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\NSECP{OVERVIEW}{2}
\SSEC{Abstract}{2}
\SSEC{Five-page Summary of the Project}{3}
 \SSSEC{Detour: Analysis of a discovery}{3}
 \SSSEC{What AM does: Syntheses of discoveries}{99}
 \SSSEC{Results}{99}
 \SSSEC {Conclusions}{99}
\SSEC{Viewing AM as some common process}{99}
 \SSSEC{AM as Hill-climbing}{99}
 \SSSEC{AM as Heuristic Search}{99}
 \SSSEC{AM as a Mathematician}{99}
 \SSSEC{AM as a Book}{99}

\NSECP{EXAMPLE:  Discovering Prime Numbers}{99}
\SSEC{Discussion of the AM Program}{99}
 \SSSEC{Representation}{99}
 \SSSEC{Agenda and Heuristics}{99}
\SSEC{What (not) to get out of this example}{99}
\SSEC{Deciphering the Example}{99}
\SSEC{The Example Itself}{99}
\SSEC{Recapping the Example}{99}

\NSECP{AGENDA}{99}
\SSEC{AM's Search}{99}
\SSEC{Constraining AM's Search}{99}
\SSEC{The Agenda}{99}
 \SSSEC{Why an Agenda?}{99}
 \SSSEC{Details of the Agenda scheme}{99}

\NSECP{HEURISTICS}{99}
\SSEC{Syntax of the Heuristics}{99}
 \SSSEC{Syntax of the Left-hand Side}{99}
 \SSSEC{Syntax of the Right-hand Side}{99}
\SSEC{Heuristics Suggest New Tasks}{99}
 \SSSEC{An Illustration: ``Fill in Generalizations of Equality''}{99}
 \SSSEC{The Ratings Game}{99}
\SSEC{Heuristics Create New Concepts}{99}
 \SSSEC{An Illustration: Discovering Primes}{99}
 \SSSEC{The Theory of Creating New Concepts}{99}
 \SSSEC{Another Illustration: Squaring a number}{99}
\SSEC{Heuristics Fill in Entries for a Facet}{99}
 \SSSEC{An Illustration: ``Fill in Examples of Set-union''}{99}
 \SSSEC{Heuristics Propose New Conjectures}{99}
 \SSSEC{An Illustration: ``All primes except 2 are odd''}{99}
 \SSSEC{Another illustration: Discovering Unique Factorization}{99}
\SSEC{Gathering Relevant Heuristics}{99}
 \SSSEC{Domain of Applicability}{99}
 \SSSEC{Rippling}{99}
 \SSSEC{Ordering the Relevant Heuristics}{99}
\SSEC{AM's Starting Heuristics}{99}
 \SSSEC{Heuristics Grouped by the Knowledge They Embody}{99}
 \SSSEC{Heuristics Grouped by How Specific They Are}{99}

\NSECP{CONCEPTS}{99}
\SSEC{Motivation and Overview}{99}
 \SSSEC{A Glimpse of a Typical Concept}{99}
 \SSSEC{The main constraint: Fixed set of facets}{99}
 \SSSEC{BEINGs Representation of Knowledge}{99}
\SSEC{Facets}{99}
 \SSSEC{Generalizations/Specializations}{99}
 \SSSEC{Examples/Isa's}{99}
 \SSSEC{In-Domain-of/In-Range-of}{99}
 \SSSEC{Views}{99}
 \SSSEC{Intuitions}{99}
 \SSSEC{Analogies}{99}
 \SSSEC{Conjec's}{99}
 \SSSEC{Definitions}{99}
 \SSSEC{Algorithms}{99}
 \SSSEC{Domain/Range}{99}
 \SSSEC{Worth}{99}
 \SSSEC{Interest}{99}
 \SSSEC{Suggest}{99}
 \SSSEC{Fill/Check}{99}
 \SSSEC{Other Facets which were Considered}{99}
\SSEC{AM's Starting Concepts}{99}
 \SSSEC{Diagram of Initial Concepts}{99}
 \SSSEC{Summary of Initial Concepts}{99}
 \SSSEC{Rationale behind Choice of Concepts}{99}

\NSECP{RESULTS}{99}
\SSEC{What AM Did}{99}
 \SSSEC{Linear Task-by-task Summary of a Good Run}{99}
 \SSSEC{Two-Dimensional Behavior Graph}{99}
 \SSSEC{AM as a Computer Program}{99}
\SSEC{Experiments with AM}{99}
 \SSSEC{Must the Worth numbers be finely tuned?}{99}
 \SSSEC{How finely tuned is the Agenda?}{99}
 \SSSEC{How valuable is tacking reasons onto each task?}{99}
 \SSSEC{What if certain concepts are eliminated/added?}{99}
 \SSSEC{Can AM work in a new domain: Plane Geometry?}{99}

\NSECP{EVALUATING AM}{99}
\SSEC{Judging Performance}{99}
 \SSSEC{AM's Ultimate Discoveries}{99}
 \SSSEC{The Magnitude of AM's Progress}{99}
 \SSSEC{The Quality of AM's Route}{99}
 \SSSEC{The Character of the User-System Interactions}{99}
 \SSSEC{AM's Intuitive Powers}{99}
 \SSSEC{Experiments on AM}{99}
 \SSSEC{How to Perform Experiments on AM}{99}
 \SSSEC{Future Implications of this Project}{99}
 \SSSEC{Open Problems: Suggestions for Future Research}{99}
 \SSSEC{Comparison to Other Systems}{99}
\SSEC{Capabilities and Limitations of AM}{99}
 \SSSEC{Current Abilities}{99}
 \SSSEC{Current Limitations}{99}
 \SSSEC{Limitations of the Agenda scheme}{99}
 \SSSEC{Limiting Assumptions}{99}
 \SSSEC{Choice of Domain}{99}
 \SSSEC{Limitations of the Model of Math Research}{99}
 \SSSEC{Ultimate powers and weaknesses}{99}
\SSEC{Final Conclusions}{99}

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\ASEC{CONCEPTS}{99}
\ASSEC{LISP Representation}{99}
 \ASSSEC{The `Compose' Concept}{99}
 \ASSSEC{The `Osets' Concept}{99}
\ASSECP{Concepts created by AM}{99}
\ASSECP{Maximally-Divisible Nos}{99}

\ASEC{HEURISTICS}{99}
\ASSEC{Heuristics for dealing with Anything}{99}
\ASSEC{Heuristics for dealing with Any-concept}{99}
\ASSSEC{Heuristics for any facet of Any-concept}{99}
 \ASSSEC{Heuristics for the Examples facets of Any-concept}{99}
 \ASSSEC{Heuristics for the Conjecs facet of Any-concept}{99}
 \ASSSEC{Heuristics for the Analogies facet of Any-concept}{99}
 \ASSSEC{Heuristics for the Genl/Spec facets of Any-concept}{99}
 \ASSSEC{Heuristics for the View facet of Any-concept}{99}
 \ASSSEC{Heuristics for the In-dom/ran-of facets of Any-concept}{99}
 \ASSSEC{Heuristics for the Definition facet of Any-concept}{99}
\ASSEC{Heuristics for dealing with any Active concept}{99}
\ASSEC{Heuristics for dealing with any Predicate}{99}
\ASSEC{Heuristics for dealing with any Operation}{99}
\ASSEC{Heuristics for dealing with any Composition}{99}
\ASSEC{Heuristics for dealing with any Insertions}{99}
\ASSEC{Heuristics for dealing with the operation Coalesce}{99}
\ASSEC{Heuristics for dealing with the operation Canonize}{99}
\ASSEC{Heuristics for dealing with the operation Substitute}{99}
\ASSEC{Heuristics for dealing with the operation Restrict}{99}
\ASSEC{Heuristics for dealing with the operation Invert}{99}
\ASSEC{Heuristics for dealing with Logical combinations}{99}
\ASSEC{Heuristics for dealing with Struc\-tures}{99}
\ASSEC{Heuristics for dealing with Ordered-struc\-tures}{99}
\ASSEC{Heuristics for dealing with Unordered-struc\-tures}{99}
\ASSEC{Heuristics for dealing with Multiple-eles-struc\-tures}{99}
\ASSEC{Heuristics for dealing with Sets}{99}

\ASEC{TRACE}{99}

\ASEC{BIBLIOGRAPHY}{99}

\NNSECP{Acknowledgements}{99}

\vfill\end