Math notes / Calculus and analysis

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This is more for overview of my own than for teaching or exercise.

Overview of the math's areas

Arithmetic · 'elementary mathematics' and similar concepts
Set theory, Category theory
Geometry and its relatives · Topology
Elementary algebra - Linear algebra - Abstract algebra
Calculus and analysis
: Information theory · Number theory · Decision theory, game theory · Recreational mathematics · Dynamical systems · Unsorted or hard to sort

Math on data:

  • Statistics as a field
some introduction · areas of statistics
types of data · on random variables, distributions
Virtues and shortcomings of...
on sampling · probability
glossary · references, unsorted
Footnotes on various analyses

  • Other data analysis, data summarization, learning
Data modeling, restructuring, and massaging
Statistical modeling · Classification, clustering, decisions, and fuzzy coding ·
dimensionality reduction ·
Optimization theory, control theory · State observers, state estimation
Connectionism, neural nets · Evolutionary computing
  • More applied:
Formal grammars - regular expressions, CFGs, formal language
Signal analysis, modeling, processing
Image processing notes

From a wider perspective

Precalculus, when it is a thing, refers to secondary school coursework given to students with technical interests, to give them a thorough review of algebra and trigonometry, and of concepts that turn up in many (applied) technical fields, such as exponents, logarithms, complex numbers, vectors, trigonometric functions, and also things like conic sections, analytic geometry.

Calculus studies limits, derivatives, integrals, infinite series, and such. Alternatively, any calculation guided by the symbolic manipulation of expressions (e.g. propositional calculus, predicate calculus, relational calculus, lambda calculus, etc.). Usually taught in technical university studies.

Analysis is rooted in calculus, and sometimes considered a specific part of it. Analysis focuses more on the uses of limits (of sequences and of functions), differentiation, integration and measure, infinite series, and analytic functions, certain types of approximation, and often for both real numbered and complex numbered spaces/variables.

Some relevant concepts