Yves Nievergelt – författare

Originally published in 1999, Wavelets Made Easy offers a lucid and concise explanation of mathematical wavelets.  Written at the level of a first course in calculus and linear algebra, its accessible presentation is designed for undergraduates in a variety of disciplines—computer science, engineering, mathematics, mathematical sciences—as well as for practicing professionals in these areas. 

The present softcover reprint retains the corrections from the second printing (2001) and makes this unique text available to a wider audience. The first chapter starts with a description of the key features and applications of wavelets, focusing on Haar''s wavelets but using only high-school mathematics. The next two chapters introduce one-, two-, and three-dimensional wavelets, with only the occasional use of matrix algebra.

The second part of this book provides the foundations of least-squares approximation, the discrete Fourier transform, and Fourier series. The third part explains the Fourier transform and then demonstrates how to apply basic Fourier analysis to designing and analyzing mathematical wavelets. Particular attention is paid to Daubechies wavelets.

Numerous exercises, a bibliography, and a comprehensive index combine to make this book an excellent text for the classroom as well as a valuable resource for self-study.

This text for the first or second year undergraduate in mathematics, logic, computer science, or social sciences, introduces the reader to logic, proofs, sets, and number theory. It also serves as an excellent independent study reference and resource for instructors. Adapted from Foundations of Logic and Mathematics: Applications to Science and Cryptography © 2002 Birkhӓuser, this second edition provides a modern introduction to the foundations of logic, mathematics, and computers science, developing the theory that demonstrates construction of all mathematics and theoretical computer science from logic and set theory.  The focuses is on foundations, with specific statements of all the associated axioms and rules of logic and set theory, and  provides complete details and derivations of formal proofs. Copious references to literature that document historical development is also provided.

Answers are found to many questions that usually remain unanswered: Why is the truth table for logical implication so unintuitive? Why are there no recipes to design proofs? Where do these numerous mathematical rules come from? What issues in logic, mathematics, and computer science still remain unresolved? And the perennial question: In what ways are we going to use this material?   Additionally, the selection of topics presented reflects many major accomplishments from the twentieth century and includes applications in game theory and Nash''s

From the reviews of the first edition:

"...All the results are proved in full detail from first principles...remarkably, the arithmetic laws on the rational numbers are proved, step after step, starting from the very definitions!...This is a valuable reference text and a useful companion for anybody wondering how basic mathematical concepts can be rigorously developed within set theory."

—MATHEMATICAL REVIEWS

 "Rigorous and modern in its theoretical aspect, attractive as a detective novel in its applied aspects, this paper book deserves the attention of both beginners and advanced students in mathematics, logic and computer sciences as well as in social sciences."

—Zentralblatt MATH