Math undergrad exit essentials

[Anonymous No.7139066]

What are some things every undergraduate math student should experience during their education? Examples may include specific texts, conceptual revelations, psychedelic drugs, certain derivations or proofs, videos... etc. This can also be a thread for knowledge a student should possess on their way out.

[Anonymous No.7139093]

get involved with your department. we had an undergrad math club which was pretty cringey but it was good to get involved with my peers. managed to form a research study group through that as well. I got summer scholarship projects when I was an undergrad which were really cool. tutor for the department if possible, or marking but that's pretty shit. if you have a good idea of your interests then check out department seminars and don't be afraid to ask questions. also make friends with those professors who share your interests, they can point you in the right direction as far as your interests are concerned and I managed to get a great reference out of one of them also.

[Anonymous No.7139095]

>>7139066

>long study marathons , for example, 14 good hours a day for say 20 - 30 days

>Come out as god after those 20-30 days

[Anonymous No.7139114]

>>7139095
I know this feel and I can verify it is one of the best feels out there.

[Anonymous No.7139118]

>>7139095
is this really a thing? I am intrigued.

Math undergrad here, I hope people respond

[Anonymous No.7139123]

Prepare to be disappointed when you can't find a job related to math and end up in finance where your boss will crush your dreams.

If you don't kill yourself before 40 years old, you will then see yourself become the vilain.

Embrace it

[Anonymous No.7139135]

>>7139123
Already preparing for this inevitability. Going to kill myself when I get a phd at the age of 27 like a rock star.

>>7139118
Is what really a thing? As a math student, studying for 14 hours for 20-30 days as an undergrad sounds ridiculous. I don't think there is anything challenging enough to require that. As for coming out as a god after long study sessions, that is definitely a thing. Your brain becomes conditioned and powerful from being subjected to so much abstract reasoning. It's like the Tetris Effect except with logic.

[Anonymous No.7139161]

>>7139066

Artin's Algebra
Munkres' Topology
Baby Rudin
Stein's 4 Princeton Lectures in Analysis
Ahlfors
Folland
Papa Rudin

No excuse.

[Anonymous No.7139168]

>>7139161
All this as an undergrad? Are you saying each of these should be fully read/viewed?

[Anonymous No.7139170]

>>7139123
>end up in finance
>making bank by stealing monies from poorer investors

how is this crushing dreams? as a math major, you should hate plebs who are too stupid to steal mathematically.

[Anonymous No.7139179]

>>7139118
Yeah it's a thing. As an undergrad, it's mostly with take home finals and midterms.

I had a few tests that took the whole week to do. 4 hours a weekday and then 10 hours on sat and sun.

As a grad student, that's a difficult problem set, but the feel is pretty much the same. When you solve a problem after that much work, you're the king of your world.

[Anonymous No.7139181]

>>7139170
This is a terrible sentiment and you are scum.

[Anonymous No.7139187]

>>7139066
sexual intercourse

[Anonymous No.7139190]

>>7139118
I can't speak for long study sessions, I don't study for more than 5-6 hours a day, tops.
The feeling is real. I recently spent 3-4 hours on a problem that I felt shouldn't have taken more than 2. Despite my extreme frustration after finishing the exercise, I felt amazing knowing that I was a better mathematician (in training) than I was 4 hours before.

>>7139066
>What are some things every undergraduate math student should experience during their education?
1) At least two different approaches to proving the Cauchy Integral theorem.
2) Sex.

[Anonymous No.7139193]

>>7139161
Gimme a break. 6 analysis texts and no combinatorics? I'll give you munkres, baby rudin, and ahlfors, but papa rudin as an undergrad is a bit much. I would save measure theory for grad school and see more breadth.

Artin is a great choice for algebra. I would add Hoffman & Kunze, since it makes doing Artin a lot easier and if you haven't had a theoretical treatment of linear algebra, you haven't learned it.

Ditch all the other analysis you mentioned and take a proper course in Combinatorics.

Personally, I'd like to see more geometry in undergrad math. Something like Greenberg's Euclidean and Non Euclidean Geometries. You get the axiomatic method, tons of great proofs, and more history and philosophy of math than most undergrads see in 4 years. Fuck the naysayers, geometry is the shit.

[Anonymous No.7139210]

>>7139193
Why do you enjoy geometry so much?

[Anonymous No.7139212]

>>7139193
Passionate post, I like it.

[Anonymous No.7139223]

This is in another thread.

[Anonymous No.7139252]

>>7139210
>Why do you enjoy geometry so much?

Personally, I like the methods of constructing things and then proving things about your constructions. I also like working directly from the axioms, and systematically building up a collection of true facts.

In grad school I noticed that many of my fellow students never took geometry past high school and I think that's a shame. Not considering the things I like about it, it's actually useful. In the past two semesters I've seen a strong background in geometry come in handy, writing axiomatic proofs about affine and projective planes, and proving that the chromatic number of the real unit distance graph is no more than 7 (you tile the plane with hexagons of diameter 0.99, but you have to prove a few things about maximal distances in those hexagons. my friend was stumped and all I had to do was draw a few lines and by looking at the picture I knew the result was confirmed and it was easy to prove.)

I just don't like the idea that geometry is baby math. It's got a rich history, there are still deep results, it requires creativity, and I just think every undergrad should be exposed to these things beyond the high school level.

[Anonymous No.7139270]

>>7139193
>Fuck the naysayers, geometry is the shit.
unfortunately all of your positives don't carry over well to the graduate level which focuses on topology a lot more. I agree though, geometry and combinatorics are underdeveloped at the undergrad level.

[Anonymous No.7139271]

>>7139252
I like all of those things you said. I am only just beginning a math degree this coming fall but I am looking forward to any geometry I will get to do. Do you work with or around anyone in grad school that was older when they got their start? I am almost 30 trying to reassemble my academics after not coping very well with depression for like a decade.

[Anonymous No.7139289]

>>7139270
>unfortunately all of your positives don't carry over well to the graduate level which focuses on topology a lot more.

That's certainly true, though I believe it's beneficial for a math major to have knowledge of the history and philosophy of their field, if not only from a cultural perspective. Geometry is a good way to get this while also getting some solid math. The book I mentioned isn't just a rewrite of Euclid either, more than half of it is dedicated to non-Euclidean geometries.

But I get your point. If an undergrad were forced to choose between topology and eucl/non-eucl geometries, topology is the obvious choice. I'd even say differential geometry over eucl/non-eucl. I mean, there's a reason it's not even offered in a lot of departments. I simply resent that.

>>7139271
>Do you work with or around anyone in grad school that was older when they got their start? I am almost 30 trying to reassemble my academics after not coping very well with depression for like a decade.

While a good portion of students in my program are either fresh out of undergrad of fresh out of their masters, there are a handful aged 28-30, and several PhD students in their low to mid 30s.

As an undergrad, one of my main collaborators was 30-something and had a wife and 5 year old. He was the most dedicated student I worked with.

[Anonymous No.7139296]

>>7139223
>things every math major should know
what, calc 1-2 and and an introduction to proofs course?

[Anonymous No.7139312]

>>7139296
That's high school math.

[Anonymous No.7139323]

>>7139312

[Anonymous No.7139526]

The more I study mathematics the more my humanity leaves me. In my present state, I am emotionally detached but consciously tuned in. It feels like I was once an actor in the play of life. Slowly, I am making my way off stage to enjoy the show as a member of the audience. A math student's journey is a hollowing and transcendent experience.

[Anonymous No.7139546]

>>7139526

try starting out emotionally detached already.

[Anonymous No.7139568]

Learning to flip burgers is essential.

[Anonymous No.7139575]

>>7139066

Just keep an open mind OP. Your first 4 years are a wonderful time to explore and experiment.

[Anonymous No.7139579]

Mathematics is at once a powerful blue-pill and a powerful red-pill.

[Anonymous No.7139607]

Try LSD at least once and try to time it after a prolonged period of studying and/or learning.

Do not settle for the minimum level of comprehension required to finish your homework and pass exams. Always understand what you are learning to the point of being able to discuss it verbally with comfort.

Take an intro programming course.

Understand isomorphisms and explore the concept. Shit's dope.

Explore! Mathematics is one of the few things in life that highly rewards creativity and logic simultaneously. If you read a theorem that interests you, why not try to prove or disprove the contrapositive? Notice a pattern in something? Form a conjecture and set out to prove it.

If you want to go to grad school, it is typical to have three letters of recommendation. Try to form relationships with professors and faculty accordingly.

Educate yourself on pure logic. It is pretty and helps tremendously with your reasoning skills when working through proofs.

Related to above, realize that math follows logic. When you have shown something through rigorous proving, allow yourself to accept it as absolute truth. A big part of maturing mathematically is developing confidence and certainty in your work. (This is assuming you didn't botch the proof).

Learn to value creativity. Thinking logically is the easy part.

[Anonymous No.7139711]

>>7139187
underrated post

[Anonymous No.7139714]

>>7139223
Only one I had to look up was 11). Don't know how I could have forgotten that easy as shit proof.

[Anonymous No.7139725]

bumping an awesome thread.

I've been bouncing around in University for too many years, I've done a little of everything. switched majors 4 times and dropped out for 3 years to start my own homework mill because I've never been challenged by anything.

Then I discovered the rigor and challenge of pure math and I've become a math math major. In one way it sucks to find this out at 26 but I'm ready to focus until I get at least a master's because shit is fucking dope and I love it. I've accomplished a lot of fucking, travelling, working and partying so I'm ready for this. gonna do as many of the things in the thread as I can.

[Anonymous No.7139729]

>>7139575
>that filename

My jimmies are slightly agitated

[Anonymous No.7139815]

>>7139066

Thinking exercises. Lets say you are a long train/bus journey. Just drink a cup of coffee and think about a mathematical theory/proof from intuitive level, and in your head.

That shit with coffee can be orgasmic. !

[Anonymous No.7139867]

>>7139118
Hell yes. I remember my first fractal geometry course: I missed the first month of lessons because I was having some issues and basically I had to study one month worth of pages in a very little time. I then decided to spend 3 days closed in my room eating nothing but junk food and drinking coffee, studying like a beast.

The fourth day my mind was overhwelmed, I could look around and see cantor sets and space-filling curves everywhere. When you study for a long time (I've done this sort of marathon many other times) you perceive the world sort of slowing down, so that you can analyse data faster. At least this is what happens to me. Of course, different effects for different subjects: algebra makes me go fucking numb, I just stare at nothing creating rings and algebras and noticing them in the way objects are organised in the space around me. Studying geometries (algebraic, non-euclidian, ecc) gives me a sort of euphoric high. The world becomes much more interesting. Calculus makes me feel like having a super advanced computer in my glasses when I'm walking, and I try to calculate the gradient of the streets and see saddle points. Then I talk to my roommate and all disappear because she's stupid.

But yes, I can definitely relate to this, and have met many people who share the same feeling.

[Anonymous No.7139869]

>>7139526
I beg to differ. Math helped me understanding an enormous number of things in my life. As opposed to what you say, math made me completely understand the importance of emotions and irrational feelings. You must first listen to your body if you want to listen properly to your mind! Being detatched won't give you anything. This may sound a little hippie, but it's true. Stay with us Anon, and enjoy math nonetheless.

[Anonymous No.7139875]

>>7139223
Math enthusiast and the only one I can't do is deriving Newton's method as I never learned it. Also, 14 is impossible if you haven't seen it before. The pic is shit, that's what every STEM field scientist should be able to do.

[Anonymous No.7139878]

>>7139118
You can do it for even just a few days and you will ace any test if you do. But you have to do it in total solitude, and keep up a high level of focus. It's hard to do if you are already addicted to a habit.

[Anonymous No.7139881]

Prove <span class="math">\sqrt[n]{2}\not \in \mathbb{Q},\; n\geq 3,\; n\in\mathbb{N}[/spoiler]

[Anonymous No.7139887]

>>7139881
x^n-2 is irreducible for n>=3 by Eistenstein's criteria?

[Anonymous No.7139892]

>>7139875
>14 is impossible if you haven't seen it before

Ahah bullshit. It's a pretty easy concept. Associating object with the set of integers (bijective function from a set to Z+) it's an easy abtraction of counting. I used to do that as a child, even though I didn't have the mathamtical terms: once you realise that numbers form a set, you just need to keep thinking about it and explore the concept and perhaps reverse it. Then, if you truly know the construction of the reals you should be able to at least get a feeling of their uncountability. Once you do that, you only need to find a way to prove that using one-to-one correspondence. Cantor's diagonal argument is not the only method.

[Anonymous No.7139895]

>>7139887
Overkill. Also criterion*

[Anonymous No.7139905]

the circlejerking ITT is almost unbearable

>studying 14hrs a day

then what the fuck are you doing here

[Anonymous No.7139910]

>>7139905
2/10 made me think of an actual reply

[Anonymous No.7139913]

Something that has always troubled me in these threads is when you talk about proving certain equations and theorems, does this mean coming up with such equation or theorem from scratch or researching the proof and copying it.

Kind regards,

An aspiring math student

[Anonymous No.7139918]

>>7139913
Almost always it means "I have seen a proof of this before, can sketch the main ideas, and if you pressed me I could fill most of the details."

It's not about looking up a proof and copying it though. It's about studying the proof until you're convinced the result is true because you understand the logic and why each step was taken. With that level of understanding, it's not very hard to sketch the idea of the proof.

[Anonymous No.7139930]

>>7139913
Wel it depends. For instance, many books prove a main theorem from which you can derive corollaries and sometimes asks you to derive them as an exercise. So you must understand the proof profoundly in order to completely be able to see the pic picture. Also some secondary theorems may not even have a proof in the book and you have to come up with one yourself: of course this is usually an easy task. But sometimes it doesn't simply involve taking the definition and adjusting it. Sometimes it takes a lot of time, but eventually you feel very very good.

[Anonymous No.7139932]

>>7139066
Seriously try to read and understand a math paper.

So many people come out of undergrad having never read a single paper, so they are wholly unprepared for real mathematics.

[Anonymous No.7139983]

>>7139892
>hindsight bias

[Anonymous No.7140030]

guys what are book goods to intro on topology and what background do i need

[Anonymous No.7140034]

>>7140030
good books*

[Anonymous No.7140046]

lmao book goods

[Anonymous No.7140149]

pls dont make fun of me im dyslexic

[Anonymous No.7140218]

Should be able to prove that there is no formula for finding roots of a polynomial of degree larger than 4

[Anonymous No.7140269]

>>7140149
lol dyslexitard

[Anonymous No.7140275]

>>7139312
engineering have nothing to do with you you idiot
electromagnetism includes differential geometry
communication includes probability
engineering also include complex functions (i dont know about the analysis part)
but most of it is bullshit

[Anonymous No.7140298]

>>7139223
>prove the pythagorean theorem
wtf, i didnt know if it were provable

[Anonymous No.7140305]

>>7140298
Seriously?

[Anonymous No.7140306]

>>7139095
I can verify this is a thing during finals week

Great feel when you wreck the final and all that hard work comes out

[Anonymous No.7140312]

>>7139066
Take a class that proves Stoke's Theorem

The build is fucking great, from differentiation and integration to differential forms and manifolds

[Anonymous No.7140327]

Set goals to get your PhD in Math because if you don't, might as well skip college and go straight to a McDonald's job.

[Anonymous No.7140361]

>>7139066
taking a crack at a general solution to navier stokes.

[Anonymous No.7140688]

>tfw started off as math education major
>my university is literally laughable EXCEPT for its education department
>do so many drugs first year, ruin grades
>eventually get my shit together
>realize i dont wanna teach fuck ass high schoolers i just wanna do math
>switch to pure math degree
>depressed because i barely have a 3.0 at a fucking liberal arts college going into fourth year

at least my transcript shows improvement with every semester and ive aced all my high level math courses but god damn... to any prospective students: DONT fuck your first year up. its literally not worth it. just save it for the summer and the weekends.

[Anonymous No.7141292]

>>7140298
>>7140305

Depends on your axioms. The parallel postulate, triangle postulate (or weaken forms like "there exist a triangle who's angles sum to 180°" or "the sum of angles in any triangle are the same"), equidistance postulate, triangle area property (Wallis axiom), three points property, Playfair's axiom, Proclus' axiom, and Pythagoras' theorem (among many others) are all equivalent "flatness" axioms.

[Anonymous No.7141314]

>>7139875
>Also, 14 is impossible if you haven't seen it before

HAHAHA, no: P(ℕ)->[0,1) : s->x | digit_n(x)=1 if n∈s, 0 otherwise

[Anonymous No.7141329]

In general, is a computer science minor necessary or is the intro to programming class going to be enough? Say I want to go to grad school for pure math.

[Anonymous No.7141346]

>>7139118
I'm sure he's exaggerating, but you do have to study a lot. It's NOTHING compared to any other major that isn't science.

And I agree that you feel like god after studying hard and understanding everything. You keep craving for more and you realize how deluded you were before thinking you were smart. You also realize how retarded everyone else is even more which might make you feel sad.

[Anonymous No.7141448]

This seems like a good place to ask. I am a sophomore in nuclear engineering thinking about adding math as a double major. I don't give a fuck about the double, I just like math and don't want to waste my work in engineering. Will I still be able to get anything out of my degree or will be so bogged down with work that I will get nothing out of my classes? I currently have the highest grade in my nukE program and I take harder classes than my peers for reference on my capabilities. I want to pursue math instead of engineering for grad school.

[Anonymous No.7141467]

I'm a second semester junior, at an alright state university, but I haven't really found anything in mathematics that's interesting to the point of wanting to pursue it in higher ed. I was really interested when, in Algebra, we constructed familiar objects (rationals from naturals, complex from reals), but where would that fall in terms of topics? I want to learn further but I just have no idea how to ask about these things

[Anonymous No.7141553]

Bump 4 m4th :^)

Is simply wanting to wield a practical understanding of algebraic topology a good enough reason to go for a math phd?

If i do 3 more spanish courses i can slap a spanish minor on a math degree but is it even worth it?

[Anonymous No.7141584]

>>7141314
That requires proving that P(X) has greater cardinality than X, which is a bit trickier.

[Anonymous No.7141585]

>>7139881
use fermat's last theorem

[Anonymous No.7141609]

>>7141584
>which is a bit trickier

No, it's even easier. Assume f is an surjection from A to P(A), define α∈P(A) as ∀a∈A a∈f(a) ↔ a∉α. Clearly α∉f[A] and f isn't a surjection.

[Anonymous No.7141617]

A comment from the sciences

fuck you you fucking shits
Do I need to understand the proofing and foundation of this particular method? No, I need it for one particular type of question, tops

TOO BAD
TIME TO SPEND ANOTHER HOUR AND HALF PROOFING THESE STATEMENTS
OH SORRY DO YOU NEED HELP UNDERSTANDING THE BACKGROUND OF THE QUESTION
HERE'S TWENTY HOURS OF HOMEWORK, I'M SURE YOU CAN FIGURE IT OUT YOURSELF

Why they don't make DiffEQ for non-majors I will never know

[Anonymous No.7141620]

>>7141617
but they do you fucking retard.
if you fail your babbies first solving methods for odes because its too proof intensive you should consider switching majors

[Anonymous No.7141624]

>>7141617
DiffEq is for non-majors, you're just a pleb in your field.

[Anonymous No.7141626]

>>7139729

Why? People shouldn't provide the homeless with a place to sleep?

[Anonymous No.7141628]

>>7141620
I failed it because I have a chronic issue with being fucking BORED

Why show up for class when I have to teach it all to myself
which I'm not going to do anyway because I have more important shit to be doing

proofs are fine but not your jargon-soaked piss
it's all well and good and simple for people who use it day in and day out but it's a little much to expect me to adapt to your environment when I could achieve the same thing by using a calculator I find online and twenty minutes on wikipedia

[Anonymous No.7141630]

>>7141624
it's still taught by math professors who treat it like a math-major class
it's one thing to see that differential equations are applicable to theoretical color chemistry, it's another to teach a broad spectrum of fundamentals and then not touch on the applications at all.

[Anonymous No.7141646]

>>7141628
I would say that for sciences, a lot of proof is unnecessary. Like, there's no reason for you to know the proofs of the various hyperplane theorems, and various other useful high-level results.

But intro diffy Q is different. The problems and proofs you do in that class are not interesting for a mathematician, nor are they particularly useful. But for someone who studies science, you'll be able to see deep connections regarding how math can model physical systems. Any second order differential equation you solve is a solution of a mechanics problem. In your first differential equations class, you should touch the surface of Kepler's laws, mass transport equations, the heat equation, and the wave equation. All of these are integral to one discipline or another. You can see how a statement about a physical system can be converted into mathematics, then using rigorous methods turned into a prediction about the behavior of a system. That's science in action. If we mathematicians didn't have jargon-soaked piss, you wouldn't be able to make a prediction in many cases (i.e., what do when given a mechanics problem involving a case of non-constant acceleration if you don't have differential equations? Cry?), which is the whole point of studying science.

[Anonymous No.7141677]

>>7141329
Probably you would be safe with a coding sequence. Like C/C++ 101, 102 or something. Then express that you code outside of school somehow.

[Anonymous No.7141692]

>>7141448
Talk to your advisor.

>>7141467
Talk to your advisor.

>>7141553
Talk to your advisor.

>>7141329
Talk to your advisor.

...

This poster is either trolling or genuinely believes what he is posting. In either case, he can safely be ignored.
>>7141628
>>7141617

[Anonymous No.7141694]

What are more things math students should experience in their undergrad?

[Anonymous No.7141733]

>>7141694

not that all do, but what most should do is take a course in computational complexity theory or information theory. pretty cool areas of math.

[Anonymous No.7141742]

>>7141617

proofs are useful for ANYONE. it helps get your mind straight about what the fuck you're doing.

just because you're not a mathematician doesn't mean you should just blindly manipulate symbols the rest of your life without understanding the reasoning behind it.

[Anonymous No.7141800]

>>7141630
this is because it's not a science class.
If you want applications then take science classes you fucking pleb.
If you want the tools you take your ode class.
it's that fucking easy

[Anonymous No.7142560]

>>7139312
>tfw my schools math major only covers high school tier with advanced electives in soft science tier
>tfw when I have the degree and don't know shit

[Anonymous No.7142785]

>>7142560
>tfw when I have the degree and don't know shit
time for grad school noob

[Anonymous No.7142788]

>>7142560

That sounds like a BA in Math.

[Anonymous No.7143240]

>>7141677
So is coding really as important as everyone says it is? like say i major in math but double minor in french and ancient greek. Even if I take a coding sequence I would be less attractive? It seems to me that coding would be important sure, but computer science is for computer scientists right? And coding outside of school, are we talking like amateur raspberry pi robots and shit? Or like, I have my own app in the google store?

[Anonymous No.7143306]

>>7143240
If you want a job with just a BS, yes it is important. While coding is something that is mathematician can easily pick up, no employer wants to spend money paying you to learn on the job. If you don't have a few side projects or an internship/co-op related to coding, it will be much harder for you.

[Anonymous No.7143324]

>>7143306
I was talking about grad school in the above post. Maybe the guy that missed it and I should have been more clear about it. Would a grad school be that interested in a comp sci minor or should I just take the coding sequence and fill my schedule with whatever the hell else I want?

[Anonymous No.7143326]

>>7143324
*maybe the guy that commented above missed it

[Anonymous No.7143332]

>>7139168
how long does it take you to read a book? Don't you have any passion?

[Anonymous No.7143344]

Is it possible to enjoy solving integreals?

[Anonymous No.7143345]

>>7139223
Someone want to post solution to number 2?

[Anonymous No.7143349]

>>7143345
I don't know why they put it on there since it uses a technique that is literally only used for that one fucking integral.