Is just following Harvard 55's curriculum the superior route for undergraduate mathematics as an autodidact?

is just following Harvard 55's curriculum the superior route for undergraduate mathematics as an autodidact?

Please post the complete curriculum

>take home exam
Is this a joke?
I honestly cant believe that such a thing exists.

In all my classes homework is only needed to be accepted to take the exam and the note you get at the end is 100% a 1.5-2 hour exam. (occasionally they are oral exams)

You are basically gifted 50%-70% for free because only an idiot would not do the homework and getting 100% on the final is a given.

How can such a well known university have lower standards then my shitty local university?

>has never done an actual take home exam for a higher level mathematics course
dude stop, it's not linear algebra. some proofs are designed to take over the course of a day (if not longer) in the span of a group discourse and it's not the type of thing you'll just find on math stackexchange

I know that some proofs are longer but that is what homework is for and why you need to do decent in homework to be able to take the exam.

How can anyone NOT think that take home exams are a joke. You can just work together with you friends, someone will get the answers and then you all just write down variations of the proof.

>it's not linear algebra
My linear algebra exam was 2 hours and proofs only, what kind of argument is that even.

1.5-2 hour exams are jokes. Nothing meaningful can be tested on a in class exam for a higher level math class. I have had classes that have done both types of exams, the take home exams always had much more interesting questions.

>You can just work together with you friends, someone will get the answers and then you all just write down variations of the proof.

Honor system. In higher level math there is no point of cheating. Anyone doing it will just be fucking themselves over, so no one actually cares.

>1.5-2 hour exams are jokes. Nothing meaningful can be tested on a in class exam for a higher level math class
Thats why most higher level math exams are oral here. A professor can find out if you know your shit pretty fast, but that is not possible for 100+ people classes.
>interesting questions.
That is not the point of an exam. That is what homework is for. An exams aims to confirm whether or not you have the required knowledge, they should not be interesting.
>Honor system. In higher level math there is no point of cheating.
But the university has to guarantee that you have reached certain levels of education. How is that possible if it is an "honor system" where you can easily cheat your way through to a degree. Our exams are controlled extremely tight, you cant even go to the toilet alone.
How can you enforce standards based on a honor system?

>An exams aims to confirm whether or not you have the required knowledge,

I'd argue take home exams do that in a better way.

On a in class exam, you will have to give problems that can be solved in a sufficiently short amount of time, which means they can only be so many steps away from just applying the definitions of things and various preproved theorems from class.

On a take home exam, you can give problems that really require the students to seriously think through how the stuff they learned in the class can be applied to prove the theorem. For instance, my Complex Analysis final had us lay the foundations of Holomorphic Dynamics.
>How is that possible if it is an "honor system" where you can easily cheat your way through to a degree.

If the questions are difficult enough, the only way to really cheat is to work together with other students. Which means you have to convince multiple students cheating is a good idea, and even if you do, who cares? In the real world mathematicians hardly work alone. If the problem doesn't have a cookie cutter solution, then the students will still have to seriously think through the material of the course.

>On a in class exam, you will have to give problems that can be solved in a sufficiently short amount of time, which means they can only be so many steps away from just applying the definitions of things and various preproved theorems from class.
I completely agree with that, but I dont think the solution is a take home exam. As I said, most of my higher math courses have oral exams.
> my Complex Analysis final had us lay the foundations of Holomorphic Dynamics.
Something like that can be tested really well in an oral exam, the professor can easily find out how much exactly you understand of it, by expanding on certain topics or asking question about topics you might know, but skipped in your explanation (which also leads to a fairer evaluation). And he has the guarantee, that everything you say is really in your head.

>If the questions are difficult enough, the only way to really cheat is to work together with other students. Which means you have to convince multiple students cheating is a good idea, and even if you do, who cares? In the real world mathematicians hardly work alone.
You are also right here, but the point of an exam is not to test how effectively you can work in a group, but to find out whether you know the material or not.
This is what happens here in homework which is usually turned in in groups of 2-3 and me and my friends are varying from finding solutions alone to talking about the problems together, which obviously is what happens in the real world and the fun part of mathematics.

In the end, I was just surprised that such an prestigious university as Harvard allows such soft enforcement of standards, where you have very little guarantee (except for the word of the student) that the student really understands the material.

>someone will get the answers and then you all just write down variations of the proof.
lmfao not every math dept is like your's, it's extraordinarily easy to detect reuse
You don't do mathematics clearly, don't pretend to please
anyways, unless your in class exam is 14 hours long there are some concepts critical to higher learning in math that simply cannot be digressed to a typical 2 hour exam like you would in calculus
>My linear algebra exam was 2 hours and proofs only, what kind of argument is that even.
damn d00d got me there

>where you have very little guarantee (except for the word of the student) that the student really understands the material.

the fucking proof in of itself, and it's very fucking easy to see if they just mocked someone else's
jesus man

>lmfao not every math dept is like your's, it's extraordinarily easy to detect reuse
I talked about people working together to get the result.
This means, although people understood the answer (and were able to produce a proof different to the rest or even just got the basic idea how the proof works and did the rest alone) they have NOT shown that they were able to come up with the solution itself, which negates the point of the exam.
>anyways, unless your in class exam is 14 hours long there are some concepts critical to higher learning in math that simply cannot be digressed to a typical 2 hour exam like you would in calculus
Of course. And I never argued that having a 2 hour exam where you sit down and calculate a bit is the superior form of exams. I was just surprised the Harvard would allow such soft enforcement of standards.
>damn d00d got me there
?

>the fucking proof in of itself, and it's very fucking easy to see if they just mocked someone else's
No. Just learning the basic Idea of the proof from someone else significantly reduces your workload and if you do the rest yourself (which most likely is the easy part) no one will be able to tell, except that you both had an Idea which lead to the proof, which can hardly be considered cheating.

thanks for derailing the thread asshole

You are welcome.

And as the answer to your question: No one here knows, Veeky Forums is 10% homework and 90% flat earth, 0.999...=/=1 threads, just try if it works for you.

>because only an idiot would not do the homework
that's me!

>autodidact mathematician

That's a myth.

>dude stop, it's not linear algebra
It's literally a course on linear algebra and group theory.

Are you really still an autodidact if you read math books?

>Something like that can be tested really well in an oral exam

Not really. The exam was proving a few theorems that lay the foundations of a subject similar, but distinct, from what we had studied. It takes awhile to put together the connections, much more time than I think would be appropriate for an oral exam.

> I was just surprised that such an prestigious university as Harvard allows such soft enforcement of standards, where you have very little guarantee (except for the word of the student) that the student really understands the material.

I don't think cheating is really a problem with pure math students. Someone isn't studying pure math to get some high paying job, they are studying it because they love math. I think most students would be too proud to cheat themselves like that. At least thats the way I think. I would rather get a B with my own work than an A by cheating.

>I don't think cheating is really a problem with pure math students.
I completely agree with you, but I was just surprised that Harvard wouldnt have tighter regulations for such things.
It is one thing to trust your students, but giving out degrees where you can not be absolutely sure that the person knows everything they claim to seems like a loss of credibility.

Math 55 does not cover all the mathematics an undergraduate should know, it covers the basics of linear algebra, group theory, and real/complex analysis sure, but there's a hell of a lot more you need to know to have what should be considered a "good" undergraduate education. Also if you're just trying to find the hardest math class to audit, you haven't, not by a long shot, there's far harder course loads in math than just Math 55, it really is a meme how much people think of this class, it by no means is outside of the reach of any remotely dedicated student. Now if you want something that actually has some bite to it, and would bring you from 1st year undergrad to beyond what most 3rd year phd students know then ecole normale superieure, but even that honestly can be handled by a reasonably dedicated student. Point is math is usually played up to some absurd degree when really a lot of it can be learned pretty quickly. The entire content of a standard linear algebra course can be learned in a few days, not joking, a lot of it really isn't that hard, if anything there are just a lot theorems, though you really only need a few main theorems for the most part. Let me demonstrate, if you were a freshman you could with no higher math experience (having only taken cal I and II, maybe cal III) you could with some effort finish all these books in a year and know more than you'd learn from math 55, though ecole in total will cover a bit more.

>cont.

Any book that has basic proof techniques like transitions to advanced math

Stein Shakarchi (Four volumes covering Fourier/Real/Complex/Functional analysis at a basic level appropriate for undergraduates)

Rudin (Alternatively you can read rudin's books, I personally prefer them to steins basic analysis series. Stein does have some nice harmonic analysis books though. Baby rudin starts from set theory, so no overhead barring the ability to do proofs. You can then continue to his next two books from there)

Munkres (A really basic text on general/algebraic topology, there are better texts but this is standard, janich's topology is better. Assumes very basic analysis)

Milnor (His differential topology text is basic but to the point, you can then read janichs differential topology book or maybe madsens book to get up to speed with basic manifolds, spivaks books also work, his calculus on manifolds and diff geo. If you really want to learn a lot go with fomenkos texts, he'll take you through a large amount of diff geo and diff/alg topology)

Arnold/jost (The theory ODE's and PDE's can be learned from these texts, they are very good. If you just wanna learn techniques to solve them then go with pde for scientists and engineers)

Dummit and Foote (Assumes you know nothing about algebra, halmos has a decent linear algebra text same with shivlov, there's tons out there)

Lint (A course in combinatorics, just need some basic algebra, will cover all the discrete math you'll need for a while)

There's some extra material concerning more pure/applied math (number theory, logic, probability, or stochastics) but many of these aren't considered standard for one reason or another. You can read the majority of these books in a year (maybe spending 5-6 hours a day reading/doing problems), taking you beyond the standard math "education" that most universities spoon feed you.

"autodidact"

youre a faggot and i promise you will never obtain a meaningful understanding of anything.