>Analysis: The Study of Precision >Algebra: the Study of

>>9139828
>>Geometry: The study of Space
no topology is the study of space

>>Number Theory: The study of Quantity
it's not clear how most of algebraic number theory can be thought of as quantities

>>9139837
what would geometry be? i can't really separate it from algebra in terms of space and structure.

>>9139837
Topology is a subfield of Geometry you shit head

>>9139828
i disagree on some
>analysis: the study of change
>Algebra: the study of symbolic manipulation
>geometry: the study of shape
>calculus: analysis for dummies
>number theory: the study of number systems
number theory is so fundamental that i have trouble defining. also that's not a jab against Algebra. i think Algebra is probably the most beautiful subject. functional analysis is the most amazing love child between subjects

what's other people's opinions?

>>9139828
Calculus is a subfield of analysis. Also, I don't know why you think analysis is just about precision. I'm not even sure what that's supposed to mean.

>>9139861
>what's other people's opinions?
you are a moron

>>9139858
no it fucking isn't. topology is about the space, geometry is about things which inhabit that space

>>9139864
what the fuck are you smoking. topology is about homomorphisms

>>9139863
Nice. glad you gave me constructive criticism and contributed positively.

if you disagree, give legitimate feedback and post your own ideas.

>>9139864
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space
>and the properties of space

>>9139858
>Topology is a subfield of Geometry you shit head
Wrong.

>>9139868
>homomorphisms
that's true. biggest hard-on in that whole subject. i still think the properties of spaces is the core of the subject though.

>>9139870
sure. you need to discuss the space in order to talk about things in that space. measure theory is also about size, but i would group measure theory with analysis more than geometry.

>>9139870
It is, from my own observations, that geometry is more the study of local properties of space. Things like curvature and how curves work and shit. Topology is more how the space of which geometry is happening itself works. Things like, connectedness, compactness etc.

For example, you take a torus, equip it with the standard metric (topology, hence bestowing it a set of topological properties) and then maybe study curves on it (do geometry)..

File: 06e107945968a0bd128d37a846493364--minions-funny-quotes-minion-sayings.jpg (42KB, 589x600px) Image search: [Google]

42KB, 589x600px

>>9139878
this is a nice interpretation. i like it.

>>9139828
>Analysis: The Study of inequality autism in as many dimensions as you want (especially large cardinalities)
>Algebra: the Study of invariants
>Geometry: The study of metrics
>Number Theory: random and often unrelated incredibly hard fundamental questions about numbers that got thrown into a single field for no real reason

>>9139885
>number theory
i kek'd

>>9139861
OP was right on analysis
It was a branch invented by Cauchy to counter the non rigorous approach to infinite sums by earlier mathematics like Euler
It is the study of precision