Thinking in Problems How Mathematicians Find Creative Solutions /

• Main Author: Roytvarf, Alexander A. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Boston : Birkhũser Boston : Imprint: Birkhũser, 2013.
• Subjects: Mathematics.; Algebra.; Global analysis (Mathematics).; Combinatorics.; Analysis.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-8176-8406-8

This concise, self-contained textbook gives an in-depth look at problem-solving from a mathematician<U+0019>s point-of-view. Each chapter builds off the previous one, while introducing a variety of methods that could be used when approaching any given problem. Creative thinking is the key to s...

Table of Contents:

• Preface
• Using the Stars on Problems
• Understanding the Advanced Skill Requirements
• Acknowledgements
• Jacobi Identities and Related Combinatorial Formulas
• A Property of Recursive Sequences
• A Combinatorial Algorithm in Multiexponential Analysis
• A Frequently Encountered Determinant.- A Dynamical System with a Strange Attractor
• Polar and Singular Value Decomposition Theorems
• 2x2 Matrices Which Are Roots of Unity
• A Property of Orthogonal Matrices
• Convexity and Related Classical Inequalities
• One-Parameter Groups of Linear Transformations.- Some Problems in Combinatorics and Analysis that can be Explored using Generating Functions
• Least Squares and Chebyshev Systems
• References
• Index of Terms.