Math notes / Calculus and analysis

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 Logic Semi-sorted : 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 Machine learning goals, problems, and glossary 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 Varied text processing

From a wider perspective

Precalculus, when it is a thing, refers to secondary school coursework given to students with technical interests, to given them thorough review of algebra and trigonometry, and 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, infinite series, derivatives (ordinary and partial), integrals, multivariate calculus, and such. Alternatively, any calculation guided by the symbolic manipulation of expressions (e.g. propositional calculus, predicate calculus, relational calculus, lambda calculus, etc.).

You may get some taste of this in high school, but is more thoroughly taught in technical university studies

Analysis (especially real 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.

Crudely put, calculus had useful ideas and applications before we understood exactly how or why it worked - ideas from people like Newton and Leibniz were pretty informal, and arguably not always consistent. Analysis is the name we give to the work that gives it a more rigid foundation which drew on work from centuries, and was very gradual to finish itself.