SQT Stupid Question Thread

I need to convert these things within the limits to fractions but I have no idea how.

I'm on my third year of math and want to study eventually a PhD in one of the fields of analysis, algebraic topology or algebraic geometry (I'll have to decide after I take these classes, which are the ones that most interest me). I have a choice of 2-3 modules this year and I'd want to know which of these would benefit me most in such a future:

Number theory (abstract algebra prereq):
>unique factorisation, ideals, euclidean rings, fields, algebraic integers, quadratic fields and integers, discriminant and integral bases, factorization of ideals, the ideal class group, units in quadratic fields

Dynamical systems (complex analysis and calc III prereq):
>Smooth ODEs: existence and uniqueness of solutions.
>Autonomous ODEs: orbits, equilibrium and periodic solutions.
>Linearisation: Hartman-Grobman, stable-manifold theorems, phase portraits for non-linear systems, stability of equilibrium.
>Flow, Fixed points: Brouwer's Theorem, periodic solutions, Poincare-Bendixson and related theorems, orbital stability.
>Hopf and other local bifurcations from equilibrium, bifurcations from periodic solutions.

Geometry (Complex, Calc III, algebra prereqs):
>The Euclidean group as group of isometries.
>Conjugacy classes and discrete subgroups.
>The affine group.
>Proof that every collineation is affine.
>Ceva and Menelaus Theorems.
>Isometries and affine transformations of R3.
>Rotations in terms of quaternions.
>The Riemann sphere, stereographic projection, and Mobius transformations.
>Inverse geometry.
>Projective transformations.
>Equivalence of various definitions of conics.
>Classification and geometrical properties of conics.
>Models of the hyperbolic plane.
>Hyperbolic transformations.
>Hyperbolic metric in terms of cross-ratio.
>Elementary results in hyperbolic geometry.

(cont)

PDEs (Calc III and real analysis prereqs):
>First order equations and characteristics.Conservation laws and their weak solutions.
>Systems of first-order equations and Riemann invariants.
>Hyperbolic systems and their weak solutions
>Classification of general second order PDEs
>Poisson,Laplace, Heat and Wave equations:existence and properties of solutions

Galois Theory (algebra prereq):
>Field Extensions: Algebraic and transcendental extensions, splitting field for a polynomial, normality, separability.
>Results from Group Theory: Normal subgroups, quotients, soluble groups, isomorphism theorems.
>Groups acting on fields: Dedekind's lemma, fixed field, Galois group of a finite extension, definition of Galois extension, fundamental theorem of Galois theory.
>Galois Group of Polynomials: Criterion for solubility in radicals, cubics, quartics, 'general polynomial', cyclotomic polynomials.
>Ruler and Compass Constructions: definition, criterion for constructability, impossibility of trisecting angle, etc.

>(a)
are you kidding me? simplify it
>(b), (c)
substitute 1/x = t, dont forget to change the limit

>trolling in the SQT thread
for what purpose

I'd go for Dynamical systems or PDE since those are easily applied to real world stuff right away...

I'm specifically going for a phd in pure maths dude, application is the least of my worries

How was that post trolling?

Do all of them pussy

if only, can only do 6 modules and i've already chosen 3-4