Should I avoid taking discrete mathematics and Calc 2 together in the fall?

Whats up guys, just finished my spring semester of Calc 1. I completely surpassed my expectations and mightve snuck in an A and at worse, a really high B. These are pretty big strides for me as I struggled with math for the longest time (mainly due not applying myself throughout high school) I’m pretty good conceptually, I do really well absorbing the material during lecture and breaking it down during my study time on my own without too much trouble. I am a bit slow at my arithmatic at times, which led to subpar quiz scores for timed quizes. So yea, not the brightest by any means, maybe above average at best on my really good days.

Anyways, my counselor has me signed up for discrete math and calc 2 plus a music course in the fall. I hear calc 2 is MUCH harder than calc 1 and discrete mathematics is a bit harder as well. For you average-slightly above average joes out there, what do you think is the call here? Move my schedule around and play it safe, or just take it head on give it my best? Im not scared of a challenge, I just dont really have a good idea of what Im up against

submitted by Nevin Manimala Nevin Manimala /u/NORCAL_SPARK
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What area/field of maths intersects Algebra, Geometry and topology? Also, something regarding with Analysis.

Hello,

What area of maths combines algebra, geometry, and topology? Also is research in Analysis that dead or less interesting all of a sudden? I spoke to someone saying that they would rather focus Analysis if they had lived in the 50s-70s, something like that. I actually do not mind Analysis (nothing against it as well), but there have been talks of it, having fewer opportunities? I would not know though. But somehow doing algebra feels much more stimulating to me than Analysis. So I feel I would want to go on the algebra route.

Anyways, I have a bit of a plan that goes like this:

  • For my Masters, I’ll plan to focus on Homological Algebra.

  • For my Doctorate, I’ll plan to focus on Topology/Geometry (also what areas from Homological Algebra could I apply to Top/Geo). I have read some stuff on Cohomology and it had kind of pique my interest.

Also your story of how you went about finding your area/field? And tell me why you love it?

I want to go on the Master’s route and just so I could secure myself later as well. I know that some people go from undergrad to doing a Doctorate.

Thanks,

MuchCry

submitted by Nevin Manimala Nevin Manimala /u/MuchCry
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Are there good generalization(s) of the q-gamma function and the q-polygamma functions?

The q-analogue of the gamma function (https://en.wikipedia.org/wiki/Q-gamma_function) is a generalization of the gamma function.

Is there a generalization of the q-gamma function with a reasonable expression and useful properties ?

submitted by Nevin Manimala Nevin Manimala /u/Aftermath12345
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Is it okay to leave real analysis till the end of my degree?

I’m trying to map out my final two years of courses, and there’s certain classes I’m really excited to take. Group theory, graph theory, ring and field theory, abstract algebra, advanced linear algebra etc.

None of these require real analysis as a pre-req, although my college does require two terms of analysis for the math major. I know most people take this as an intro to proofs in 3rd year, but I also understand it ends up being an absolute ass kicker. I’ve already taken discrete math and had an intro to proofs/graph theory as a CS major. Is there any downside to leaving this until the end of my degree? I feel like I’d rather tackle it once I’m more comfortable with abstract math concepts. Or is it better to get it out of the way early?

Honestly, I’m so sick of calculus and not exactly looking forward to analysis…

EDIT: Thanks for the outpouring of advice!

submitted by Nevin Manimala Nevin Manimala /u/CriticalNoise
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I have nothing to write with, nothing to write on, and nowhere to go. What’s some interesting math I can do mentally?

Just to pass the time, cause I’ll be sitting here another 5 hours.

Maybe some fun theorems to try to prove?

submitted by Nevin Manimala Nevin Manimala /u/111122223138
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Perfectly overlapping dragon curve

IF YOU WANT TO SKIP TO THE IMAGE OF THE FRACTAL, CLICK THE LAST LINK IN THIS POST

I’ve been messing around with a fractal generating program I made a while ago, and when it comes to the subject of dragon curves, there are several famous ones (the Heighway Dragon and the Golden dragon are two of them). There’s not really a good strict definition of a “dragon curve” that I’ve found, but the Golden Dragon and Heighway Dragon have almost the same motif, one of them simply has a different angle and line proportions: https://i.imgur.com/m2uBwy9.png (Golden Dragon) https://i.imgur.com/J3pEsxD.png (Heighway Dragon)

Of the many similar fractals you can get by manipulating these angles and proportions, one particularly interested me: if you manipulate the proportions just right, you end up with a curve that almost perfectly overlaps itself https://i.imgur.com/A0DzjxO.png

Today I sat down and decided I was going to figure out the exact right proportions I need to get a perfect overlap. For that to happen, these two corners on iteration 5 need to be in the same place: https://i.imgur.com/VZY0tOl.png

To understand how I went about solving this problem, let’s start by labeling our triangle’s sides and angles:

https://i.imgur.com/2GmaAKp.png For the purpose of simplifying the math, we’re going to start with the assumption that side C is 1. Note that this triangle is NOT a right triangle.

Here is iteration 2: https://i.imgur.com/DxShJQD.png

This shows iteration 1 (outlined in red) morphing into iteration 2. note the proportions of iteration 1 are equal to those of the motif triangle. https://i.imgur.com/6HTTLl4.png

We know that this triangle is similar to our original: https://i.imgur.com/jhWqcVC.png because during the iteration, both sides A and B are multiplied in length by side B and offset by angle a to make the sides of that triangle.

Here’s where it gets interesting; I’m going to take iterations 2 through 5 and paste them on top of each other: https://i.imgur.com/1JgyU9z.png

Take a look at this: https://i.imgur.com/1YvUjrL.png On those 3 iterations, the red line iterates 3 times, each time being multiplied by the length of side A and being rotated by angle b. In the end, the endpoint of it is the point we want to match up with the end of the blue line. The blue line is side B of the original triangle! That means for the triangle we want, we need side A to be the length of side B when it is multiplied by side A 3 times, and to be lined up with side B when it is rotated by angle b 3 times. That gives us these equations:

A4 = B

b*3 = c

The first step to solving this is to take of our law of cosines:

A2 = B2 + C2 – 2BC*cos(a)

B2 = A2 + C2 – 2AC*cos(b)

C2 = A2 + B2 – 2AB*cos(b)

Using substitution for the latter two with C = 1, B = A4 and b = 3c, we get these two equations:

A8 = A2 + 1 – 2 * A * cos(c/3) 1 = A2 + A8 – 2 * A5 * cos(c)

Alright, we have 2 equations and 2 variables! We can solve it now! Unfortunately, this set of equations sort of explodes when you try to solve it by hand, so instead of spending all day doing that (assuming you can even figure out how) we’re going to plug it into Wolfram Alpha: http://www.wolframalpha.com/input/?i=0+%3C+c+%3C+pi,+1+%3D+A%5E2+%2B+A%5E8+-+2+*+A%5E5+*+cos(c),+A%5E8+%3D+A%5E2+%2B+1+-+2+*+A+*+cos(c%2F3),+solve+for+A,+c+is+real

This gives us 2 answers, obviously we want the set where A is positive:

A≈0.844772 c≈1.60217

All I have to do now is some simple math and get the point which to enter for the apex of our triangle, and we have a winner!

https://i.imgur.com/SoBHovc.png

Here’s a larger picture of what I call the “Perfectly Overlapping Dragon Curve”: https://i.imgur.com/8jEPyWF.png

submitted by Nevin Manimala Nevin Manimala /u/Helix_Snake
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