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Acknowledgments
1 Introduction and Motivation
1.1 Introduction
1.2 Motivation
1.3 Implementation
1.4 Grading
1.5 Organization
2 Computer Exploration of Mathematical Concepts
2.1 A Prime Project
2.2 A Golden Prime Project
2.3 A Rather Normal Project
2.4 Collatz Collapse
2.5 Fractions of Fractions
2.6 Diffusion by Chance
2.7 Random Investing
2.8 Infinite Digits with Finite Storage
2.9 Follow the Rules!
2.10 Chaotic Rabbits
2.11 Smoothing Out Tangles
2.12 Shortening Voices Everywhere
2.13 Student Poster Example
3 Numerical Algorithms
3.1 Bit by Bit
3.2 Getting to the Root of the Problem
3.3 Things that Periodically Fit
3.4 Going with the Flow
3.5 SupercaliFRACTAListic!
3.6 Chain Reactions
3.7 The World’s Largest Linear Algebra Problem
3.8 Shifting the Way We Think About Linear Algebra
3.9 Facing Reality with Eigenfaces
3.10 Matrix Surgery: Operating on Matrices
3.11 Student Poster Example
4 Advanced Numerical Analysis
4.1 Matrices of Matrices
4.2 Wrapping Around Matrices
4.3 Getting Smaller
4.4 Improved Hearing
4.5 You Match I Match
4.6 Seeing More Clearly
4.7 Eigenvalue Computing Side-by-Side
4.8 Delayed Understanding
4.9 Student Poster Example
Bibliography
Index