What does a typical 4 year undergrad math curriculum look like? I want to self study.
What does a typical 4 year undergrad math curriculum look like? I want to self study
Noah Brown
Other urls found in this thread:
math.uga.edu
bulletin.uga.edu
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Adam Green
Pre-calc (if you need), calc, linear algebra, differential equations, vector calc, statistics, discrete math, abstract algebra, analysis.
Depends on your specialization, though. For pure math, you'd probably have to take abstract algebra 2 and analysis 2.
Matthew Reed
I've already done everything except for the last three. Is that really all that there is? I was expecting at least some set theory or topology or something.
Josiah Peterson
It depends on the college, major, etc
Isaiah Myers
Yeah, there's usually more.
Just go to the websites of some universities' math departments. They usually have this information.
Aiden Cooper
The set theory I took was integrated into my statistics class
Nolan Sanders
For pure math at my school you need either topology or differential geometry.
For applied you need numerical methods
Ayden Garcia
you haven't done all of that, it's deceptive because some math classes are called just like engineering classes. also that list is pretty shit. let me give you better advice. Even if the "Linear Algebra" and "Differential Equations" have the same name, they are very different, proof-based classes.
Warm-up (not really math but I guess it helps):
Some calculus sequence
Engineering Statistics (calculus-based)
Some introductory calculus-based discrete math
Core:
Set theory (Axioms of ZFC, construction of N, Z, R)
Linear Algebra (Finite-dimensional vector spaces, dual spaces, Rational / Jordan normal forms)
Real Analysis 1 (Analysis in R^n, the derivative and riemann integration)
Group Theory [Algebra 1?] (Theory of groups, with a focus on finite groups, classification of Abelian groups, Sylow theorems)
Ring Theory [Algebra 2?] (Theory of rings, ideals, euclidean domains, UFDs, PIDs, some capstone theorem maybe Bezout)
Some of these:
Complex Analysis (Analysis in C, Cauchy theory, residue theory)
Analysis on Manifolds [Real Analysis 2A?] (Analysis on manifolds, up to Stoke's Theorem)
Measure Theory [Real Analysis 2B?] (Measure theory, maybe probability?, lebesgue measure and integration)
Field Theory [Algebra 3?] (Field extensions and Galois Theory)
Ordinary Differential Equations (Solution of linear systems by JNF, Picard et al, qualitative study and Poincare-Bendixon)
Differential Geometry (Study of differentiable manifolds)
Topology (Study of topological spaces)
Functional Analysis (Analysis in metric spaces of functions, banach spaces, hilbert spaces, etc)
Operations research (Linear optimization and simplex method, lagrange multipliers, convex optimization)
James Stewart
Calc 1,2,3,4
Linear algebra
Proofs/number theory
Intermediate analysis
Electives
This can be considered your specialization.
Complex analysis
College geometry
Differential geometry
Topology
Numeric methods
Stats
There's usually a specialization for finance as well
Ryder Cruz
that's naive set theory, not real set theory
Andrew Rodriguez
>implying I'm not a mechanical engineer
Lead by example, freshman
Jack Carter
here are my undergrad math courses, but i took a bit more than average. numbers indicate quarters it took to complete.
lower div:
single/multivariable calculus 4
linear algebra 1
differential equations 1
upper div:
linear algebra 1 (consider 2)
complex analysis 1
set theory 1
combinatorics/graph theory 1
odes 1
nonlinear dynamics 1
analysis 2 (consider 3 for measure theory)
abstract algebra 3
numerical methods/analysis 2
differential geometry 2
topology 1
mathematical modeling 1
enumerative combinatorics 1
algorithms 1
math research w/ professor 1
personally, i think the very rigorous courses in linear algebra, analysis, and abstract algebra were the most beneficial. if you want to find yourself more useful, however, numerical methods, combinatorics, probability theory, and machine learning are invaluable.
Connor Miller
Calculus x2
Vector Calculus
Ordinary Differential Equations
Partial Differential Equations
Linear Algebra x2
Proofs
Real Analysis x2 (at baby Rudin's level)
Abstract Algebra x2 (at Artin's level)
Topology x2 (point-set and algebraic)
Probability x2
Complex Analysis
Geometry
Electives x4
Dominic Flores
>I've already done everything except for the last three
So you've done nothing yet.
Anthony Brown
Needs more applied desu, like stochastic processes and linear and convex optimization
Aiden Mitchell
>artin's level
too easy
Nolan Myers
Year 1: calculus 1-3, linear algebra, algebra I, probability, numerical analysis
Year 2: ODE, combinatorics, algebra II, real analysis, graph theory, linear programming
Year 3: fourier analysis, complex analysis, PDE, non-linear programming, algebraic topology, functional analysis, differential geometry
Year 4: triple integrals
Matthew Jackson
They can do Lang as an elective
Landon Reed
Triple integrals is Calculus 3
Austin King
it's a joke :^)
Xavier Reyes
I won't pretend my math degree was the most rigorous, but here is the curriculum:
math.uga.edu
You can look up the classes here:
bulletin.uga.edu
That website also has old syllabi, but you might be able to find newer versions by googling and finding the professor's site.