Any Math Majors?

How do you know if a degree in (pure) mathematics is right for you? I have always been good at math but I assume that is not enough. The highest level of math that I have taken is Calc I which is baby-tier. I am really enjoying Calc II so far, I am doing well in my engineering courses but the only thing that really gets me excited is Mathematics. It's the only course I dream about and really care to do on my own. Math majors of Veeky Forums can you tell what made you pursue a degree in applied or pure mathematics? And whether you think you made a good choice or not. What are rigorous proofs like? Please excuse me for the naive questions

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Take a proof based course and you will know.

And do applied math (especially if you have a background in engineering ). You will still get to do plenty of proofs, the only difference is that you will have a chance of being hired after graduation.

Double major in pure math and engineering.

>applied math
>in undergrad

Those courses are nothing more than watered down pure math courses. If you want applications then double with engineering.

im an internet math gebius

The first thing that steered me towards "real" math was competitions in high school. That sort of math can be a good indicator; if you love geometry you're probably going to like math in general. It's not foolproof (some contest babbies get frustrated and quit when they meet problems they can't solve in 5 minutes and a clever loophole) but it's pretty good.

Just try courses out to see if you like them. A good sampler would be something like intro analysis+abstract algebra+something like number theory or combinatorics. You'll almost certainly like at least one of those if you're going to enjoy anything further.

>What are rigorous proofs like?
It's not really anything unusual or arcane. You start with precise, formal definitions (these are more important than the theorems) and then you argue by step-by-step logic how they imply some basic theorems. Then you can use the basic theorems to argue more fancy ones and it all piles up on itself.

>proof based course
Americans are dumb

If you really read your calculus book, you'll find many rigorous proofs as well as some exercises (which most likely you won't be assigned as homework but they'll be in the book nevertheless) that ask you to do rigorous proofs. Read the proofs in the book and then attempt the exercise proofs.

You are right, but I assume anyone doing a b.s. in pure math is planning on grad school.

But on the chance that he isnt...go to graduate school! Otherwise you're only options are actuary and code monkey.

Alright genius, how would you describe abstract Algebra and real analysis/adv calc?

They are fundamnetal math courses faggot. The basics of your professional career. Taking three courses so you can take a derivative or an integral is a waste of time and should be asked for anyone entering STEM.

Taking 3 courses to take the derivative or integral? When did I ever say that?

And in addition to being fundamental courses they are full of proofs (vs. full of computation based problems).

You see both in any decent course.

most non proof based classes dont give a shit about the proofs, they'll show you them but never ask you to do a proof, they know the people are there to learn the computations so they can do applications even though their applications will all be done by a computer anyway they force them to learn the skills

If you are a math major in a decent uni, that doesn't exist.

im talking about classes for biology students and shit dude the calc classes and lin alg classes they take don't bother with proofs. obviously math majors wouldn't take those classes a lot of unis have a computation based and a more theoretical version of each basic math class

Can confirm undergrad applied math isn't good (without major connections). I did pure math BS then got an MA in applied stats, I would advise anyone looking to do applied for a career to do a pure BS, and then get an applied MA.

thats actually really fucking hot

>intro analysis+abstract algebra+something like number theory or combinatorics
aren't those all upper-level undergrad courses

>Otherwise you're only options are actuary
Actuary is a great option though

They're definitely not the classes the vast majority of students take in their first year, but they'll give you a real taste of what actual rigorous mathematics is like. In fact I would say that they're the first real math courses you can take at a university.

Those are literally my first year math courses.

well youre retarded if you think that's the norm

I'll see what I can fit in next semester. Thanks
Something I'll consider.
I will definitely do this.

Is highly competitive and it's not math, it's business with a tiny bit of stats.

Are you just making calculations used stuff you've been given, and are you satisfied with this, or are you interested to see why the things work? I kinda knew what to do when I had proved the formulas for derivatives, the sum formulas for trigonometric functions, some sequential stuff, some set theoretic stuff, etc. in high school. Have you done anything similar?

It's certainly not enough to be good at calculus. It depends on what makes you "good" at math. Did you understand the nitty gritty details of calculus? Or did you just memorize the computations? Are you prepared for hard work and dedication, and do you like to learn for the sake of learning?

I went into mathematics because I love the challenge. It was an amazing choice, I feel very good doing what I love to do.

Mathematics in the first courses will feel like full of formality. You will have to erase what you think you know and start taking things slow, in a new, rigorous language. This is what a first proofs course feels like: you seem to be manipulating strange symbols into coherent sentences. Think learning your ABCs and then learning a few words and how to make sentences from it.

But that's clearly not the end goal of learning the ABC, right? A writer is not someone who writes a lot of correct sentences, but someone who writes meaningful, beautiful prose. Math is like that, once you know the language of rigorous mathematics you can start abstracting and it becomes a tool that you use to communicate your "intuition", this mysterious ability to "sense" truth in things that one gets through hard work and experience. The way mathematicians communicate proofs to each other when they talk is not though the super formal language, it's through smart, simple pictures, through hand gestures, through colorful language, but everyone understands everything they say is based on very careful rigor.

In general it's a very nice journey, I feel like I grow as I go along. We have a small slack chat with some people who are into learning math, if you want to chat you can create a throwaway email and post it here asking for an invite.

You can also read nice stuff from Tao's blog. That will probably help you have a better idea of what math is.
terrytao.wordpress.com/career-advice/there’s-more-to-mathematics-than-rigour-and-proofs/

>and are you satisfied with this
No
>Have you done anything similar?
The closest thing I did were the "proofs" for the power rule and quotient rule. I did a few other things in high school like apply math that wasn't currently being applied at that level in other classes (like physics) but nothing too impressive. I wasn't very motivated until recently so I always got by with decent grades.
>Did you understand the nitty gritty details of calculus?
During Calc I I made sure that I actually knew what I was doing and why I was doing it. I also explored the practical applications of each section. I still use things like newton's approximation when I don't have a calculator. The field definitely interests me but like you and I have said just liking math isn't good enough.

But I really like the way you described proofs. Thanks for this response.

I didn't mean liking math isn't good enough, I said it isn't enough in the sense that you'll also need to be willing to put in hard work down the line, like anything in life. Liking it is all you need to start, you can incursion into it without much trouble at first.

What do you think is so interesting in math?

not op, but thanks for this.

i feel a bit like op, i posted on here before asking how to survive a BSc math major, as an experienced (8 years) senior software developer.

I basically want to up skill myself because I want to work on computability problems, hopefully. I can basically do the CS degree in my sleep, but I consider learning applied math skills to be extremely important to my future work, and to doing my current work better. I feel like I understand a lot of math, maybe even have a bit of intuitive sense for regular calc/ode problems (modelling, and solutions for them before actually solving them) but I don't consider myself to be one of the big dogs like Leslie Lamport, or Dijkstra.

Anyway, the value in math became impossible to ignore after i found out about Dijkstra's algorithm, and Lamport Timestamps. I want to do things like that. Do you guys think I could survive the degree?

Sorry for the low quality post.

That's what I meant. Liking the subject won't necessarily translate into being competent enough to perform well as a math major (or any major).

I don't think my answer will be good enough so I am not going to answer.

Try doing proofs. If you like them you'll like math. You can try completing Mathematical Reasoning by Sunderstrom, it's a free intro proofs/set theory book that will give you a taste of grown-up math. If you really like it pure math is probably okay for you.

Applied math people take worse courses at my school. Like, they take a shittier version of analysis. It's a meme.

Combinatorics and Graph Theory are the only areas you can study in undergrad that will look anything like Djikstra's algorithm. To survive in math you just have to practice, study alot and not be too retarded. But much of what you take will not be useful for programming. If you do a math degree, focus on abstract algebra, combinatorics and graph theory, analysis will not be as useful to you.

IDK, some people see a pretty sunset and go "wow, I love that" and others walk on by without looking. Mathematicians appreciate the sunset.

Are you interested in the underlying general ideas? If so, then welcome aboard. If not, then it's probably not the path for you to walk, unless you know for sure you want to apply it to something. Math itself is not just calculating stuff.

That's pretty well said. Loving the thing isn't enough, though. It requires a lot of work, too.

Probably.

Short books that really help "deep work" by cal newport, "a mind for numbers" by Barbara Oakley.

Totally transformed how I learn and made it much more effective. I am studying physics on my own, tracking the college curriculum. Currently finishing off the math for third year.

As well as math I would consider statistics and machine learning. If you can really understand these you are in a strong position. It is amazing how many e.g. professors of medicine have absolutely no clue about statistics.

Pic does not refer.

The people who seem to do well are those who love doing the 'puzzles'.

When a proof is hard they like it because it is fun working it out.

>Math itself is not just calculating stuff.
Yeah I understand that.

Just downloaded it. Thanks.