Should You Be Doing Undergrad Research in Math Before Grad School?

In this video I talk about undergraduate research in mathematics. How much does it matter? What do you all think?

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[andreyrussanov]

As always, you seem to answer the exact question I had on my mind.

[bryanxu]

yeah, I totally agree with you, feel like accumulating knowledge and enhancing skills to prepare for future research is more important. It's just way too hard to do meaningful research at undergrad level at least in math.

[myung]

I’ve been doing some research in knot theory as an undergrad . Honestly I wanted to do it just for fun and to help pinpoint fields of interest. I do agree I’m definitely not at a high enough level mathematically to publish anything without large amounts of help. But that and grad school admissions aside, the experience feels valuable to me personally.

[senselessnothing]

Undergrads are usually way too immature as mathematicians to write something worthwhile, often they don't have enough mathematics under their belt. Back in the 18th or even 19th century when axiomatics and formalism weren't as much of a big deal you could present some good stuff as an undergrad, you could write "the curve rotates clockwise", "the set has no holes" and nobody would care beyond that.
I'd say a chunk of modern applied mathematics work, say in physics or probability, could be written by undergrads, though as we know sooner or later they get formalized properly by actual mathematicians.

[AGuitarFreekOfficial]

I would say the main thing undergrad research can (sometimes) provide is the understanding of what research feels like and can therefore help you decide if grad school is right for you. I think it often seems much different than what one might expect as an undergrad.

[davida]

Question: How to stop watching youtube videos about doing math and actually do math instead, lol

[igor-math-br]

In Brazil, we have an national public project, called Cientific Initiation, or IC as we call it. So, basically, what you do in an IC is, during one year, you study at least 3 basic results of an graduate class (for example, my IC is on banach's fixed point theorem and how it applies to ODE, in the picard's theorem). You receive an advisor and have the opportunity to present your material at a congress, in October, called CONIC (I would love to see The Sorcerer watching my presentation haha)
But anyway. It's an good idea, we receive an "financial help" of 80 dollars per month and it's and great step for those looking in some specific direction (unfortunately, an number theorist was not available at my department at the time I started the burocratic process, but an analyst, and great professor, adopted me, so I'm happy)

[amritsahota]

Could you make a video where you discuss some of the classes you took in undergrad and grad school. Would be very interested to know which some of your favorite courses or courses that you enjoyed the most were. Thanks I love your videos!

[EconJohnTutor]

I had some undergraduate research experience. Regardless of whether it helps or not, its fun and helps you find research interest. I think its cool to show off and it gives you personality. Then again i don't run admissions :)

[davidkalichman]

Another great video, so concise and informative. Thank you sir as always!

[gregoriousmaths]

Related query: How does one do mathematical research?

[maypiatt]

8 gradschools out of 17!! That’s super impressive to me, I really wanna do math and become a professor and I ended up in community college and couldn’t do research in my freshman and sophomore years because of it, and this helped ease my fears about it a lot

[douglasstrother]

The graduation requirement from the UC Santa Cruz Physics Department was a Senior Thesis. After reviewing a number of topics in upper division Electromagnetism and associated mathematics, problems marked with a star (*) as "challenging" would be good starting points for an undergraduate research project.

Explore the same thing in Mathematics. Look at the 'hard problems' and the bibliography to find a suitable project.

[Hi_Brien]

Say you weren't strong early in your degree journey, you didn't really learn one of the foundational courses very well, but you passed it by the skin of your teeth after binge studying. You want to get into grad school, at what point in your degree do you think it is a good idea to finally teach yourself the foundational subject you aren't terribly strong in? Luckily I can say I'm not in this hypothetical situation, but it seems like a useful topic

[leeming]

Hey Math Sorcerer,
I watched a video with Terrance Tao, talking about the Classification of Finite Simple Groups
He said that, parts of it were computationally provable, (see: Gonthier et al. Feit–Thompson theorem computer-checked using the Coq proof assistant).
This had me very intrigued, However.

I recently watched 'Tibees" video on "A Mathematician's Apology
" about Hardy.
Like him, I too feel I am too old to contribute anything significal to mathematics.

I know that for undergrad Discrete Maths, and the etc is what the foundations are, and haven't even started!
I have failed the introductory to Sophmore Undergrad courses many times and am not gifted, and am old but did receive an Associate of Mathematics.
Despite my struggle, and frustration, my mind loves what math does and can do.

Is chipping away at this MEGA theorem computationally, viable, or even worth it?
Or will the standard axiomatic math be more than sufficient to claim the truth and validity?

Am I way out of line for thinking to ask my professors and advisors about this?
At what level does one even start learning about the Classification of Finite Simple Groups
?
Thank you for giving me hope to pursue my B.A. in Mathematics despite my old age :-)


I hope that what I may not be able to succeed at, you may invigorate Your students like me to tackle their dreams.

P.S. Hope the storms have eased off, so you can get some action on the waves during this GNARLY heat-wave.
Stay chilled my dude!

[frosty]

Do you think research on your own is possible ? Because in my own country we only have lectureres in college and not full professor so we dont have opportunity to get research advisor in undergrad. Would you make a video on this subject ? Some resources and ways to conduct research on your own ?

[TheNachoesuncapo]

Have you listened finite simple group of order two by the klein four?

[ashishKjr]

Video Request: Can you make some videos on how to prepare for grad school entrance examinations?

[MultiCoolman]

Do you have any tips for a high school student (12th grade) that wishes to do research in algebra, topology or differential geometry?

I studied Algebra and Galois theory at the level of Artin - Algebra and topology at the level of Munkres and Hatcher. I have also taken a university course in proof-based linear algebra. Now, I am trying to read through Lang - Algebra and category theory. However, I can't find a professor to work with as the university I am taking classes at part-time has mostly applied math research and very few pure math research. How important is a professor in trying to do research?

Right now I am trying to read papers on arXiV on group theory, but while I somewhat understand the paper, I struggle with extending it or generating a unique enough idea to merit any kind of research.

[osainkiyoshi]

Can you do a series for teaching Michael spivak calculus book, i am reading it and i absolutely understand nothing..