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-ErrorAnalysis -- PART IV: NUMERICAL ALGORITHMIC ENGINEERING -- Chapter 16: Languages and Systems -- Chapter 17: Implementation Techniques and Software Development.