MAA, 2009 - 207 pagine
Every mathematician (beginner, amateur, and professional alike) thrills to find simple, elegant solutions to seemingly difficult problems. Such happy resolutions are called ""aha! solutions,"" a phrase popularized by mathematics and science writer Martin Gardner. Aha! solutions are surprising, stunning, and scintillating: they reveal the beauty of mathematics. This book is a collection of problems with aha! solutions. The problems are at the level of the college mathematics student, but there should be something of interest for the high school student, the teacher of mathematics, the ""math fan,"" and anyone else who loves mathematical challenges. This collection includes one hundred problems in the areas of arithmetic, geometry, algebra, calculus, probability, number theory, and combinatorics. The problems start out easy and generally get more difficult as you progress through the book. A few solutions require the use of a computer. An important feature of the book is the bonus discussion of related mathematics that follows the solution of each problem. This material is there to entertain and inform you or point you to new questions. If you don't remember a mathematical definition or concept, there is a Toolkit in the back of the book that will help.
Cosa dicono le persone - Scrivi una recensione
Nessuna recensione trovata nei soliti posti.
algebra angle binary binomial coefficient Bonus Cassini's identity characteristic polynomial circle column congruence cookies count cube cycle type cyclotomic polynomial diagonal diagram digits divides divisors edges elementary symmetric polynomials elements equal equation equilateral triangle exact cover example expected number factor Fibonacci numbers finite follows formula function geometric series given triangle Gobbling Algorithm graph Hence hour hand identity inequality International Mathematical Olympiads intersection isometry labeled linear magic square mathematics matrix modulo multiple number of coins number of stones obtain occur odd number Oddball pairs parallelogram Pascal's triangle paths perimeter permutation permutation matrices plane positive integers probability problem proof prove random rational number real numbers rectangle recurrence relation rotation satisfy second player win sequence side lengths solve strings subsets Sudoku Suppose symmetric polynomials symmetry tetrahedron theorem Titu Andreescu Toolkit values vector vertex vertices yields