Comments on: My Journey Through Mathematics https://pthree.org/2011/04/22/my-journey-through-mathematics/ Linux. GNU. Freedom. Thu, 11 Jan 2018 12:06:15 +0000 hourly 1 https://wordpress.org/?v=5.0-alpha-42199 By: deepak https://pthree.org/2011/04/22/my-journey-through-mathematics/#comment-115833 Thu, 07 Jul 2011 12:24:37 +0000 http://pthree.org/?p=1705#comment-115833 mast nahi hai yaar

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By: Jef Spaleta https://pthree.org/2011/04/22/my-journey-through-mathematics/#comment-115726 Tue, 26 Apr 2011 20:40:53 +0000 http://pthree.org/?p=1705#comment-115726 I'm not sure where you put graph theory in that grouping. It's just ...different. I wouldn't necessarily call it an algebra.

-jef

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By: Aaron https://pthree.org/2011/04/22/my-journey-through-mathematics/#comment-115725 Tue, 26 Apr 2011 19:35:40 +0000 http://pthree.org/?p=1705#comment-115725 @Jef Spaleta- Fair enough. All math is an extension of set theory and the axioms based on them. But, I think it's fair to say that there are various branches of mathematics that are drastically different than others. For example, Real Analysis is drastically different from Number Theory which is turn is drastically different from Numerical Analysis, and so on. It's fair to say, that while they all have a parent root, they can be quite different. I was hoping to learn these various differences.

Which brings to my mind, and maybe I should put this in a separate post altogether, but here are the various branches of mathematics that I'm familiar with- hopefully, I can learn something from each:

  • Calculus and Analysis
  • Geometry and Topology
  • Algebras
  • Set Theory and Logic
  • Probability, Statistics and Combinatorics

In regards to the various topics you presented, I would LOVE to learn Graph Theory. In fact, it's offered this fall semester, and if it aligns on the same days as Modern Algebra, I'm all over that like white on rice.

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By: Jef Spaleta https://pthree.org/2011/04/22/my-journey-through-mathematics/#comment-115723 Tue, 26 Apr 2011 16:36:48 +0000 http://pthree.org/?p=1705#comment-115723 @Aaron
Well everything is just an extension of set theory. We should all just be taught that in 3rd grade and be done with math forever.

In terms of math bag of tricks, I found Graph Theory's heavy reliance on inductive proof very different than the other math courses in a get my brain thinking out of the box standpoint. Graph theory is very fun to play with as a napkin proof hobby. Very doodle friendly.

Linear Programming and Non-linear Programming were interesting as well in terms of getting a better understanding the problem space of optimization in high dimensional spaces. Badly named subjects to be sure.They should have been called Linear and Non-Linear Optimizations.

One of the best math classes I had was an Asymptotic class which was very very interesting. Graduate level class for physics actually. Practical application of taking limits when working with differential equations in order to order terms and shake out dominate solutions out of horribly non-linear situations. Very useful. A class full of bags of tricks that I wouldn't have minded seeing in a math rigorous approach.

-jef

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By: Aaron https://pthree.org/2011/04/22/my-journey-through-mathematics/#comment-115722 Tue, 26 Apr 2011 12:39:10 +0000 http://pthree.org/?p=1705#comment-115722 @Jef Spaleta- No offense taken, I just wanted to be clear for future readers that this isn't a bragging post, but meant to be an informative one. Many people who aren't involved with mathematics beyond high school, or what is required for their degree, think Calculus is the highest level of math one could learn. Hopefully, this post was meant to be enlightening to those people that there is a great deal of mathematics beyond calculus, and even beyond undergraduate school (even though that's not explicit here). Anyway, no offense taken, so no need to apologize.

My school only offers BVPs and PDEs every other year (BVP in the fall, and PDE in the spring). It was offered this past year, so it will be two more years before offered again, and hopefully, I'll be pursuing my masters degree in mathematics at that point.

When I was looking at the courses that I wanted to take for my undergraduate degree, I decided that I would align all of the applied mathematics requirements as electives for the general math emphasis. This turned out to be a smart move (a story I won't go into here), as I needed to switch my emphasis from general math to applied math. BVPs and PDEs weren't requirements for the general track of the applied emphasis, only for the physics track. Further, I wanted to take as many diverse courses as possible during my studies, while still maintaining the requirements for graduation, and it seemed to me (I am likely wrong), that BVPs and PDEs are just extensions of ODEs. Because I have already taken ODEs, I wanted to see what else was out there that was completely unrelated to what I had already studied.

Come this fall, even though I am now graduated, I will be taking the Modern Algebra track, so I can still say that I have met all the requirements for both the general and applied requirements, even if the school won't give me two degrees.

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By: Jef Spaleta https://pthree.org/2011/04/22/my-journey-through-mathematics/#comment-115721 Mon, 25 Apr 2011 23:39:34 +0000 http://pthree.org/?p=1705#comment-115721 @Aaron,

It was meant as a bit of self-deprecating snark. Apologies if it came off as some sort of comment on your scholarly career as it was not intended to be. Though saying it was not what I intended is no excuse for causing offense, so apologies once again.

However, the comment about seeking out cross-disciplinary experience with PDEs and BVPs was meant to be taken seriously.

-jef

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By: tyg https://pthree.org/2011/04/22/my-journey-through-mathematics/#comment-115718 Sun, 24 Apr 2011 17:08:23 +0000 http://pthree.org/?p=1705#comment-115718 Check this site out for a great list of open content math books:

http://linear.ups.edu/curriculum.html

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By: Aaron https://pthree.org/2011/04/22/my-journey-through-mathematics/#comment-115717 Sun, 24 Apr 2011 12:50:29 +0000 http://pthree.org/?p=1705#comment-115717 @Jef Spaleta- This post wasn't meant to be a "mine is bigger than yours" competition. It was meant to be interesting, in that I had the opportunity to study a great deal of mathematics during my undergraduate career, and I wished to share what I learned.

@Johan- Complex analysis was offered during a time that I could take it with modern algebra, however, they adjusted the days it will be taught, and I can no longer take the course. Differential geometry isn't offered at my school, although I do plan on taking differential topology in graduate school.

@Jonathan Carter- Maths ftw! 🙂

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By: Jonathan Carter https://pthree.org/2011/04/22/my-journey-through-mathematics/#comment-115716 Sat, 23 Apr 2011 14:12:09 +0000 http://pthree.org/?p=1705#comment-115716 Wow, you're really lucky to have been able to learn so much already! I hope to one day take some time off and learn some maths.

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By: Johan https://pthree.org/2011/04/22/my-journey-through-mathematics/#comment-115714 Sat, 23 Apr 2011 03:24:27 +0000 http://pthree.org/?p=1705#comment-115714 I'd definitely recommend taking a complex analysis course. If you can find a course in basic differential geometry, that's also fun.

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By: Jef Spaleta https://pthree.org/2011/04/22/my-journey-through-mathematics/#comment-115713 Fri, 22 Apr 2011 22:02:59 +0000 http://pthree.org/?p=1705#comment-115713 I'm tempted into getting into "mine is bigger than yours" competition with regard to math text books. But I will refrain.

A suggestion, if you want to really followup on the non-discrete side of applied math, audit some physics or engineering classes, especially anything that deals with fluid-like systems or fields. BVPs and PDEs are the lingua franca in those spaces and the best way to learn the language is to use them in conversation. I said this as a Math/Physics double major undergraduate.

-jef

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