This text is intended to provide graduate and advanced undergraduate students as well as the general mathematical public with a modern treatment of various theorems and examples in mathematics. A carefully arranged mixture of theorems, examples, exercises, hints and discussions sharpens and highlights many of the fundamental aspects of the subject matter, and constitutes a rounding out and elaboration of the standard parts of algebra, analysis, geometry, logic, probability, set theory, and topology. Essentially self-contained, the book presents this material with a treatment sensitive to the progress mathematics has made in the last 25 years.
Theorems and Counterexamples in Mathematics
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Inside This Book
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First Sentence:
By definition a group is a nonempty set G and a map G x G {x, y} xy G subject to the following axioms: i. If x, y, z G then x(yz) = (xy)z (associativity). Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Axiom of Choice, Topological Algebras Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
By definition a group is a nonempty set G and a map G x G {x, y} xy G subject to the following axioms: i. If x, y, z G then x(yz) = (xy)z (associativity). Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Axiom of Choice, Topological Algebras Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 19
books:
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18
books
cite this book:
See all 18 books citing this book
- Real Analysis by Andrew M. Bruckner in Back Matter
- Unsolved Problems in Number Theory (Problem Books in Mathematics / Unsolved Problems in Intuitive Mathematics) by Richard Guy in Front Matter
- Exercises in Integration (Problem Books in Mathematics) by C. George in Front Matter
- Algebraic Logic (Problem Books in Mathematics) by Semen G. Gindikin in Front Matter
- An Outline of Set Theory (Problem Books in Mathematics) by James M. Henle in Front Matter
See all 19 books this book cites
- Problems in Mathematical Analysis II (Student Mathematical Library, Vol. 12) by W. J. Kaczor in Back Matter
- Problems and Theorems in Classical Set Theory (Problem Books in Mathematics) by Peter Komjath in Back Matter
- A Dictionary of Inequalities by Peter Bullen in Back Matter
- Unsolved Problems in Number Theory (Problem Books in Mathematics / Unsolved Problems in Intuitive Mathematics) by Richard Guy in Front Matter
- Problems in Mathematical Analysis III (Student Mathematical Library) by W. J. Kaczor in Back Matter
See all 18 books citing this book
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