PART I: RATIONALE AND FOUNDATIONS

The discussion here is premised on the paper that accompanies this proposal.

Chapter 1: Algorithmics---The Spirit of Computing

Chapter 2: Number ---The Language of Science

Chapter 3: Bringing Number Under the Rubric of Algorithm

PART II: NUMERICAL ALGORITHMIC SCIENCE

Chapter 4: Algorithms on Graphs and Networks

Chapter 5: Uni-Dimensional Equation-Solving and Optimization

Chapter 6: Matrix-Based and Tensor-Based Computations

Chapter 7: Linear Programming before the 1984 Revolution

Chapter 8: Unconstrained Nonlinear Optimization

Chapter 9: Nonlinear Equation-Solving

Chapter 10: Constrained Nonlinear Optimization

Chapter 11: Linear Programming after the 1984 Revolution

Chapter 12: The Many Other Facets of Numerical Algorithmics

PART III: CONVERGENCE, COMPLEXITY, AND NUMERICAL ERROR

Chapter 13: Global Convergence and Asymptotic Rate-of-Convergence

Chapter 14: Complexity Classes and Analysis

Chapter 15: Roundoff-Error Analysis

PART IV: NUMERICAL ALGORITHMIC ENGINEERING

Chapter 16: Languages and Systems

Chapter 17: Implementation Techniques and Software Development