A Mathematics Sampler: Topics for the Liberal ArtsNow in its fifth edition, A Mathematics Sampler presents mathematics as both science and art, focusing on the historical role of mathematics in our culture. It uses selected topics from modern mathematics including computers, perfect numbers, and four-dimensional geometry to exemplify the distinctive features of mathematics as an intellectual endeavor, a problem-solving tool, and a way of thinking about the rapidly changing world in which we live. A Mathematics Sampler also includes unique LINK sections throughout the book, each of which connects mathematical concepts with areas of interest throughout the humanities. The original course on which this text is based was cited as an innovative approach to liberal arts mathematics in Lynne Cheney's report, "50 HOURS: A Core Curriculum for College Students," published by the National Endowment for the Humanities. |
Contents
Chapter 1 on problem solving sets the tone for the entire book | 1 |
Chapter 7 introduces fourdimensional geometry by way | 7 |
NUMBER THEORY | 19 |
Copyright | |
18 other sections not shown
Common terms and phrases
1-1 correspondence 4-space algebra algorithm axiom system bers called cardinal number chapter circle construct cosets cross section data set decimal defined definition denoted described Determine digits divisors edge path equal Euclid's Euclidean geometry exactly example Exterior Angle Theorem false Figure five-number summary formula given graph hypersphere idea infinite sets integers interior angles intersection Lagrange's Theorem line segment logical mathematicians mathematics mean ment Mersenne Mersenne primes natural numbers non-Euclidean geometries notation NP-complete number theory odd numbers ordered pairs outcomes pattern perfect number plane possible postulates prime factorization prime number probability problem proof properties proved pseudosphere radius random rational numbers real numbers represent sample space scores Selection Sort sequence set-builder notation solution solve square standard deviation statement steps subgroup subset Table Theorem tion tour triangle true vertices words WRITING EXERCISES