Mathematical Experiments on the Computer
Academic Press
Published on 16. December 1982
522 pages
978-0-08-087424-1 (ISBN)
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Mathematical Experiments on the Computer
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Ulf Grenander
Mathematical Experiments on the Computer
Book
01/1982
Academic Press
€91.61
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Content
- Front Cover
- Mathematical Experiments on the Computer
- Copyright Page
- Contents
- Preface
- Acknowledgments
- Part I: EXPERIMENTS ON THE COMPUTER
- Chapter 1. Definition of the Subject
- Chapter 2. History of the Project
- Chapter 3. Case Studies
- Experiment 1: From Statistics
- Experiment 2: From Linear Algebra
- Experiment 3: An Energy Minimization Problem
- Experiment 4: Neural Networks (Static Problem)
- Experiment 5: Limit Theorems on Groups
- Experiment 6: Pattern Restoration
- Experiment 7: Modeling Language Acquisition
- Experiment 8: Study of Invariant Curves
- Experiment 9: Neural Networks (Dynamic Problem)
- Experiment 10: High-Dimensional Geometry
- Experiment 11: Strategy of Proofs
- Chapter 4. Other Areas
- Chapter 5. Software Requirements
- Chapter 6. Hardware Requirements
- Chapter 7. Practical Advice
- Part II: A MATHEMATICIAN'S GUIDE TO APL
- Chapter 8. Language for Mathematical Experiments
- 1. Mathematical Languages
- 2. Requirements for the Language
- 3. The Choice of APL
- 4. How to Learn APL
- Chapter 9. MathematicaI Objects-Data Structures
- 1. Hierarchies of Objects
- 2. Scalars
- 3. Vectors
- 4. Sets
- 5. Matrices
- 6. Other Arrays
- Chapter 10. Functions-APL Statements
- 1. Praxis of Writing APL Code
- 2. Numerical Mixed Functions
- 3. Structural Mixed Functions
- 4. Mixed Functions for Selection
- 5. Mixed Functions for Selection Information
- 6. Transformations of Data
- Chapter 11. APL Operators
- 1. The Notion of an Operator
- 2. Reduction
- 3. Scan
- 4. Axis Operator
- 5. Inner Product
- 6. Outer Product
- Chapter 12. APL Programs-Defined Functions
- 1. Definition Mode
- 2. Flow of Control
- 3. Managing Memory
- 4. Writing Code Praxis
- Part III: DESIGNING MATHEMATICAL EXPERIMENTS
- Chapter 13. Designing the Experiment
- 1. Choice of Data Structures
- 2. Looking for the Unexpected
- 3. Prepare for Continued Experiments
- 4. Interpreting the Results
- Chapter 14. An Experiment in Heuristic Asymptotics
- 1. Guessing About Asymptotics
- 2. Synthesis of the Patterns
- 3. Recognition of Monotonic Patterns
- 4. Some Experiments
- 5. Oscillatory Patterns
- 6. Experiments with Oscillating Patterns
- 7 . Conclusions
- Part IV: MATHEMATICAL SOFTWARE FOR EXPERIMENTS
- Chapter 15. Organizing a Program Library
- 1. Why a Library?
- 2. External Documentation
- 3. Internal Documentation
- 4. Comments in the Code
- 5. Program Style
- Chapter 16. Algebra
- ADD
- BALANCE
- CHOLESKYC
- CHOLSKYR
- CONVERT
- CUBIC
- DIVBY
- ELMHES
- EVAL and EVAL2
- HSHLDR
- INVERSE
- JACOBI
- MATMULT
- MAGNITUDE
- MULLERM
- MULT
- MINUS
- PDIVBY
- POLY
- POLYC
- POLFACT
- POWER
- QUARTIC
- REVERSE1
- REVERSE2
- SYNDIV AND SYNDIV1
- TQL
- Chapter 17. Analysis
- BSPL
- CONFORMAL
- COSFILON and SINFILON
- DETERMINANT
- GRAMS
- INTEGRAL
- INTEQ
- KUTTA
- MRFFT and MRFFTl
- NEWTON
- ROOT
- SIMPSON
- SPLINE
- SPLINT
- SPLDER
- TRAPEZOIDAL
- Chapter 18. Arithmetic
- CONFRAC and RATIONAL
- FACTOR
- GCD and SCM
- PRIMGEN and PRIMGN
- Chapter 19. Asymptotics
- ASYMPTOTICS
- CDIVDIFF
- CGAUTOR
- CONCAVEMAJ and CONVEXMIN
- CORDER1 and CORDER2
- FIT
- FITO
- FWEIGHT
- GDIFFEQ
- G10, G11, G12, G13, G21, G22, G23, G24, G25, G26, G27
- LSQ
- MON
- MONMAJ and MONMIN
- NORM
- OSC
- PRINTOUT
- RERROR
- Chapter 20. Geometry
- ADDC and ADDC1
- AREA
- ATAN
- AXF and CIRCUM
- DCNP, DECOMP, DEQUAD
- DIST, DISTANCE, DISTPT
- GEODESIC, CHRISTOFFEL, GEOAUX
- HULL1
- LINSERIES
- MATRANS
- PERIM
- POLY, SFACE, STFORM
- SUPPORT
- ROTATE, SCALE, TRANS
- RMVFVT
- VADD
- Chapter 21. Graphs
- CONNECT
- CONVERT, MATMAK
- REACH, COMREACH
- Chapter 22. Probability
- BERN
- BETA
- BIN
- BINDF and BINFR
- CHI2
- CHISQ
- CONVOL
- DISC
- DISCRETE
- EQDIST
- EXPON
- FISHER
- GAMMA
- GAUSSDF
- GAUSS and SGAUSS
- GEOM
- MARKOV
- MULTINOM
- NEGBIN
- PARETO
- POIS
- POISSONFR, POISSONFR2, POISSONDF, POISSONDF2
- SAMPLE
- STUDENT
- UNIF
- Chapter 23. Special Functions
- CHEB1 and CHEB2
- ERF
- HAAR
- HERMITE
- LAGUERRE
- LEGENDRE
- Chapter 24. Statistics
- ANALYZE
- FREQTAB1
- FREQTAB2
- HISTOGRAM1 and HISTOGRAM2
- HISTOSPLINE
- KOLMOG
- MODE
- QUANT
- RUNS1
- RUNS2
- SPECTR1
- STEMLEAF
- SIGN
- TRENDS
- Chapter 25. Utilities
- COMPOSE, EDIT
- LISTALL
- LISTDV
- PRINTAB
- SORT1
- SPLICE
- TIMER
- TITLEC
- References
- Solutions to Exercises
- Index
