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 