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What is the highest and hardest level of mathematics you have taken at either the undergraduate or graduate level? Also include your major.
>>
triple integrals

I'm a math PhD.
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>>6562435
/thread
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>>6562435
>mfw I learned triple integrals in high school
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>>6562434

Here's how my math undergrad went:

Trigonometry
Precalculus
Calculus 1 - 3
Differential Equations
Linear Algebra

So I suppose Linear Algebra.
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>>6562435
>triple integrals
holy shit, I've done quadruple integrals before

somebody gimme muh phd
>>
>>6562461
Oh yeah? Well I once transformed the coordinates of a triple integral to 3 entirely new ones using a highly experimental new item called a "Jacob-Ian".

Named after Jacob McLean and Ian Thompson.

I wouldn't be surprised if you hadn't heard of it. It's all very new and difficult. You couldn't possibly understand.
>>
Calc 2 since we never really went over things. Most of the time we had to read the book and then the teacher would do any problems we didn't get.

It was very different from my usual "teachers actually teaching" routine
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>>6562434
Engineering Mathematics
Matrix math, Adjoint operators, some complex stuff I don't remember (probably those harmonic equations or somethin), and variational calculus

I'm an engineer.
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Topology, linearly ordered spaces and group theory. Also a quantum chemistry: Group theory course, but I'm a chemistry major also
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>>6562534
I've also taken abstract algebra but that was before group theory, so I count group theory as higher
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I've done research in stochastic dynamics and quantum/statistic mechanics. Shit is pretty hard.
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Curved Manifolds
Majoring in Physics
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Unit 1 VCE general maths.

Linear equations, financial math, univariate data.

Get on my lvl fgts
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>>6562555
As an undergrad you took that?
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>>6562548
What's this like? What are some examples of applications?
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>>6562434
I think my most difficult math class was linear algebra 2. I was able to get a B in it so I guess that's okay.
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>>6562569
Wow you're a real scholar
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>>6562570
>As an undergrad you took that?

I took a General Relativity class (for maths and mathematical physics students) as a physics undergrad (and failed).

Is that not common in America?
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>>6562640
Saying you took a general relativity class and a class on curved manifolds are very different things.
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>>6562447
you took MV, that's not fucking triple integrals m8.
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>>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.
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>>6562672
practice makes perfect with analysis, the more you see of it the more you know.
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>>6562670
What is triple integrals/ What are triple integrals?
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>>6562672
Fucking analysis proofs. Complex analysis in general was a pain in the ass. Real analysis as an undergrad wasn't too bad but that's because the professor made it a joke class basically.
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>>6562690
gay
>>6562687
\int (\int (\int 0 \, \mathrm{d} x) \, \mathrm{d} y) \, \mathrm{d} z
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>>6562692
How is that different from triple integrals in MV
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>>6562694
they aren't.
it's a shitty meme that should die, but no mods lol.
>>
\int\int\int dx dy dz
niggers
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>>6562434

I can do trip int in my head

>real analysis
>the hard part of stats, where you aren't given formulas
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>>6562569
HSC general maths representan
>>
>>6562729
>>6562569
What is HSC and VCE?
>>
>>6562735
Australian curriculums for different states.
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mathematical analysis for physicists

the first semester was hard calculus and the second semester was hard linear algebra
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i took a course called mathematical physics - classical mechanics. was mostly differential geometry and later symplectic geometry upto the KAM-theorem.
physics major.
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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.
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>>6562434
I tried a research project in algebraic topology, without any real grounding in the subject.

It was frustrating.
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>>6563137
pretty hard subject to get grounded in tbf.
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>>6563139
I should elaborate. The combinatorial roots of the subject have been buried in algebraic abstraction which has itself been buried in categorical abstraction.
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>>6563143
I will say, I remember being surprised at the amount of combinatorics that kept surfacing. I could still really stand to improve my combinatorics.
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>>6563143
This.

Homological algebra is very unsatisfying if you're not aware of the historical motivations for studying it.
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>>6563147
Well it didn't used to be called combinatorial topology for nothing.
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>>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.
>>
Basic understanding of algebra up to introductory level 2 reporting in.

I'm curious as to what the highest math courses represent. What are you calculating at high levels of calculus?
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>>6562435
I'll tell you what I had trouble with in Calculus.

Going from rectangular to Cylindrical to Spherical coordinates for the same graph!
>>
solving quadratic equations
>>
>>6563195
What's the point of this reply?

No seriously I mean it.
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>>6563193

learn the formula. easy enough.
>>
>>6563199
To test your autism.

Nice dubs by the way
>>
>>6563195

Quadratic formula
>>
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.
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>>6563213

'vector' should be 'matrices, vector spaces and vector calculus'
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>>6563199
OP asked what's the highest math I learned. My highest math is quadratic equations. Not everyone is a math genius like you.
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Engineering major here. I've learned,

The hairy ball theorem.

Evaluating nontrivial zeros of real valued second degree polynomials (ie, finding roots of dick shaped functions).

Real analysis and general topology (I just loved learning about open and closed balls).
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>>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.
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>>6563208
So pointing out how a person is pretending to be a retard, somehow equates to me being an autist?
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I once took a derivative .... of a derivative!

shit was so cash
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>>6563220
>doesn't get trips
Why even bother arguing?
>>6563222
Cool man!
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I'm a biochem major so I only have to go through differential equations.

Fuck math.
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>>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.
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Common core complex analysis. You need to break it up to make a 10+i.
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>>6562434
Diff Eq.
I don't even want to take Vibrations because it seems like you'd be assraped.
Harmonic Eqs annoy the fuck out of me.
Fuck resonance.

Mech E.
>tfw can't escape it
>>
Uhh, I'd say integral transforms. And I'm a chemistry major.
>>
Intermediate Algebra
I'm a math major
>>
I'm taking:

cal II
linear algebra
intro to math

how fucked am I? any suggestions on how to study/prepare?
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>>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
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>>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."
>>
stats because its so incredibly fucking boring
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>>6562521
Has cocksucking been good for you thus far? I imagine it has considering your enthusiasm.
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>>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.
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>>6562456
are you me?

considering taking signal processing or prosthetic mechanics or both.
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>>6563319
>Linear algebra is just very boring and tedious. I think it's the most boring class I've ever taken.
i can agree.
>>
>>6562508
>Most of the time we had to read the book and then the teacher would do any problems we didn't get.

I've never had a college math class that wasn't exactly like that. I'm actually pre-reading textbooks over the summer for my upcoming math classes because I want to be more prepared.
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Classic Geometry

Thought it would be babby-tier, a good warm before I tackle on Differential Geometry.
Nope.
>>
>>6563193
>he can't derive the formulae himself

Come on, dude. It's all Trig! Isn't that a pre-req to taking any sort of calculus?
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>>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.
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>>6563368
Impressive, bro. I'm always amazed of people who can figure out the math on their own, even if it's through sheer will and brute force at first.
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Honestly the hardest math class I had was trigonometry since it was so different from algebra, and I had taken that as well as algebra in community college so it was more thorough than a high school.

I have now finished calc III and linear algebra taking diff eq next semester
>>6563365
>wearing shoes at the beach
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Non-monotonic logic.
Most of them are fucking shit at doing what they're supposed to.

Also a little abstract algebra and group theory.
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>>6562692
So basically integrating something three times in not a triple integral?
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MS Math here, now junior college prof.

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!

(?°?°)?? ???
>>
>>6563413
How's being a Junior college proffesor going?
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I'm taking Linear Algebra and Differential Equations for summer school.

How good am I? :D
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>>6563399
pretty sure that's the opposite of what I said
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>>6562434
This thread is full of autism.
>>
>>6562434

The second grad-level abstract algebra class pretty much slaughtered me.
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>>6563551

Autists are usually good at maths.
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Algrebra

Get on my level
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>>6562461
Infinite integrals

\lim_{n\to\infty} \iint\cdots\int_{-\infty}^{\infty} f(x)\,dx_1\,dx_2,...,dx_n

#REKT
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>>6563626
Fuck you \TeX[\math] gimmick.
>>
EE major

Highest level material was ODE
Hardest material was calc 2
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>>6563559
Real autists are usually mentally retarded. You have no idea how rare savants are.
>>
Complex Calculus in my Calc 3 class. My Mathematical Methods for Physics class also had some neat stuff like the Fourier transformation. I'm still doing my degree in physics.
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>>6563869
>"mentally retarded"
>"mentally"

Socially retarded.
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>>6563985

They are socially retarded as a result of a much broader mental disability.
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Singular Perturbation Theory and Matched Asymptotics. Triple deck theory, etc.
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>>6563985
No, you uneducated fucktard. I meant "mentally retarded". Most non-savant autists are of below average intelligence.
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>>6563988

I don't even know what these conditions are anymore, it seems like everything means something different on the Internet.
>>
complex analysis
electrical engineering
>>
>>6563869
>tfw high functioning autistic math major
>lack of social skills
>scared to leave my dorm

A-at least math is interesting
>>
Introduction to Operator Algebras
Finishing my bachelors in pure maths
>>
Grad: PDEs with applications to boundary value problems
Undergrad: linear algebra & ODEs

I'm trying to pick up some differential geometry relevant to my project (I'm in materials science) not sure if I'll get to take a class in it or not.
>>
Differential Equations.

>Computer Science
>>
I'd say either Measure Theory or Functional Analysis
>>
>>6564017
You don't need social skills if you're good enough at math. I mathed so hard one time that I was drowning in pussy for a week.
>>
>>6564043
What are operator algebras? Like, can you give a quick rundown of the axiomatic system?
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Could you send me the linear notes from paul? Thanks a lot. ([email protected]).
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>>6564553
just signed you up for a gay newsletter.

lol.
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>>6563190
This was some good bait, I'm disappointed that nobody took it.
>>
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.
>>
Set theory. But really, you can go deep in any of the major areas.
>>
>>6564626
>>
>>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.
>>
>>6564633

computer science > math
>>
>>6564636
Sorry, I don't know very many CS buzzwords. Are "AJAX" and "programming paradigm" satisfactory?
>>
>>6564642
yes
>>
>>6564626
Sorry, but I'm totally drunk.

Anyway, any algebraic structure should be modeled by some axiomatic system. Like how a vector space is just a couple axioms on top of ring theory axioms.
>>
>>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.
>>
Basic Math
>>
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.
>>
>mfw galois theory in 3rd year algebra
I may have finally met my match /sci/. This shit is so hard can't fucking remember all these shitty lemmas and their proofs
>>
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?
>>
>>6565010
Like what?
Dedekind's lemma?
Dedekind-Artin Theorem?
It only seems to be hard because it's quite unrelated with everyday branches of math.
>>
As a 2nd year undergraduate its probably measure theory until stochastic analysis next year
>>
highest
>diff eq

hardest
>linear algebra

petroleum engineer here
>>
>>6562434

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.
>>
>>6563368

Nicely done, anon. Most people would have dropped in your circumstance.
>>
Stats major. Linear Algebra. Fuck all of you
>>
Electrical Engineer

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:

College Algebra
Trigonometry
Calc 1
Calc 2
Calc 3
>>
>>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.
>>
>>6565116
What kind of shitty statistics program doesn't require real analysis?
>>
>>6565121

Thanks anon, I'll definitely look into it. I'm on a month break right now until classes begin, I'll look it up.
>>
>>6562434

Complex analysis, DEs, and fourier series/transforms all rolled up into one horrible course
>>
>>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.
>>
I guess complex analysis, libear algebra (check Hilbert spaces ) and vector calculus....all these are a must for physicists
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