﻿ Notation as a Tool of Thought

Notation as a Tool of Thought
Kenneth E. Iverson

 0. Introduction 1. Important Characteristics of Notation 1.1 Ease of Expressing Constructs Arising in Problems 1.2 Suggestivity 1.3 Subordination of Detail 1.4 Economy 1.5 Amenability to Formal Proofs 2. Polynomials 2.1 Products of Polynomials 2.2 Derivative of a Polynomial 2.3 Derivative of a Polynomial with Respect to its Roots 2.4 Expansion of a Polynomial 3. Representations 3.1 Number Systems 3.2 Polynomials 3.3 Permutations 3.4 Directed Graphs 3.5 Symbolic Logic 4. Identities and Proofs 4.1 Dualities in Inner Products 4.2 Partitioning Identities 4.3 Summarization and Distribution 4.4 Distributivity 4.5 Newton’s Symmetric Functions 4.6 Dyadic Transpose 4.7 Inner Products 4.8 Product of Polynomials 4.9 Derivative of a Polynomial 5. Conclusion 5.1 Comparison with Conventional Mathematical Notation 5.2 The Introduction of Notation 5.3 Extensions to APL 5.4 Mode of Presentation Acknowledgments Appendix A. Summary of Notation Appendix B. Compiler from Direct to Canonical Form References Citation Errata