PART I: RATIONALE AND FOUNDATIONSThe discussion here is premised on the paper that accompanies this proposal.Chapter 1: Algorithmics---The Spirit of ComputingChapter 2: Number ---The Language of ScienceChapter 3: Bringing Number Under the Rubric of AlgorithmPART II: NUMERICAL ALGORITHMIC SCIENCEChapter 4: Algorithms on Graphs and NetworksChapter 5: Uni-Dimensional Equation-Solving and OptimizationChapter 6: Matrix-Based and Tensor-Based ComputationsChapter 7: Linear Programming before the 1984 RevolutionChapter 8: Unconstrained Nonlinear OptimizationChapter 9: Nonlinear Equation-SolvingChapter 10: Constrained Nonlinear OptimizationChapter 11: Linear Programming after the 1984 RevolutionChapter 12: The Many Other Facets of Numerical AlgorithmicsPART III: CONVERGENCE, COMPLEXITY, AND NUMERICAL ERRORChapter 13: Global Convergence and Asymptotic Rate-of-ConvergenceChapter 14: Complexity Classes and AnalysisChapter 15: Roundoff-Error AnalysisPART IV: NUMERICAL ALGORITHMIC ENGINEERINGChapter 16: Languages and SystemsChapter 17: Implementation Techniques and Software Development

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