دانلود کتاب Thinking in problems : how mathematicians find creative solutions / 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