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High Quality Content by WIKIPEDIA articles! Wac?aw Franciszek Sierpi?skov (Russian: ?vatswaf fra??t?i??k ??r?p?i?sk?i) (March 14, 1882, Moscow ? October 21, 1969, Warsaw) was a Polish-Russian mathematician. He was known for outstanding contributions to set theory (research on the axiom of choice and the continuum hypothesis), number theory, theory of functions and topology. He published over 700 papers and 50 books. Three well-known fractals are named after him (the Sierpinski triangle, the Sierpinski carpet and the Sierpinski curve), as are Sierpinski numbers and the associated Sierpi?ski problem. ... Read more

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High Quality Content by WIKIPEDIA articles! In the mathematical discipline of general topology, Stone??ech compactification is a technique for constructing a universal map from a topological space X to a compact Hausdorff space ?X. The Stone??ech compactification ?X of a topological space X is the largest compact Hausdorff space "generated" by X, in the sense that any map from X to a compact Hausdorff space factors through ?X. If X is a Tychonoff space then the map from X to its image in ?X is a homeomorphism, so X can be thought of as a subspace of ?X. For general topological spaces X, the map from X to ?X need not be injective. ... Read more

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This book is an introduction into modern cardinal arithmetic in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice (ZFC). A first part describes the classical theory developed by Bernstein, Cantor, Hausdorff, König and Tarski between 1870 and 1930. Next, the development in the 1970s led by Galvin, Hajnal and Silver is characterized. The third part presents the fundamental investigations in pcf theory which have been worked out by Shelah to answer the questions left open in the 1970s.

Reviews:

"The authors aim their text at beginners in set theory. They start literally from the axioms and prove everything they need. The result is an extremely useful text and reference book which is also very pleasant to read." - The Bulletin of Symbolic Logic

"The book should be required reading for every advanced graduate student of set theory. Several courses at various levels could be based on the earlier chapters. There is a useful set of exercises at the end of most sections in the first four chapters." - Mathematical Reviews

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Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics.

In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces ordinals and cardinals, transfinite induction, the axiom of choice, Zorn’s lemma, empirical induction, and fallacies and induction. He also explains how to write inductive proofs.

The next part contains more than 750 exercises that highlight the levels of difficulty of an inductive proof, the variety of inductive techniques available, and the scope of results provable by mathematical induction. Each self-contained chapter in this section includes the necessary definitions, theory, and notation and covers a range of theorems and problems, from fundamental to very specialized.

The final part presents either solutions or hints to the exercises. Slightly longer than what is found in most texts, these solutions provide complete details for every step of the problem-solving process.

Customer Reviews (3)

A "must have" for everyone whose passion lies in the mathematics!
This book quickly became one of my favorites for it's richness of the examples from all fields of mathematics, ranging from number theory to probability and statistics.
Not only does it provide you with the huge armory for being able to tackle very tricky mathematical statements, it also has a good introduction to each field with needed theorems and proofs.
Also, author's great sense of humor make the book even more enjoyable to read! It is an absolutely "must have" for anyone, who call himself a mathgeek.

Fantastic resource!
This book covers a phenomenal amount of material on the many uses of mathematical induction: from identities, inequalities and sequences, to number theory, set theory, topology, logic, graph theory, recursion, algebra, geometry, probability and many more.

I think this book would make a great resource for any student of mathematics, not only for the wealth of problems (and solutions), but also for the chapters on how to write a proof by mathematical induction and as a guide to common proof techniques.The first part also contains fascinating chapters on the history and theory of induction that provide a detailed exposition of the set theory underlying the principle of mathematical induction.

Working mathematicians and instructors will also find this book amazingly useful, as both a sourcebook of problems and background when teaching mathematical induction and as a reference for the proofs of a huge number of useful theorems in each of the subjects that are covered.

Not a Handbook
Not a Handbook.
Highly disorganized collection of problems and solutions.
Problems scattered through the book.
Solutions in remote pages. ... Read more

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With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and up-to-date treatments of the Hahn–Banach theorem. This edition explores the theorem’s connection with the axiom of choice, discusses the uniqueness of Hahn–Banach extensions, and includes an entirely new chapter on vector-valued Hahn–Banach theorems. It also considers different approaches to the Banach–Stone theorem as well as variations of the theorem.

The book covers locally convex spaces; barreled, bornological, and webbed spaces; and reflexivity. It traces the development of various theorems from their earliest beginnings to present day, providing historical notes to place the results in context. The authors also chronicle the lives of key mathematicians, including Stefan Banach and Eduard Helly.

Suitable for both beginners and experienced researchers, this book contains an abundance of examples, exercises of varying levels of difficulty with many hints, and an extensive bibliography and index.

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We prove that the Continuum Hypothesis is equivalent to the Axiom of Choice. Thus, the Negation of the Continuum Hypothesis, is equivalent to the Negation of the Axiom of Choice.The Non-Cantorian Axioms impose a Non-Cantorian definition of cardinality, that is different from Cantors cardinality imposed by the Cantorian Axioms.The Non-Cantorian Theory is the Zermelo-Fraenkel Theory with the Negation of the Axiom of Choice, and with the Negation of the Continuum Hypothesis. This Theory has distinct infinities.ISBN 0980128714ISBN-13 9780980128710 ... Read more

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This digital document is an article from Quarterly Journal of Business and Economics, published by University of Nebraska-Lincoln on September 22, 1989. The length of the article is 4390 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: An experimental study of the Allais paradox over losses: some preliminary evidence.
Author: Don N. MacDonald
Publication: Quarterly Journal of Business and Economics (Refereed)
Date: September 22, 1989
Publisher: University of Nebraska-Lincoln
Volume: v28Issue: n4Page: p43(18)

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Product Description
This digital document is an article from University of Pennsylvania Law Review, published by University of Pennsylvania, Law School on June 1, 1998. The length of the article is 8902 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

From the supplier: Debates on commensurability and incommensurability along with comparability and incomparability and their resulting answers will always be insufficient guides to proper decisionmaking. The most important element to consider when approaching matters of how to make proper decisions is the viewpoint toward the matters and the decisions to be made. Dispositions toward attitudes and viewpoints themselves can be instrumental reasons in decisionmaking.

Citation Details
Title: Instrumental commensurability.(Symposium: Law and Incommensurability)
Author: Frederick Schauer
Publication: University of Pennsylvania Law Review (Refereed)
Date: June 1, 1998
Publisher: University of Pennsylvania, Law School
Volume: 146Issue: n5Page: 1215-1233

Distributed by Thomson Gale ... Read more