| 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 |
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| Citation |
| Errata |