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The Bend in the River

Subfields of mathematics: a dictionary

Algebra (classical)
The study of 18th century French history.
Algebra (modern)
A subject comprised almost entirely of vacuous definitions and trivial proofs.
Analysis (complex)
The rediscovery of results already known by Riemann and Euler, but unpublished.
Analysis (real)
The subject one studies when one does not like the concept of equality.
Calculus
A subject one is subjected to.
Category theory
A subject in which meaningful statements are obfuscated to make them seem trivial. (See mathematical logic.)
Chemistry
The application of a mixture of hand-wavy linear algebra and soupy group theory.
Combinatorics
See computer science (theoretical).
Computer science (applied)
The study of things that are small and slow.
Computer science (theoretical)
See combinatorics.
Differential equations
The study of geometry, usually performed on undergraduates using minimal geometry.
Geometry (algebraic)
Coordinate geometry, but with $ \mathfrak{fraktur} $ fonts.
Geometry (classical)
The study of badly drawn circles.
Geometry (differential)
Calculus, but with topology.
Linear algebra
Not the study of lines.
Mathematical logic
A subject in which trivial statements are obfuscated to make them seem meaningful. (See category theory.)
Number theory
A loose grouping of theorems, roughly collected together because they deal with the 20,000th decimal place of the values of some function from $ \mathbb{Z} $ into the reals.
Physics
A sub-branch of the study of differential equations.
Set theory
See topology (point-set).
Statistics
Integration over lumpy sets.
Topology (geometric)
The study of objects one can place in a display-case to impress non-mathematical visitors.
Topology (point-set)
A collection of pathological examples to scare the children of analysts.
Date: 2 April 2019   Author: tbitr1
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