Why Math (Undergraduate Texts in Mathematics)

1 Arithmetic Review.- 1.1 Basis Rules.- 1.2 Division, Fractions, and Exponents.- 1.3 Percentages.- 1.4 Rates.- 2 Prime Numbers and Fractions.- 2.1 Prime Numbers and Factorization.- 2.2 Greatest Common Factor.- 2.3 Rationals and Irrationals.- 3 The Pythagorean Theorem and Square Roots.- 3.1 The Theorem.- 3.2 Square Roots Which Are Irrational.- 3.3 Computation of Square Roots by Successive Approximation.- 4 Elementary Equations.- 4.1 Equations in One Unknown.- 4.2 The Use of Two or More Unknowns.- 4.3 Graphing.- 5 Quadratic Polynomials and Equations.- 5.1 Solution of Quadratic Equations.- 5.2 Applications of Quadratic Equations.- 5.3 Quadratic Polynomials.- 6 Powers and Geometric Sequences.- 6.1 Applications of Powers.- 6.2 More on Half-Lives.- 6.3 Compound Interest and Related Matters.- 6.4 IRAs and Similar Tax Sheltered Accounts.- 6.5 Geometric Series-the "Sum" of a Geometric Sequence.- 7 Areas and Volumes.- 7.1 Areas.- 7.2 Volumes.- 7.3 Surface Area of a Solid (versus Volume).- 7.4 Computation of Cube Roots.- 8 Galilean Relativity.- 8.1 Displacement and Velocity Vectors.- 8.2 Doppler Effect.- 8.3 Components of Vectors.- 9 Special Relativity.- 9.1 Simultaneity and Einstein’s Postulate.- 9.2 Time Dilation.- 9.3 Length Contraction.- 10 Binary Arithmetic.- 10.1 Decimal, Binary, and Ternary Representation of Integers.- 10.2 Subtraction and Division in Base Two.- 10.3 Applications.- 11 Sets and Counting.- 11.1 Set Notation.- 11.2 Counting.- 12 Probability.- 12.1 Elementary Ideas and Examples.- 12.2 Mutually Exclusive Events.- 12.3 The Basic Rules.- 12.4 Quality Control (optional).- 12.5 Expectation.- 12.6 Conditional Probability.- 13 Cardinality.- 13.1 Countable Sets.- 13.2 Countably Many Countable Sets.- 13.3 The Reals vs. the Rationals.- Answers to Odd-Numbered Problems.