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Combinatorics: An Introduction, by Theodore G. Faticoni
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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.
- Sales Rank: #2189740 in Books
- Published on: 2013-01-29
- Original language: English
- Number of items: 1
- Dimensions: 9.50" h x .90" w x 6.50" l, 1.30 pounds
- Binding: Hardcover
- 328 pages
From the Back Cover
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.
About the Author
THEODORE G. FATICONI, PhD, is Professor in the Department of Mathematics at Fordham University. His professional experience includes forty research papers in peer-reviewed journals and forty lectures on his research to colleagues.
Most helpful customer reviews
2 of 2 people found the following review helpful.
I wanted to find ways to teach the subject of permutations/combinations better, and found Faticoni's book in the new books ...
By Roberto Verzola
I teach what might commonly be called "Math 101" to college undergraduates. I wanted to find ways to teach the subject of permutations/combinations better, and found Faticoni's book in the new books section of our library.
The author explains things clearly alright, and in a way that was understandable (I have no PhD in math), but within less than an hour of cursory reading, I already found two serious errors and several minor ones. Obviously, there are probably more if one read the book more thoroughly, looking specifically for errors.
The first serious error (p.15) is found in the box which says, "The implication and its converse are logically equivalent. One can be substituted for the other without loss of Truth." Instead of "converse", the right term is "contrapositive". Indeed, in the text, if A -> B, the author defines the converse as B -> A and the contrapositive as not B -> not A.
The second is found in the author's definition of the complement of "at least 1 way" (p.114) as "A' = the set of ways that T can be done in exactly 1 way or done not at all." "Done not at all" is correct, but "done in exactly 1 way" is not, because this belongs to A, not its complement.
Having found these two errors, I lost confidence on the book.
To me, these errors seemed to confirm the comments of the author's students (search "Faticoni rate your professor") that he often makes mistakes, but does not correct them.
Minor issues:
in p.40-41, there's a heading entitled "Two-Circle Venn Diagrams", but the diagrams involve squares, not circles. The other Venn diagrams are also squares. The next section has the heading "Three-square Venn diagrams", which matches the actual diagrams better.
In p.304, the author introduces the "ZFC axioms" without ever explaining what ZFC or what the axioms are. Neither could ZFC be found in the index. Since the book defines and explains much more basic concepts, ZFC ("Zermelo-Fraenkel set theory with the axiom of Choice", according to Wikipedia) deserves at least a description of some sort.
That said, I learned a few things from the book, though I would want to confirm any new thing I learn with another book that contains fewer errors.
Roberto Verzola
University of the Philippines
0 of 1 people found the following review helpful.
Excellent book!
By carlos alexandre gomes da silva
A delight, this book contains the entire program of a basic course in combinatorics. You will not regret purchasing. It is an excellent addition to your library!
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