950341

Category: Computers

Page: 281

View: 4397

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.