User:Prime.mover/Source Work Progress

Progress
I reckon it's about time I started on another item of displacement activity, that is: documenting how far I have got with the task of transferring the contents of the works on my bookshelf into pages on.

This will of course be an ongoing task.

In chronological order of works:


 * : First Article: $\S 1$: The Conception of Power or Cardinal Number -- barely scratched the surface


 * : Still unstructured.


 * : $\S \text{II}.6$: Logical Constants


 * : $\text{I}.1$: Definition and examples of semigroups


 * : Chapter $0$: Algebraic Concepts


 * : Still to be started. Edition to be reviewed.


 * : Appendix $1$: Some Results from the Elementary Theory of Numbers: Theorem $12$


 * : $\S 4.2$: The Construction of an Axiom System: $RST \, 1$


 * : $\S 17$: Well Ordering


 * : $\S 2.2$: confusion over definition of piecewise differentiable.


 * : $\S 3.3$: Neighborhoods and Neighborhood Spaces: Exercise $3$: Got bogged down in Neighborhood Spaces, and I have basically skipped the exercises.


 * : Started at $3.1.1$: Binomial Theorem, up to $3.1.14$: Generalized Mean


 * : $\S 1.4$: Theorem $4.2$


 * : $\S 2.5$: Corollary $2.25.1$ -- revisit


 * : $\S 1.1$: Exercise $1 \ \text{(c)}$


 * : $\text{III}$: 'ALL' and 'SOME': $\S 1$


 * : Chapter $1$: The Group Concept: Examples: $(10)$


 * : Problems


 * : $\S 2.3$: Truth-Tables: Exercise $6 \ \text{(ii)}$


 * : Chapter $1$: The Laplace Transform: Some Important Properties of Laplace Transforms: $5$. Laplace transform of derivatives: Theorem $1 \text{-} 10$


 * : $\S 30$: Transpose of Row Matrix is Column Matrix -- another pass as follows:


 * : Chapter $1$: Algebraic Structures: $\S 1$: The Language of Set Theory


 * : $\S 1.10$: Theorem $31$ -- exercises not done


 * : $1$: Subgroups: Problem $1.1$


 * : $\text{III}$: More About Continuity -- may need revisiting from start


 * : Chapter $1$: Triangles and Polygons: Theorems and Corollaries $1.27$


 * : $\S 3.5$: Well-ordered sets. Ordinal Numbers: Example $2$


 * : $\S 1.2$. The Usefulness of Integral Transforms


 * : $\S 1$: Some examples of groups: Example $1.13$


 * : Lots done, but there are gaps -- working through from beginning as follows:


 * : $\S 4$: Geometric Formulas: $4.24$: Solid geometry $4.25$ to $4.48$ to be done


 * : $\S 1.1$: Rings and Algebras: Problem $1.1.3$


 * : $\text{II}: \ 41: \ 7$


 * : $\text {4-3}$ Riffling: Exercise $1$


 * : Chapter $2$: The Symmetric Groups: $\S 79 \delta$


 * : $\S 1.20$: Decomposition of a Set: Definition $20.1$


 * : Chapter $1$: Variables and Functions


 * : $\S 2$: Sets and functions: Functions of several variables
 * Revisiting this book


 * : $\S 3$: Appendix $\text B$: Newton


 * : $\S 1.3$ Axiom Schema of Abstraction and Russell's Paradox


 * : $4.2$: Preliminary Quantification Rules


 * : $1.3$ A paradoxical decomposition of the sphere: Theorem $1.2$


 * : Chapter $1$: Numbers: Decimal Representation of Real Numbers


 * : $\S 8$


 * : up to $8.2.3$: Definition:Uniform Convergence/Real Numbers -- may be gaps


 * : $\S 4.2$: Trees and Probability -- there are gaps


 * : Appendix $\text{A}.6$: Mathematical Induction: Problem Set $\text{A}.6$: $41$ Complete except for final set of exercises (they go up to $55$) and some simple exercises on logic


 * : $2$: Examples of Groups and Homomorphisms: $2.3$


 * : $2.2$: The summation convention


 * : $2$: Functions, Limits and Continuity: The Elementary Functions: $9$ -- undergoing a second pass to fill in the exercises, as follows:


 * : $1$: Complex Numbers: Supplementary Problems: Conjugate Coordinates: $116 \ \text{(a)}$


 * : $\S 3.4$: Cyclic groups: Exercise $9$


 * : $\S 2$: The Two-Person, Zero-Sum Game with Equilibrium Points


 * : $\S 1.3.2$: Power series: $(1.47)$


 * : $\S 1.8$: Problems: $1 \ \text{B}$


 * : Chapter $14$: The classification of finite abelian groups: Proposition $14.2$


 * : $\S 1.2.9$: Generating Functions: Exercise $14$: Mostly complete up to this point. Much of the detailed work on algorithms has been left undone.


 * : $2$. Definition of Equivalence. The Concept of Cardinality. The Axiom of Choice: Definition $2.2$


 * : $\S 1.4.2$: Mathematical induction


 * : $\S 2.3$: Relations: Theorem $2.3.1$ -- then the thread gets confused


 * : Chapter $8$: The System of the World

More or less complete

 * : Complete
 * : Complete
 * : Complete


 * : Complete


 * : Complete


 * : Appendix only


 * : Exercises: Chapter $1$: Exercise $1 \ \text{(iv)}$
 * Section $39$ has been omitted as it is a discursion with an imprecise structure.
 * The bulk of the exercises remain to be documented.


 * : Basically complete, apart from exercises


 * : Complete


 * : as complete as necessary


 * : Basically complete


 * : Complete


 * : Appendix $\text A$


 * : Complete
 * except for a number of sundry results in section $142,857$

Other progress
Prime number sequence: 643