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:


 * : Chapter $\text{I}$: Preliminary Explanations of Ideas and Notations


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


 * : Preface


 * : Chapter $\text I$: Introductory: $\S 1.21$ Formation of Partial Differential Equations through the Elimination of Arbitrary Constants


 * : Chapter $\text {I}$. Complex Numbers: $1.1$ The introduction of complex numbers into algebra


 * : Chapter $\text {I}$: Number: $1.1$ Introduction


 * : Chapter $\text {I}$: The Error Function; Beta and Gamma Functions: $1 \cdot 1$. The study of functions


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


 * : Chapter $\text I$: Functions and Limits: $\S 3$: Bounds of a Function: Theorem $\text{A}$
 * There are some examples not processed
 * Still some work to be done structuring which has some entries not yet included in the source flow


 * : Chapter $\text {I}$: Sets of Points: $1 \cdot 1$. The algebra of sets


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


 * : Historical Introduction


 * : Chapter $0$: Algebraic Concepts


 * : Chapter $1$: The Real and Complex Number Systems: $\text{1-2}$ Arithmetical properties of real numbers


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


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


 * : Chapter $\text {I}$: Introduction: $1.1$. What numerical analysis is about


 * : Chapter $1$: Linear Differential Equations with Constant Coefficients: Problems for Chapter $1$: $10$


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


 * : Chapter $\text {II}$: Topological Spaces: $\S 11$. Continuity on the Euclidean line


 * : Chapter $\text{I}$: The Theory of Space Curves: $1$. Introductory remarks about space curves


 * : Chapter $1$: Polynomials; The Remainder and Factor Theorems; Undetermined Coefficients; Partial Fractions: $1.2$. The remainder and factor theorems


 * : $\S 17$: Well Ordering


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


 * : Chapter Two: $\S 3$. A Fourier Theorem: Theorem $1$


 * Revisit from $\S 2.2$: confusion over definition of piecewise differentiable. Recheck entire work, for certainty.


 * : Chapter $1$: Introduction: $1.1$. Statistics


 * : 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: $(10)$


 * : Chapter $1$: The Real and Complex Number Systems: Real Numbers: $1.38$. Decimals


 * : Problems


 * : Chapter $2$: Probability and Discrete Sample Spaces: $2.3$ Probabilities in discrete sample spaces


 * : $\S 2.3$: 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


 * : $\S 1$ Fluid Properties and Definitions


 * : Chapter $1$: Rectangular Cartesian Coordinates and Rotation of Axes: $1.1$ Rectangular cartesian coordinates


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


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


 * : Chapter $\text{I}$: Sets and Functions: Functions


 * : 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 $20.1$ -- running through it again, as follows:


 * : Chapter $1$: Sets, Functions, and Relations: $\S 1.1$: Sets and Membership


 * : Chapter $1$: Variables and Functions


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


 * : $\text I$: Amusing Problems: $1$. Observant Children


 * : $\S 3$: 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 $1$: Real Numbers and Functions of a Real Variable: $1.1$ Real Numbers


 * : Chapter $1$: Introductory Concepts: $1$. Basic Building Blocks: $4$. LINEAR VECTOR SPACE


 * : 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
 * To be reprocessed from start.


 * : Chapter $\text {II}$. The Celestial Sphere: $19$. Declination and hour angle.


 * (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


 * : Chapter $1$: Preliminaries: $1.1$ Set Theory


 * : $2$: 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 $2$


 * : $\S 1$: Numbers: $1.1$ Natural Numbers and Integers


 * : $1$ Vectors and matrices: $1.1$ Matrices


 * : $\S 2$: 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.


 * : $0$ The origins of complex analysis, and a modern viewpoint: $1$. The origins of complex numbers


 * : $\S 5.1$: Distribution Functions
 * due to be reprocessed


 * : $\S 1$: Informal statement calculus: $\S 1.3$: Rules for manipulation and substitution
 * Second pass needed. Many examples not documented.


 * : $\S 1$: Entropy = uncertainty = information: $1.1$ Uncertainty: Exercises $1.1$: $2.$






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


 * : Chapter $1$: Introduction: $1.1$ Classification of Differential Equations


 * : Chapter $1$: Introduction: $1$ Nonlinear systems, bifurcations and symmetry breaking


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


 * : Chapter $1$: The Romance of Numbers: $1$


 * : 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 $2.2$
 * to be reviewed


 * : $\S 1.4.2$: Mathematical induction
 * to be reviewed


 * : $\S 1$: 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


 * : Chapter $1$: General Background: $\S 4$ Larger and smaller: Theorem $4.1$ (Cantor's theorem)



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