>>6562434 highest level was probably stochastic processes, it was mixed undergrad and grad students with about 1/3 of the class being the latter, however i was really interested in it and as such didnt really have much trouble
the most difficult for me was analysis, i really struggled with it both semesters and just barely managed to scrape by with Bs, i dont really know why it was so difficult as id taken other proofs classes before and did fine with abstract algebra the same semester as analysis 1 but i was just really not good with it.
as far as highest level in terms of course numbers, thatd probably be numerical analysis unless actuarial science counts in which case itd be life contingencies, both classes were fairly easy though, i am much stronger at applied shit like numerical analysis than at pure math and actuarial science is really not conceptually difficult just a metric fuckload of material to memorize and apply.
math major obviously, dual majored with econ, im headed to grad school for applied math in the fall and am really scared grad level analysis is gonna rape me next semester.
Not the most advanced math class I took but at that time it was the hardest: Intrroduction to partial differential equations. Learning shit like conormal distributions, Bessel potential spaces and hyperfunctions all within one semester course seemed pretty weird to a 2nd year BSc student with almost no prior knowledge.
>>6563156 I'd replace "Homological Algebra" with "Homotopy", I guess you are still grounded in Complexes/Simplicial sets but why you would bother studying such things in the first place can be difficult to see for a novice. Homological algebra and it's applications to algebra is better motivation than it's topological roots anyway imo.
I'd be interested to see more people's paths, particularly if self-taught. Here was mine:
I started by going through "The Chemistry Maths Book" by Erich Steiner. It took me anywhere between 4-6 hours per day for the entire summer between 1st and second year of university. I knew a bit from A-level mathematics, but nothing serious. I learned about
- multi-variable and single variable calculus - complex numbers - Orthogonal Functions and Integral transforms - Differential Equations (incl. power series methods) - Linear Algebra - Statistics
In third year, I've started to steadily learn from "Mathematical Methods" by Riley and Hobson. I had a thing with Boas's book for a few months, but it didn't work out. I learned about
- Vector - More about ordinary differential equations + special functions - Complex analysis - Tensors - Group theory and Representation Theory
It's been a year since I graduated now and after a year or two, I may feel comfortable enough to move on to Sadri Hassani's book, "Mathematical Physics". I'm not quite sure what a manifold is, but I'm very excited to find out.
>>6562434 I've only studied stuff like analysis and algebra at university, but outside of class have being learning algebraic geometry, algebraic topology and quantum groups, amongst other things. >>6562447 You must be new here.
>>6563227 (me) >>6563220 I don't understand what's so hard to understand. I'll break it down for you since you're having a difficult time. Here is OP's question. >What is the highest and hardest level of mathematics you have tekn at either the undergraduate or graduate level? Also include your major Anon responded with: solving quadratic equations. Sure, it might not specify what level, but I graduated high school with some basic knowledge of pre-calc and even know that it falls under the category of either algebra level one, or two.
>>6563310 you're not v fucked at all since that's baby math-we've all been there before you can look up paul's notes for calc II there used to be linear algebra notes on his page but he took them down, you should be able to find them elsewhere if you cannot find them elsewhere reply back with your email i send them when I get home if i remember or see the thread again
>>6563310 Those are all pretty easy. Linear algebra is just very boring and tedious. I think it's the most boring class I've ever taken.
I'm a CS student, graduated, haven't started grad school. I took 3 calculus classes, combinatorics, statistics, DEs, all the standard stuff for an engineer.
I think I found numerical methods the most difficult. That was a scientific computing class offered at my school. That covered quadrature, ODEs, splines, interpolation, eigenvalue problems. The professor made the class difficult. IIRC the average on the first exam was a low D. And everyone in the room was "smart."
>>6563322 I agree with this guy. And computer programming. Goddammit did I hate computer programming. nothing but autism in that class, all radiating out from the teacher. I tried talking to come people in that class who always seemed to be reading, but all they could talk about was fucking YA and children's books. THEY WERE IN FUCKING UNIVERSITY.
>>6563365 I took calculus I in college without taking any trig or precalculus. Was freaking out for the first 3 weeks so I taught myself it and memorized the unit circle. Came out with a B+, it was bretty gud.
My hardest purely undergrad was Abstract Algebra. Took a joint undergrad/grad as an elective: Complex Analysis. Headaches started at "multi-valued function". Grad School: Concept-wise: Topics course in Applied Analysis, Hilbert Spaces & Integral Equations taught by department chair. Annoying: Mathematical Statistics I -- Memorize PDF CDF and MGF of all distributions. Yeah, see above -- MS MATH, not STAT!
highest: Graduate level probability course hardest: precalculus, so much useless information favorites: discrete mathematics, calculus 2 easiest: probability have taken calc 1,2,3,linear alg,discrete,stats,probability
going to take theory of parrallel algorithms in the fall
>>6564495 It's not about axioms. The term "operator algebra" generally refers to the Banach algebra of bounded linear operators on a complex Hilbert space. You can add other structure, for example a C* algebra is a Banach algebra with an involution that satisfies some properties that make it act like the operator adjoint (look the exact definition up on Wikipedia, I don't feel like listing a bunch of properties here).
The usual example of a finite dimensional C* algebra is the Banach algebra of n x n complex matrices with matrix multiplication as the product, the operator norm to make it a Banach algebra, and the matrix adjoint (i.e. conjugate transpose) to make it a C* algebra. This can also be seen as the Banach algebra of bounded linear operators on the Hilbert space C^n since finite-dimensional spaces are all complete, linear operators on finite-dimensional spaces are all bounded/continuous, and of course the space of n x n complex matrices and the space of linear operators on C^n are canonically isomorphic.
C* algebras come up in harmonic analysis and representation theory as certain completions of the group algebras of locally compact groups. Operator algebras in general form the mathematical backbone of quantum mechanics and quantum information theory, and they're a huge deal in general in contemporary functional analysis and abstract harmonic analysis and noncommutative geometry.
>>6564631 Sorry for not including enough fancy-sounding math words. Galois cohomology. Derived category. Homotopy type theory. Hodge cycle. Calabi-Yau manifold. Short exact sequence. Tensor. Tensor. Tensor. Tensor. Tensor.
>>6564710 A few things: The phrase "operator algebra" doesn't have one definite, universal definition like "Banach algebra" or "vector space" do but the usual thing it refers to is the Banach algebra consisting of the bounded linear operators on a complex Hilbert space. You can find an axiomatic definition of a Banach algebra or a C* algebra or whatever but trying to define anything but the simplest algebraic structures (these aren't even purely algebraic structures) using lists of axioms is silly, and if all you know is that list of axioms then you don't really understand what the structure is or what it's for. I say "It's not about axioms" because it really isn't, and if you know enough about math to understand what an operator algebra is, then "a Banach algebra is a complete normed algebra" should be perfectly clear. A vector space is not a ring, it's an abelian group with a field acting on it but I guess since you're drunk, whatever.
Linear algebra is pretty hard. For some reason it's only taught at night-classes and by Russian professors who bore me to death. I literally almost died on many occasions during the two times I failed Linear Algebra because I was so bored I was ready to try learning that "magic trick" the Joker uses in The Dark Knight using myself to practice. Have you ever had to put a pen back in your backpack so you don't inadvertently stab yourself with it during a momentary lapse of judgement?
Oh and I learned about "Quantum Calculus" in this one class.
Well, I'm doing Meteorology with a Math minor right now, so which do you want: the hardest and highest I've taken so far, or the hardest and highest that I know I will have to take at some point in the future?
I took a Detection and Estimation Theory class as a EE. It was a grad level course, but I petitioned to take it as an undergrad. It wasn't especially difficult, but the topics it covered were considered higher. It's probability theory covering, among other things, Cramer-Rao lower bound, hypothesis testing and the Neyman-Pearson criterion, and Kalman filtration.
I studied signal processing, for the most part.
I sat in a real analysis and probability class that was a bit over my head. Also sat in on an introductory information theory class.
So, here's what I officially took that could be considered math: Calculus Differential Equations Applied Linear Algebra Applied Complex Analysis (Bio)Statistics Probability and Stochastic Processes Discrete and Continuous Signals and Systems Digital Signal processing (2 semesters of it) Statistical Digital Signal Processing Detection and Estimation Theory
and if you stretch it a bit: Digital Communications Wireless Communications
>>6563869 >Real autists are usually mentally retarded
I think there's a slightly negative correlation between ASD and intelligence, but, by and large, intelligence and autism are independent of each other. People who think autistic people are all really smart, though are wrong.
Highest: Calc 3 Hardest: Calc 1 - I had so much difficulty in trying to wrap my head around derivatives and integrals. I made it out with a C in the class. Brought down by GPA quite a bit, but I got an A in Calc 2 and a B in Calc 3, so......yeah.
I'm taking differential equations over my summer break, can anyone tell me what I'm going to do and how hard it's going to be from Calc 3?
Don't know if this serves anything, but here's a list of the math classes I've taken in order:
>>6565117 >I'm taking differential equations over my summer break, can anyone tell me what I'm going to do and how hard it's going to be from Calc 3?
It depends on your class, but, usually, the breadth of topics is smaller than Calc III. Go to Khan Academy's playlist, which is really pretty concise. Exact Equations is really the only topic you even need Calc III as a prereq for. Most of it can be inferred from calc II.
>>6565123 Consider the possibility that anon's Linear Algebra class was taught harder than his Real Analysis class.
On another note, though, if it's an applied math curriculum and not a pure math curriculum, real analysis isn't really essential at the undergraduate level. I didn't encounter anything in undergrad where knowing the definitions of countable infinities, sigma algebras, finite fields, and measures, actually lead to different conclusions than one would get from drawing a Venn diagram. These things are for graduate school, really.
>>6565133 If you're majoring in statistics I'd think that you'd take a fair bit of probability theory and mathematical statistics but I guess it would depend on the program. At my school, fourth year is essentially like grad school and a few students will get to that point in third year but most schools don't do that. I take the "shitty" part back, but it seems like something you'd want to take if you want to learn any of the theory.
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