APL Programs for the Mathematics Classroom

1. Introduction.- 1.1 Graphics.- 1.2 Idioms.- 2. Arithmetic and Numbers.- 2.1. Basic Programs with Integers.- 2.2. Square and Triangular Numbers.- 2.3. Multiplication and other Tables.- 2.3.1. Log Tables.- 2.3.1. Trig Tables.- 2.4. Isomorphisms.- 2.5. Primes and Factors.- 2.6. HCF and LCM.- 2.7. Recurring Decimals.- 2.8. Numbers in Different Bases.- 2.9. Roman Numerals.- 2.10. Encoding and Decoding.- 2.11. Problems involving Base 10 Digits.- 2.12. Computer Arithmetic.- 2.13. Counting Series Forwards and Backwards.- 2.14 Complex Numbers.- 2.14.1. Complex Roots of Unity.- 3. Algebra and Sets.- 3.1. Some Basic Algebra.- 3.2. Roots of Quadratics.- 3.3. Matrix Operations.- 3.3.1. Determinants.- 3.4. Polynomials.- 3.5. Arithmetic and Geometric Progressions.- 3.6. Sets.- 3.7. Polynomial Coefficients from Roots.- 4. Series.- 4.1. Recurrence Relations.- 4.2. Tests for Monotonicity.- 4.3. Convergence.- 4.4. Binomial Coefficients.- 4.4.1. Pascal's Triangle.- 4.5. Successive Differences of Series.- 4.6. Fibonacci Numbers.- 4.7. Series relating to pi.- 4.8. Series for e.- 4.9. A Series for ?2.- 4.10. Trig Series.- 4.11. Continued Fractions.- 4.12. Interpolation.- 5. Formulae and Tables.- 5.1. Compound Interest.- 5.1.1. Present Values.- 5.2. Mortgage Repayments.- 5.3. Triangle Formulae.- 5.4. Longest and Shortest Journeys.- 5.5. Pythagoras's Theorem and Norms.- 5.6. Pythagorean Triples.- 6. Geometry and Pattern.- 6.1. Parametric Plotting.- 6.1.1. Conic Sections.- 6.1.2. Hypocycloids and Epicycloids.- 6.2. Envelopes.- 6.2.1. Conic Sections.- 6.2.2. Hypocycloids and Epicycloids.- 6.3. Transformations.- 6.4 Perspective Drawing.- 6.5. Co-ordinate Geometry in Two Dimensions.- 6.6. Polar and Cartesian Coordinates.- 6.7. Patterns by Plotting Large Numbers of Points.- 7. Calculus.- 7.1. Numerical Integration.- 7.1.1. Upper and Lower Bounds for Integration.- 7.1.2. Trapezium Rule.- 7.1.3. Simpson's Rule.- 7.1.4. Adaptive Simpson's Rule.- 7.2. Root Finding.- 7.2.1. Bisection Method.- 7.2.2. Iteration Method.- 7.2.3. Newton-Raphson Method.- 7.3. Ordinary Differential Equations.- 7.3.1. Euler's Method.- 7.3.2. Mid-point Method.- 7.3.3. Trapezium Method.- 8. Probability and Statistics.- 8.1. Discrete Probability Distributions.- 8.1.1. Binomial Distribution.- 8.1.2. Poisson Distribution.- 8.1.3. Hypergeometric Distribution.- 8.2. The Birthday Problem.- 8.3. Descriptive Statistics.- 8.3.1. Variance.- 8.3.2. Standard Deviation.- 8.3.3. Partition Values.- 8.3.4. Mode and Range.- 8.4. Random Numbers from Various Distributions.- 8.5. Simulations.- 8.5.1. Dice/Coins etc..- 8.5.2. Buffon's Needle.- 8.6. Frequency Distributions.- 8.6.1. Stem-and-leaf Plot.- 8.6.2. Two-way Frequency Distribution.- 8.6.3. Scatterplots.- 8.7. Regression.- 8.8. Correlation.- 8.8.1. Covariance and Correlation Matrices.- 8.9. Non-parametric Tests.- 8.9.1. Runs Test.- 8.9.2. Rank Correlation.- 8.9.2.1. Spearman's Coefficient.- 8.9.2.2. Kendall's Coefficient.- 8.9.3. Sign Test.- 8.9.4. Wilcoxon Signed Rank Test (W-test).- 8.9.5. Mann-Whitney Rank Sum Test (U-test).- 8.9.6. Goodness of Fit.- 8.10. Statistical Tables.- 8.10.1. Normal probability density fn..- 8.10.2. Student t probability density fn..- 8.10.3. Gamma and Chi-squared proby. dens. fns..- 8.10.4. F probability density funtion.- 8.11. Sample Sizes.- 9. Combinatorics.- 9.1. Permutations in Lexical Order.- 9.2. Derangements.- 9.3. Combinations.- 9.4. Selections.- 9.5. Compositions and Partitions.- 9.6. Latin Squares.- 9.7. Magic Squares of Odd Order.- 10. Games and Miscellaneous.- 10.1. Deal a Hand at Whist.- 10.2. Chessboard.- 10.3. Mastermind.- 10.4. Life.- 10.5. Recursive Algorithms.- 10.5.1. Tower of Hanoi.- 10.5.2. Ackerman's Function.- 10.6. Optical Illusions.- Appendix 1. Graphics.- Appendix 2. Idioms and Utilities.- A2.1. Rounding, Averaging, and Removing Duplicates.- A2.2. Sorting and Ranking.- A2.3. Statement Joining.- A2.4. Branching and Prompting.- A2.5. Matrix Manipulation.- A2.6. Replication.- A2.7. Without.- A2.8. Bit Manipulation.- A2.9. Some String Handling Functions.- A2.10. Testing for Numeric/Character.- A2.11. Timing Function Execution.- Appendix 3. Graphics Functions in I-APL.- Index of Topics.- Index of Programs and Variables.