UID:
almafu_9958110721202883
Format:
1 online resource (545 p.)
ISBN:
1-281-76354-3
,
9786611763541
,
0-08-087424-X
Series Statement:
Pure and applied mathematics ; 105
Content:
Mathematical experiments on the computer
Note:
Description based upon print version of record.
,
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
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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
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Chapter 10. Functions-APL Statements1. 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
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1. Choice of Data Structures2. 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
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Chapter 16. AlgebraADD; 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
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CONCAVEMAJ and CONVEXMIN
,
English
Additional Edition:
ISBN 0-12-301750-5
Language:
English
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