APL Programs for the Mathematics Classroom - Brossura

Thomson, Norman D.

Brossura

ISBN 10: 0387970029 ISBN 13: 9780387970028

Casa editrice: Springer New York, 1989

Riassunto

The idea for this book grew out of proposals at the APL86 con­ ference in Manchester which led to the initiation of the I-APL (International APL) project, and through it to the availability of an interpreter which would bring the advantages of APL within the means of vast numbers of school children and their teachers.

Su questo libro

Contenuti

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.

Product Description

Book by Thomson Norman D

Dettagli dell'edizione

• Editore: Springer New York
• Data di pubblicazione: 1989
• Lingua: Inglese
• ISBN 10: 0387970029
• ISBN 13: 9780387970028
• Rilegatura: Copertina flessibile
• Numero di pagine: 200
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania