An Introduction To Basis Theory
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Author | : Christopher Heil |
Publisher | : Springer Science & Business Media |
Total Pages | : 549 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 0817646868 |
This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses. The self-contained presentation with clear proofs is accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications.
Author | : Matthew Katz |
Publisher | : American Mathematical Soc. |
Total Pages | : 224 |
Release | : 2018-10-03 |
Genre | : Mathematics |
ISBN | : 1470442906 |
This book takes the reader on a journey through Ramsey theory, from graph theory and combinatorics to set theory to logic and metamathematics. Written in an informal style with few requisites, it develops two basic principles of Ramsey theory: many combinatorial properties persist under partitions, but to witness this persistence, one has to start with very large objects. The interplay between those two principles not only produces beautiful theorems but also touches the very foundations of mathematics. In the course of this book, the reader will learn about both aspects. Among the topics explored are Ramsey's theorem for graphs and hypergraphs, van der Waerden's theorem on arithmetic progressions, infinite ordinals and cardinals, fast growing functions, logic and provability, Gödel incompleteness, and the Paris-Harrington theorem. Quoting from the book, “There seems to be a murky abyss lurking at the bottom of mathematics. While in many ways we cannot hope to reach solid ground, mathematicians have built impressive ladders that let us explore the depths of this abyss and marvel at the limits and at the power of mathematical reasoning at the same time. Ramsey theory is one of those ladders.”
Author | : Tom Leinster |
Publisher | : Cambridge University Press |
Total Pages | : 193 |
Release | : 2014-07-24 |
Genre | : Mathematics |
ISBN | : 1107044243 |
A short introduction ideal for students learning category theory for the first time.
Author | : Andre Weil |
Publisher | : Springer Science & Business Media |
Total Pages | : 340 |
Release | : 1995-02-15 |
Genre | : Mathematics |
ISBN | : 9783540586555 |
From the reviews: "L.R. Shafarevich showed me the first edition [...] and said that this book will be from now on the book about class field theory. In fact it is by far the most complete treatment of the main theorems of algebraic number theory, including function fields over finite constant fields, that appeared in book form." Zentralblatt MATH
Author | : Richard Ryan |
Publisher | : Guilford Publications |
Total Pages | : 770 |
Release | : 2018-11-06 |
Genre | : Psychology |
ISBN | : 1462538967 |
"Among the most influential models in contemporary behavioral science, self-determination theory (SDT) offers a broad framework for understanding the factors that promote human motivation and psychological flourishing. In this authoritative work, SDT cofounders Richard M. Ryan and Edward L. Deci systematically review the theory's conceptual underpinnings, empirical evidence base, and practical applications across the lifespan. Ryan and Deci demonstrate that supporting people's basic needs for competence, relatedness, and autonomy is critically important for virtually all aspects of individual and societal functioning."--Jacket.
Author | : Ralph Blumenhagen |
Publisher | : Springer Science & Business Media |
Total Pages | : 787 |
Release | : 2012-10-03 |
Genre | : Science |
ISBN | : 3642294979 |
The purpose of this book is to thoroughly prepare the reader for research in string theory at an intermediate level. As such it is not a compendium of results but intended as textbook in the sense that most of the material is organized in a pedagogical and self-contained fashion. Beyond the basics, a number of more advanced topics are introduced, such as conformal field theory, superstrings and string dualities - the text does not cover applications to black hole physics and cosmology, nor strings theory at finite temperatures. End-of-chapter references have been added to guide the reader wishing to pursue further studies or to start research in well-defined topics covered by this book.
Author | : Nikolai Konstantinovich Vereshchagin |
Publisher | : American Mathematical Soc. |
Total Pages | : 130 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821827316 |
The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment. This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of ``naive'' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.
Author | : Charles M. Quinn |
Publisher | : Elsevier |
Total Pages | : 246 |
Release | : 2002-02-28 |
Genre | : Science |
ISBN | : 0080488536 |
Computational Quantum Chemistry removes much of the mystery of modern computer programs for molecular orbital calculations by showing how to develop Excel spreadsheets to perform model calculations and investigate the properties of basis sets. Using the book together with the CD-ROM provides a unique interactive learning tool. In addition, because of the integration of theory with working examples on the CD-ROM, the reader can apply advanced features available in the spreadsheet to other applications in chemistry, physics, and a variety of disciplines that require the solution of differential equations.This book and CD-ROM makes a valuable companion for instructors, course designers, and students. It is suitable for direct applications in practical courses in theoretical chemistry and atomic physics, as well as for teaching advanced features of Excel in IT courses.
Author | : JV Stone |
Publisher | : Sebtel Press |
Total Pages | : 243 |
Release | : 2015-01-01 |
Genre | : Business & Economics |
ISBN | : 0956372856 |
Originally developed by Claude Shannon in the 1940s, information theory laid the foundations for the digital revolution, and is now an essential tool in telecommunications, genetics, linguistics, brain sciences, and deep space communication. In this richly illustrated book, accessible examples are used to introduce information theory in terms of everyday games like ‘20 questions’ before more advanced topics are explored. Online MatLab and Python computer programs provide hands-on experience of information theory in action, and PowerPoint slides give support for teaching. Written in an informal style, with a comprehensive glossary and tutorial appendices, this text is an ideal primer for novices who wish to learn the essential principles and applications of information theory.
Author | : Atle Ottesen Søvik |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 509 |
Release | : 2022-04-04 |
Genre | : Philosophy |
ISBN | : 3110771047 |
What are the basic building blocks of the world? This book presents a naturalistic theory saying that the universe and everything in it can be reduced to three fundamental entities: a field, a set of values that can be actualized at different places in the field, and an actualizer of the values. The theory is defended by using it to answer the main questions in metaphysics, such as: What is causality, existence, laws of nature, consciousness, thinking, free will, time, mathematical entities, ethical values, etc.? The theory is compared with the main alternatives and argued to solve problems better than the existing theories. Several new theories are suggested, such as how to understand mental causation, free will and the truth of ethics and mathematics.