Theodore G. Faticoni's Books

Categories of Modules over Endomorphism Rings

By: Theodore Gerard Faticoni

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Categories of Modules over Endomorphism Rings

By: Theodore Gerard Faticoni

It is the goal of the memoir to develop a functorial transfer of properties between [italic capital]A and [script capital]M[subscript italic capital]E, the category of modules over [italic capital]E, that is more sensitive than the traditional starting point, Hom([italic capital]A, ·). This memoir should be accessible to anyone who has a working knowledge of rings, modules, functors, and categories equivalent to that gained by reading Anderson and Fuller's text "Rings and Categories of Modules.

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Page Count

164

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821825542

ISBN 13

9780821825549

Direct Sum Decompositions of Torsion-Free Finite Rank Groups

By: Theodore G. Faticoni

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Direct Sum Decompositions of Torsion-Free Finite Rank Groups

By: Theodore G. Faticoni

With plenty of new material not found in other books, Direct Sum Decompositions of Torsion-Free Finite Rank Groups explores advanced topics in direct sum decompositions of abelian groups and their consequences. The book illustrates a new way of studying these groups while still honoring the rich history of unique direct sum decompositions of groups

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Page Count

339

Publisher

CRC Press

Published Date

ISBN 10

1584887273

ISBN 13

9781584887270

The Mathematics of Infinity

A Guide to Great Ideas

By: Theodore G. Faticoni

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The Mathematics of Infinity

A Guide to Great Ideas

By: Theodore G. Faticoni

Praise for the First Edition ". . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity."—Computing Reviews ". . . a very well written introduction to set theory . . . easy to read and well suited for self-study . . . highly recommended."—Choice The concept of infinity has fascinated and confused mankind for centuries with theories and ideas that cause even seasoned mathematicians to wonder. The Mathematics of Infinity: A Guide to Great Ideas, Second Edition uniquely explores how we can manipulate these ideas when our common sense rebels at the conclusions we are drawing. Continuing to draw from his extensive work on the subject, the author provides a user-friendly presentation that avoids unnecessary, in-depth mathematical rigor. This Second Edition provides important coverage of logic and sets, elements and predicates, cardinals as ordinals, and mathematical physics. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun readers' intuitive view of the world. With an accessible and balanced treatment of both concepts and theory, the book focuses on the following topics: Logic, sets, and functions Prime numbers Counting infinite sets Well ordered sets Infinite cardinals Logic and meta-mathematics Inductions and numbers Presenting an intriguing account of the notions of infinity, The Mathematics of Infinity: A Guide to Great Ideas, Second Edition is an insightful supplement for mathematics courses on set theory at the undergraduate level. The book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the world of counterintuitive mathematics.

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Page Count

361

Publisher

John Wiley & Sons

Published Date

ISBN 10

111824382X

ISBN 13

9781118243824

Combinatorics

An Introduction

By: Theodore G. Faticoni

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Combinatorics

An Introduction

By: Theodore G. Faticoni

Bridges combinatorics and probability and uniquely includes detailed formulas and proofs to promote mathematical thinking Combinatorics: An Introduction introduces readers to counting combinatorics, offers examples that feature unique approaches and ideas, and presents case-by-case methods for solving problems. Detailing how combinatorial problems arise in many areas of pure mathematics, most notably in algebra, probability theory, topology, and geometry, this book provides discussion on logic and paradoxes; sets and set notations; power sets and their cardinality; Venn diagrams; the multiplication principal; and permutations, combinations, and problems combining the multiplication principal. Additional features of this enlightening introduction include: Worked examples, proofs, and exercises in every chapter Detailed explanations of formulas to promote fundamental understanding Promotion of mathematical thinking by examining presented ideas and seeing proofs before reaching conclusions Elementary applications that do not advance beyond the use of Venn diagrams, the inclusion/exclusion formula, the multiplication principal, permutations, and combinations Combinatorics: An Introduction is an excellent book for discrete and finite mathematics courses at the upper-undergraduate level. This book is also ideal for readers who wish to better understand the various applications of elementary combinatorics.

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Page Count

204

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118407482

ISBN 13

9781118407486

Combinatorics

An Introduction

By: Theodore G. Faticoni

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Combinatorics

An Introduction

By: Theodore G. Faticoni

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204

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118407482

ISBN 13

9781118407486

Book's by Theodore G. Faticoni

Categories of Modules over Endomorphism Rings

Categories of Modules over Endomorphism Rings

Direct Sum Decompositions of Torsion-Free Finite Rank Groups

Direct Sum Decompositions of Torsion-Free Finite Rank Groups

The Mathematics of Infinity

The Mathematics of Infinity

Combinatorics

Combinatorics

Combinatorics

Combinatorics

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