Advice for undergraduate research in Mathematics

Hello r/math,

I highly appreciate any input and thank anyone who helps.

I am a Mechanical Engineering student with a Mathematics minor, and I am in the process of starting undergraduate research with one of my previous Math professors.

His background is in Applied Math and PDEs but he has told me I do not have enough background to do work in his field

The undergraduate courses I have taken are: Calculus I through IV (includes Vector Calculus), Discrete Structures (includes Logic, Sets & Proofs), Linear Algebra, Numerical Methods, (Ordinary) Differential Equations, Probability & Statistics, and Real Analysis (includes metric topology, single-variable analysis and rigorous proofs).

I have a strong computational background and can program well. I also have a person who will work with me with very similar credentials.

We have been struggling to find a topic appropriate to my level. Ultimately we want to do work in Robotics (the applied math aspect of it). But I really want to experience mathemtical research, because math is something I really enjoy. I frequently read a lot of math beyond my level out of thirst and fun.

What would be a realistic topic, field, or problem someone with my context could work on?

I am fine with any problem either abstract or real-life based. I seriously just want something I can work on, anything accessible is good enough at this stage.

I understand I am not asking a simple question, but any input, point, or direction would be extremely helpful. I just want the insight of people who know much more than I do.

Thank you very much.

submitted by Nevin Manimala Nevin Manimala /u/SirWafflemore
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Its not enough for me to know how to solve problems anymore…

I was struggling with Math. I was just giving up and comparing myself too much with the rest of my peers.

So I went in on Friday to get extra help and retake the test I got a 49% on.

Got my grade up to a B!

I notice as I have progressed with Math, it is not enough for me to know HOW to solve the problems. I need to know how these problems came to be, why we solve them the way we do, where these numbers come from.

So I decided I definitely want to major in Math.

And want to pair it with a degree in computer science but even then. . Its no longer enough for me to know how to do something…

I want to know the why, to dig deeper.

This sub has been helping a lot with that. And I found some amazing sites.

This is coming from someone who always did bad in Math but then something in me clicked.

Now that I know I can solve problems, I want to know… ok so how did you come to be. How is it that this formula or number is true?

I’m sure a lot of you are like this.

I know now you dont have to be mad brilliant to do math or to be passionate about it.

submitted by Nevin Manimala Nevin Manimala /u/lesbo-sith
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I think I discovered a completely novel way to multiply/divide using a graph. But, looking for someone to refute that. In either case, I hope this can help someone.

So, I play with graphs and circles literally every day of my life now. I love looking for interesting relationships, and forming theories and proofs based on them.

Anyway, I made this video to share one of my simpler discoveries. Someone long ago may have discovered this before, but I cant seem to find any literature ( though admittedly, I wouldn’t really know what to search… I’ve exhausted all my options).

I’m no mathematician in the least (although, I do love a numberphiles video or 2), but, I like numbers ; and work with them every day. I hope to learn alot by sharing this, perhaps even teach someone even.

The video is awful, and i apologize, but I hope the point comes across.

https://www.youtube.com/watch?v=rxSdscuKpkc&feature=youtu.be

submitted by Nevin Manimala Nevin Manimala /u/JaSuperior
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Need help for an Eulerian path game I made

Hello, first of all I have to say that I’m french so sorry if my english is bad.

I love to create new games and today, I put on paper something that I really like. Firstly, you make a 3×3 square with number from 1 to 9 in a random order. For exemple:

1 6 8

7 4 3

2 9 5

You have to make a trail which visit every number from 1 to 9 in order using only straight lines. You can’t walk above another number. Here’s an exemple of the moves you can make: https://imgur.com/a/kWQHX

You can’t cross lines.

You can visit the same number multiple times. However, you can’t use the same line twice (like a normal Eulerian path).

Here’s an exemple of a finished game: https://imgur.com/a/5KGRf You can notice every number was visited in order from 1 to 9 and that I used some numbers more than once to achieve it.

The reason I’m here is because I can’t find a theorem who would prove or deny that every combination possible of 1 to 9 could have an answer. For now, I have won every combinations I tried but I don’t know how to be sure it will always be possible.

Do you know an already existing theorem which could help me? Or do you know how to prove it? I’m also asking myself about 2×3 grid from 1 to 6, 4×4 grid from 1 to 16… or every imaginable type of grid.

submitted by Nevin Manimala Nevin Manimala /u/Foudubulbe
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Accelerated Master’s or go in more depth before PhD

Hello everyone,

I am a math major and I am currently in my second year of undergraduate, with ambitions to become a tenured professors. Up until a few weeks ago I had been thinking that I would earn a BS in Math and Computer Science. My plan revolved around stacking my junior with all of the math courses that would make me a strong candidate for graduate school covering Real Analysis, Abstract Algebra, Cryptography, PDEs and then my senior year would revolve around finishing up the requirements for my Computer Science BS. However after talking with multiple professors I have decided to not pursue the BS in computer science because it would involve taking courses that would have no benefit to me (Introduction to Engineering, Professionalism in Computing, etc.) and that I could just take the difficult courses that would be able to grow me as a developer. But now with this gap in my senior year I am trying to decide what courses to do and how to approach. The idea that I have been considering after talking to several professors has been to potentially graduate after next year and continue in an accelerated masters at my school and finish the accelerated masters the following year. So in 2019 I would earn my BS in math and 2020 I would earn my Masters in Math from the same school.

The snag that I have been running into has a few components. The first has been that I have always heard that students should change their graduate school from their undergraduate to gain a wider philosophy and appreciation for the material and to extend their network beyond one university. The second part that I am considering is how an admissions board will view my accelerated Masters (i.e. will it come off as a quick gimmick to improve my resume or will be seen as an asset when I apply to a PhD program). The third and most important is that I am still unsure which subset of math that I enjoy the most or is the best fit for my approach. I do not want to move into a masters into a subset of math that I lack talent or enjoyment in (this is unlikely, but I have a fear of making a poor decision). When it comes to admissions to a PhD and from masters in general, will it count against me in the application process if I may want to adjust my research focus in math between Master’s and PhD?

I am still talking with a lot of teachers, I just wanted to post this here to see if anyone was knowledgeable about what PhD admissions is like in math or may have gone through a similar process as to what I am in right now.

Thanks!

submitted by Nevin Manimala Nevin Manimala /u/runnerguide
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Play mat for toy cars is topologically toroidal

When I was a kid, I had a play mat that had the aerial view of some roads and buildings for playing with little toy cars. (An example picture of a similar mat can be found here: http://akapdx.com/16377/city-carpet/astonishing-decoration-city-carpet-car-nostalgia/)

And, as a kid, I noticed that when part of the design flows over the edge of the mat, it matches with the design at the opposite edge of the mat. This makes it like the representation of the topology of a torus that involves drawing a rectangle and pairing opposite edges.

I’m curious, how many others had a mat like this as a kid and also thought about it? And for those who did: did working it out first with the play mat make the concept of the edges being ‘the same’ easier when you came to learn about topology in math class?

submitted by Nevin Manimala Nevin Manimala /u/JNCressey
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Research for high school senior

So I’m currently a senior in high school who’s passionate about math. I want to reach out for more research opportunities to work on in the summer. I have basically no idea how to start. I mean, I plan on emailing some professors and ask them to mentor me. But I’m not really sure how much math I need to learn before it’s good to ask for these kind of things.

I’ll be happy to provide more information if needed. Any help is appreciated!

submitted by Nevin Manimala Nevin Manimala /u/dhl03
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Rebuilding the foundations of basic mathematics.

hello people of /r/math, this is my first post on this sub reddit, also i am relatively new to reddit. I come from a computer science background, where math is important(ish) but i guess you can survive without it if your lazy like me. recently i started taking a course on Linear Algebra by Dr Gilbert Strang MIT OCW, after 2/3 rd of the course was done, i realized something.

  • i was having trouble understanding the equations rather than solving them.
  • i could follow the guidelines and do the question and assignments ( to some extent), but i was having trouble grasping basics concepts such as projections, trigonometry, polynomials and roots etc.
  • i decided it was time to revisit high school mathematics once again, as much as i hate to admit it , i struggle solving basic equations from the few following topics i mentioned and i also have a hard time grasping these simple concepts, and it really does not feel good.
  • i want to be able to look at an equation (with some context) and say i know what this is saying to me, like i would be able to read a code (well written of course)

Can you guys recommend me some websites, online resources, books, maybe a plan to get a strong firm foundational grasp on the basic concepts of mathematics

  • I would also like to hear your general view on what you think are the fundamental concepts in mathematics , since i am pretty stupid and cant really tell what should really be the basics*

i checked out the basic “high school” math section on khan academy, the equations they had i could solve but i still dont understand what the equations are really trying to say except solve for variable x, hell i dont even know what a variable “x” is trying to imply.

thanks for reading the long post.

submitted by Nevin Manimala Nevin Manimala /u/dr-tenma
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