Cover image for Mathematical problems and proofs : combinatorics, number theory, and geometry
Mathematical problems and proofs : combinatorics, number theory, and geometry
Kisačanin, Branislav, 1968-
Publication Information:
New York : Plenum Press, [1998]

Physical Description:
xiv, 220 pages : illustrations ; 24 cm
Format :


Call Number
Material Type
Home Location
Item Holds
QA164 .K57 1998 Adult Non-Fiction Non-Fiction Area

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A gentle introduction to the highly sophisticated world of discrete mathematics, Mathematical Problems and Proofs presents topics ranging from elementary definitions and theorems to advanced topics -- such as cardinal numbers, generating functions, properties of Fibonacci numbers, and Euclidean algorithm. This excellent primer illustrates more than 150 solutions and proofs, thoroughly explained in clear language. The generous historical references and anecdotes interspersed throughout the text create interesting intermissions that will fuel readers' eagerness to inquire further about the topics and some of our greatest mathematicians. The author guides readers through the process of solving enigmatic proofs and problems, and assists them in making the transition from problem solving to theorem proving. At once a requisite text and an enjoyable read, Mathematical Problems and Proofs is an excellent entrée to discrete mathematics for advanced students interested in mathematics, engineering, and science.

Reviews 1

Choice Review

The main business of mathematicians consists of constructing proofs. All undergraduates looking toward graduate work in mathematics must become proficient at the mechanics of proof. Now, one may view proofs themselves as constituting mathematical objects, and the business of (some) mathematical logicians consists of proving theorems about proofs. Unfortunately, trying to use the language of mathematical logic to teach beginning undergraduates how to prove theorems makes as much sense as trying to use the language on noncommuting vector fields to teach someone how to parallel park. Kisacanin offers the sensible approach: expose students to a sampler of striking theorems, each having a sharp but elementary proof; allow them to form an intuitive concept of proof based on close examination of these examples (and let them learn some mathematical content in the process!); and let the students construct proofs of their own in the process of refining, varying, generalizing, and formalizing these model examples. On one view, the book contains few exercises, but conscientious students who at least attempt to discover all the proofs for themselves will find that, indeed, the book consists entirely of exercises. Recommended for high school and college libraries, undergraduate and up. D. V. Feldman; University of New Hampshire