Thinking in Problems: How Mathematicians Find Creative Solutions

By Alexander A. Roytvarf

Section I. Problems.- 1. Jacobi Identities and Related Combinatorial Formulas.- 2. A Property of Recurrent Sequences.- 3. A Combinatorial Algorithm in Multiexponential Analysis.- 4. A Frequently Encountered Determinant.- 5. A Dynamical System with a Strange Attractor.- 6. Polar and Singular Value Decomposition Theorems.- 7. 2X2 Matrices Which Are Roots of 1.- 8. A Property of Orthogonal Matrices.- 9. Convexity and Related Classical Inequalities.- 10. One-Parameter Groups of Linear Transformations.- 11. Examples of Generating Functions in Combinatorial Theory and Analysis.- 12. Least Squares and Chebyshev Systems.- Section II. Hints.- 1. Jacobi Identities and Related Combinatorial Formulas.- 2. A Property of Recurrent Sequences.- 3. A Combinatorial Algorithm in Multiexponential Analysis.- 4. A Frequently Encountered Determinant.- 5. A Dynamical System with a Strange Attractor.- 6. Polar and Singular Value Decomposition Theorems.- 7. 2X2 Matrices Which Are Roots of 1.- 8. A Property of Orthogonal Matrices.- 9. Convexity and Related Classical Inequalities.- 10. One-Parameter Groups of Linear Transformations.- 11. Examples of Generating Functions in Combinatorial Theory and Analysis.- 12. Least Squares and Chebyshev Systems.- Section III. Explanations.-1. Jacobi Identities and Related Combinatorial Formulas.- 2. A Property of Recurrent Sequences.- 3. A Combinatorial Algorithm in Multiexponential Analysis.- 4. A Frequently Encountered Determinant.- 5. A Dynamical System with a Strange Attractor.- 6. Polar and Singular Value Decomposition Theorems.- 7. 2X2 Matrices Which Are Roots of 1.- 8. A Property of Orthogonal Matrices.- 9. Convexity and Related Classical Inequalities.- 10. One-Parameter Groups of Linear Transformations.- 11. Examples of Generating Functions in Combinatorial Theory and Analysis.- 12. Least Squares and Chebyshev Systems.- Section IV. Full Solutions.- 1. Jacobi Identities and Related Combinatorial Formulas.- 2. A Property of Recurrent Sequences.- 3. A Combinatorial Algorithm in Multiexponential Analysis.- 4. A Frequently Encountered Determinant.- 5. A Dynamical System with a Strange Attractor.- 6. Polar and Singular Value Decomposition Theorems.- 7. 2X2 Matrices Which Are Roots of 1.- 8. A Property of Orthogonal Matrices.- 9. Convexity and Related Classical Inequalities.- 10. One-Parameter Groups of Linear Transformations.- 11. Examples of Generating Functions in Combinatorial Theory and Analysis.- 12. Least Squares and Chebyshev Systems.

• Format: Hardcover
• Language: English
• ISBN: 0817684050
• ISBN13: 9780817684051
• Release Date: January 2013
• Publisher: Birkhauser
• Length: 405 Pages
• Weight: 1.75 lbs.
• Dimensions: 1.0" x 6.1" x 9.2"