Mathematics for Liberal Arts

by Richman, Fred; Walker, Carol L.; Wisner, Robert J.; Brewer, James W.

• ISBN13: 9780787295646
• ISBN10: 0787295647
• Edition: 4th
• Format: Paperback
• Copyright: 2002-07-01
• Publisher: Kendall Hunt Pub Co

Table of Contents

Counting	1	(32)
One, two, three	1	(4)
Some counting problems and estimates	5	(3)
A fundamental counting principle	8	(5)
Permutations	13	(5)
Two complications	18	(6)
Combinations	24	(7)
Notes	31	(2)
Probability	33	(28)
What are the odds?	33	(4)
Measuring likelihood	37	(7)
Independent trials	44	(4)
Expectation	48	(6)
Conditional probability	54	(5)
Notes	59	(2)
Statistics	61	(18)
Analysis of data	61	(5)
Population and sample	66	(4)
What if it were?	70	(4)
Liars	74	(3)
Notes	77	(2)
Geometry	79	(52)
Area	79	(5)
The Pythagorean theorem	84	(6)
Squaring the circle	90	(3)
Numbers and points	93	(3)
Plotting more points	96	(4)
Plotting still more points	100	(5)
Geometric sensitivity	105	(7)
Paths	112	(7)
Geometric means	119	(3)
Counting again	122	(6)
Notes	128	(3)
Logic	131	(16)
Think of the possibilities	131	(1)
What's my number?	132	(3)
The liar paradox	135	(2)
Subject and predicate	137	(3)
Syllogisms	140	(4)
Notes	144	(3)
Exponential growth	147	(26)
The power of powers	147	(3)
Doubling time	150	(2)
Half-life	152	(2)
Explosions	154	(5)
Rates of interest	159	(11)
Logarithms	170	(1)
Notes	171	(2)
An average chapter	173	(30)
The arithmetic mean	173	(4)
Weighted arithmetic means	177	(5)
The geometric mean	182	(5)
The harmonic mean	187	(5)
Comparing the means	192	(3)
The Farey mean	195	(6)
Notes	201	(2)
What are natural numbers made of?	203	(20)
The building block of addition	203	(2)
How can I build thee? Let me count the ways	205	(4)
Building blocks for subtraction	209	(3)
The Euclidean algorithm	212	(3)
The building blocks of multiplication	215	(7)
Notes	222	(1)
Changing bases	223	(22)
Earlier number systems	223	(5)
Base five	228	(6)
Base twelve	234	(3)
Base two	237	(5)
Notes	242	(3)
Clock arithmetic	245	(22)
The twelve-hour clock	245	(6)
Arithmetic of even and odd; casting out nines	251	(3)
Zero divisors	254	(2)
Pigeonholes and inverses	256	(3)
The perfect shuffle	259	(4)
Fermat's little theorem	263	(3)
Notes	266	(1)
Secret writing	267	(18)
Simple substitution	267	(3)
The Gold-Bug	270	(3)
Letters are numbers	273	(3)
Block encoding	276	(4)
Trap-door functions	280	(2)
Notes	282	(3)
Infinite sets	285	(16)
Finite and infinite	285	(2)
Decimal representations of real numbers	287	(2)
Comparing sizes of sets	289	(4)
More comparisons	293	(4)
More infinities	297	(2)
Notes	299	(2)
Number theory selections	301	(36)
Prime numbers and divisibility	301	(3)
Some divisibility rules	304	(5)
A general divisibility rule	309	(3)
Sums of divisors	312	(2)
Deficiency and abundancy	314	(3)
Numerical perfection	317	(4)
Cordial amicability	321	(2)
How are prime numbers distributed?	323	(7)
Sums of squares	330	(3)
Pythagorean triples	333	(3)
Notes	336	(1)
A Mathematics encounters	337	(10)
Temperature conversion	338	(1)
The Greek ladder method	339	(1)
The collapsing compass	340	(1)
Catalan's conjecture	341	(1)
Egyptian fractions	342	(1)
The Pythagoreans	343	(1)
Triangle numbers	344	(1)
The four-color problem	345	(1)
Morley's Theorem	346	(1)
B Notation and arithmetic	347	(30)
The alphabet and punctuation of mathematics	347	(7)
Arithmetic of the integers	354	(5)
Arithmetic of fractions	359	(7)
Arithmetic of exponents	366	(5)
Arithmetic of equations	371	(4)
A standard deck of cards	375	(2)
Index	377