Mathematics for Liberal Arts

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

  1. Counting
    1. One, two, three, ...
    2. Some counting problems and estimates
    3. A fundamental counting principle
    4. Permutations
    5. Two complications
    6. Combinations
  2. Probability
    1. What are the odds?
    2. Measuring likelihood
    3. Independent trials
    4. Expectation
    5. Conditional probability
  3. Statistics
    1. Analysis of data
    2. Population and sample
    3. What if it were?
    4. Liars
  4. Geometry
    1. Area
    2. The Pythagorean theorem
    3. Squaring the circle
    4. Numbers and points
    5. Plotting more points
    6. Plotting still more points
    7. Geometric sensitivity
    8. Paths
    9. Geometric means
    10. Counting again
  5. Logic
    1. Think of the possibilities
    2. What's my number?
    3. The liar paradox
    4. Subject and predicate
    5. Syllogisms
  6. Exponential growth
    1. The power of powers
    2. Doubling time
    3. Half life
    4. Explosions
    5. Rates of interest
  7. An average chapter
    1. The arithmetic mean
    2. Weighted arithmetic means
    3. The geometric mean
    4. The harmonic mean
    5. Comparing the means
    6. The Farey mean
  8. What are natural numbers made of?
    1. The building block of addition
    2. How can I build thee? Let me count the ways.
    3. Building blocks for subtraction.
    4. The Euclidean algorithm
    5. The building blocks of multiplication
  9. Changing bases
  10. Clock arithmetic
    1. The twelve-hour clock
    2. Arithmetic of even and odd; casting out nines
    3. Zero divisors
    4. Pigenholes and inverses
    5. The perfect shuffle
  11. Secret writing
    1. Simple substitution
    2. The Gold-Bug
    3. Letters are numbers
    4. Block encoding
    5. Trap-door functions
  12. Infinite sets
    1. Finite and infinite
    2. Decimal representations of real numbers
    3. Comparing sizes of sets
    4. More comparisons
    5. More infinities
  13. Number theory selections
    1. Primes and divisibility
    2. Some rules for divisibility
    3. A general divisibility rule
    4. Sums of divisors
    5. Deficiency and abundancy
    6. Perfection
    7. Amicability
    8. How are primes distributed?
    9. Sums of squares
    10. Pythagorean triples
  14. Mathematics encounters
Supplementary topics: