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


 * : Preface


 * : Chapter $\text I$: Introductory: $\S 1.2$ Genesis of an Ordinary Differential Equation


 * : 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


 * : $\S 9$: Families -- Reviewing Chapter 9 with a view to making our treatment of families of sets watertight


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


 * : 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: Supplementary Problems: Laplace Transforms of Elementary Functions: $51 \ \text {(a)}$


 * : $\S 30$: 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


 * Then by chapters (work in progress):


 * : $\S 10$: Formulas from Plane Analytic Geometry: $10.10$: Area of Triangle with Vertices at $\tuple {x_1, y_1}$, $\tuple {x_2, y_2}$, $\tuple {x_3, y_3}$


 * : $\S 12$: Formulas from Solid Analytic Geometry: $12.1$


 * : $\S 39$: Probability Distributions: Poisson Distribution: $39.2$


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


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


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


 * : Chapter $2$: The Symmetric Groups: $\S 80 \alpha$


 * : $\S 1.20$: 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


 * : Chapter $1$: Computations Using Logarithms (no point doing all the exercises in this one)


 * : $\S 1.3$ 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


 * : $\S 8$ -- revisiting from start, as follows:


 * : $\S 6$. Indexed families; partitions; equivalence relations: Exercise $7$


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


 * : Chapter $1$: Theory of Sets: $\S 10$: Arbitrary Products: Exercise $1$: Work needed on establishing rigorous definitions and understandable interpretations of a general cartesian product of a family of sets indexed by an uncountable set.


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


 * : Chapter $\text I$. Spherical Trigonometry: Exercise $4$.


 * (Chapters consisting of nothing but detailed calculation have not been implemented. Exercises also not done.)


 * : Basically complete, apart from exercises: second runthrough in progress


 * : $\S 5$: Subsequences: Exercise $\S 5.21 \ (2)$


 * : $\S 4.2$: 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: $2.3$


 * : Chapter $2$: Divisibility Theory in the Integers: $2.2$ The Greatest Common Divisor: Problems $2.2$: $1$


 * : $2.2$: 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 $9$ ... second pass through:


 * : Chapter $2$: Integers and natural numbers: $\S 2.2$: Divisibility and factorization in $\mathbf Z$: Exercise $2$


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


 * : $1,41421 35623 73 \ldots$
 * The full documentation of both $0$ and $1$ has been skipped, through laziness.


 * : Notation: Alphabets and strings




 * : A Chronological List Of Mathematicians


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


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


 * : Naive Set Theory: $\S 1.6$: Functions


 * : 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


 * : $\S 1$: The Complex Numbers: Introduction: $1.1$: The Algebra $\R$ of Real Numbers


 * : Chapter $2$: 'And you do addition?': $\S 2.4$: Counting and mathematical induction: Definition $2.4.1$




 * : Chapter $9$: Patterns in Nature: Differential equations



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.


 * : 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: 733