What would an optimal curriculum in pure mathematics look like?
Describe your ideal course sequence sequentially
What would an optimal curriculum in pure mathematics look like?
Describe your ideal course sequence sequentially
They must really like snakes if they edge of his clothes says sssssssss
I deff think they should be combining math with data science and CS some probably do
Addition -> Subtraction -> Multiplication -> Division
everything else is useless academic wank you'll never need in real life
2-3 courses per semseter
Take if needed:
>Intro Formal Math (i.e. Proofs, Numbers, Sets, etc.)
Semester 1:
>Classical Real Analysis (i.e. Calculus w/ proofs + construction of reals)
>Linear Algebra
Semester 2:
>Group Theory
>General Topology
Semester 3:
>Analysis on Manifolds
>Field Theory
>Number Theory
Semester 4:
>Complex Analysis
>Commutative Algebra (Rings and Modules)
>Axiomatic Set Theory
Semester 5:
>Modern Real Analysis 1(i.e. Lebesgue Integral on R^n)
>Homological Algebra
>Riemmanian Geometry
Semester 6:
>Modern Real Analysis 2(i.e. Lebesgue Integral on general measure spaces)
>Algebraic Topology
>Probability Theory (using all the good measure theory stuff)
Semester 7:
>Functional Analysis
>Algebraic Geometry (Varieties, Schemes, and Sheaf Cohomology)
>Elective
Semester 8:
>Elective
>Elective
>Elective
I think this gives a fairly balanced curriculum.
+10 for probability theory after measure theory.
Kill yourself
Actually not a bad list
Care to make your own?
When did you need divisioin real life?
>you'll never need in real life
Unless you want to have a decent job and make money you really don't need it.
>modern algebra split into three separate courses
>another homological algebra course
>and then algebraic geometry
Algebraist spotted
I'm sure lawyers, rich Washington politicians, humanities professors at top schools, and score more such examples all know advanced math. Right? Or are they all impoverished, innumerate paupers by your reasoning?
wheres ODE, PDE and combinatorics?
It is all balanced.
Algebra:
-Linear Algebra
-Group Theory
-Field Theory
-Commutative Algebra
-Homological Algebra
-Algebraic Topology
-Algebraic Geometry
Analysis:
-Classical Real Analysis
-Analysis on Manifolds
-Complex Analysis
-Modern Real Analysis 1
-Modern Real Analysis 2
-Functional Analysis
-Riemannian Geometry
Leave them for electives. PDE really shouldn't be taken until after Functional Analysis and Modern Real Analysis anyway.
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Missing a few subfields, user?
>>Axiomatic Set Theory
Leave all the autism for that course.
16 semesters of calculus of variations
Is as understand probabilités and percentages too.