# Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry

By Spresser, Diane M. | Mathematics and Computer Education, Fall 1999 | Go to article overview

# Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry

Spresser, Diane M., Mathematics and Computer Education

MATHEMATICAL PROBLEMS AND PROOFS: COMBINATORICS, NUMBER THEORY, AND GEOMETRY

by Branislav Kisacanin

Plenum Press, 1998

My first reading of the book's title piqued my curiosity about the glue that the author might use to bind together combinatorics, number theory, and geometry into a single volume, and about the book's intended purpose. Although the dust jacket bills the book as a "gentle introduction to the highly sophisticated world of discrete mathematics" (front flap), and "an excellent entree to discrete mathematics for advanced students interested in mathematics, engineering, and science" (back flap), the author does not himself describe his work in these terms, but rather as a work "for those who enjoy seeing mathematical formulas and ideas, interesting problems, and elegant solutions" (p. vii). This seeming disconnect between the way the book's dust jacket markets the work and the author's probable intentions frames some important questions about the purpose of the work and the niche it might fill in a reader's mathematical education.

The book is an interesting collection of excursions into the topical areas of combinatorics, number theory, and geometry, which comprise Chapters 2, 3, and 4, respectively. Chapter 1 introduces set theory terminology and concepts. The book also contains four appendices on mathematical induction, important mathematical constants, and great mathematicians, plus a listing of characters in the Greek alphabet. The discussions of induction and the mathematical constants pi, epsilon, delta, and phi are especially nice, with many interesting details and historic facts.

While each topical excursion slices sufficiently into the mathematical landscape to give the reader an appreciation for the topic, the rationale for the author's choices - which problems and proofs are or aren't included - isn't always immediately apparent. In the chapter on combinatorics, for example, one encounters many of the expected basics for solving enumeration problems (e.g., simple counting techniques with sums, products, and inclusion-exclusion; permutations; combinations; generating functions) and the proofs of a number of results. At the same time, the chapter includes three probability distributions from statistical physics, for example, but devotes relatively little attention to recurrence relations. Only a few well-known problems and results from graph theory, such as the Konigsberg bridge problem and Cayley's Theorem, are included. …

• Questia's entire collection
• Automatic bibliography creation
• More helpful research tools like notes, citations, and highlights

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Highlights (0)
Some of your highlights are legacy items.
Citations (0)
Some of your citations are legacy items.
Notes (0)
Bookmarks (0)

Project items include:
• Saved book/article
• Highlights
• Quotes/citations
• Notes
• Bookmarks
Notes

#### Cited article

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

#### Cited article

Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry
Settings

#### Settings

Typeface
Text size Reset View mode
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

Why can't I print more than one page at a time?

Full screen

## Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.