Mathematics for Liberal Arts
Fred Richman, Carol L. Walker,
Robert J. Wisner, James W. Brewer

Counting

One, two, three, ...

Some counting problems and estimates

A fundamental counting principle

Permutations

Two complications

Combinations

Probability
 What are the odds?
 Measuring likelihood
 Independent trials
 Expectation
 Conditional probability

Statistics
 Analysis of data
 Population and sample
 What if it were?
 Liars

Geometry
 Area
 The Pythagorean theorem
 Squaring the circle
 Numbers and points
 Plotting more points
 Plotting still more points
 Geometric sensitivity
 Paths
 Geometric means
 Counting again

Logic
 Think of the possibilities
 What's my number?
 The liar paradox
 Subject and predicate
 Syllogisms

Exponential growth
 The power of powers
 Doubling time
 Half life
 Explosions

Rates of interest

An average chapter
 The arithmetic mean
 Weighted arithmetic means
 The geometric mean
 The harmonic mean
 Comparing the means
 The Farey mean

What are natural numbers made of?

The building block of addition
 How can I build thee? Let me count the ways.
 Building blocks for subtraction.

The Euclidean algorithm

The building blocks of multiplication

Changing bases

Clock arithmetic
 The twelvehour clock
 Arithmetic of even and odd; casting out nines
 Zero divisors
 Pigenholes and inverses
 The perfect shuffle

Secret writing
 Simple substitution
 The GoldBug
 Letters are numbers

Block encoding
 Trapdoor functions

Infinite sets
 Finite and infinite
 Decimal representations of real numbers
 Comparing sizes of sets
 More comparisons
 More infinities

Number theory selections
 Primes and divisibility
 Some rules for divisibility
 A general divisibility rule
 Sums of divisors
 Deficiency and abundancy
 Perfection
 Amicability
 How are primes distributed?
 Sums of squares
 Pythagorean triples

Mathematics encounters
Supplementary topics: