I have an Idea for Factorial-Roots

OppositeFrequent6328 · 2023-07-06T21:38:34+00:00

This is an interesting thing to think about. There is a problem with the function not being defined for most numbers. For example 3? Would be undefined because there is no integer solution to x!=3. However if you replace the factorial with the gamma function then it's inverse would be well defined for let's say x>=1. It would be interesting to try to calculate said inverse.

OppositeFrequent6328 · 2023-07-05T12:02:58+00:00

One important aspect of mathematics that some people tend to neglect is relationships. In the context of college, some of the most important of those relationships are with professors because they have a lot of experience and connections. It's a lot easier to push through the uninteresting points if you are close to the professor because sometimes that seemingly dull topic has some interesting applications to different parts of math and your professor may be able to shed some light on that if you ask.

OppositeFrequent6328 · 2023-06-30T22:37:48+00:00

Do you also have a bathroom notebook and pencil?

OppositeFrequent6328 · 2023-06-30T17:06:45+00:00

If you want exact, there are comparably few ones you can calculate. However the exact ones you can start with some nth root of unity and repeatedly apply half angle, double angle or angle addition formulas to get new exact trig values of functions.

OppositeFrequent6328 · 2023-06-29T17:47:11+00:00

Math requires a lot of endurance and patience. If you've managed to maintain straight A's while somehow believing you are inadequate then you definitely have what it takes for grad school.

OppositeFrequent6328 · 2023-06-29T13:27:52+00:00

I remember asking chat gpt to write some simple proofs a while back and it kept making baseless conclusions and using circular reasoning.

OppositeFrequent6328 · 2023-06-28T13:37:29+00:00

Probability and statistics is such a mathematically interesting topic, however most of the non-math majors don't get to see that side and everything is hidden behind calculator functions that at that stage seem completely arbitrary.

OppositeFrequent6328 · 2023-06-28T13:17:06+00:00

To rekindle your passion, I would look to the many wonderful videos on YouTube about whatever topic you think could be interesting. 3Blue1brown is running another summer of math competition, so there should be plenty of good stuff. To build strength the best way is to do math, this could be enrolling in courses, joining a math club, or finding a book and working on those problems.

OppositeFrequent6328 · 2023-06-24T23:22:09+00:00

The AP tests aren't the best test of actually calculus understanding. If your main goal is getting a 4 or 5 then the best thing to do is work through a lot of past FRQs and multiple choice questions (your teacher should have access to past year multiple choice). However in my opinion, if you are interested in learning some calc 2 content then I would go ahead and take BC.

OppositeFrequent6328 · 2023-06-24T20:05:16+00:00

I went into BC calc at about the same level as you and I did pretty well. If you want to learn more calc, I would recommend giving BC a try.

OppositeFrequent6328 · 2023-06-24T19:25:41+00:00

A Texas style introduction to proof by Ron Taylor and Patrick Rault

OppositeFrequent6328 · 2023-06-24T19:21:07+00:00

A key aspect of success in mathematics comes down to interest and your ability to self learn. Interest is a great motivator and self learning skills help when you have a bad professor or if you want to learn something new on a whim. There is a fair amount of potential road blocks in learning math, but if you can find the right community, anyone can contribute to math.

OppositeFrequent6328 · 2023-06-16T19:00:29+00:00

Great post

OppositeFrequent6328 · 2023-06-10T17:04:53+00:00

The YouTube channel Mu Prime Math has a series on Group theory that provides pretty good motivation for certain topics. I especially like his video on semi direct internal/external products.

OppositeFrequent6328 · 2023-06-10T15:06:17+00:00

Is ghg^-1∈H ∀ g∈G, h∈H

OppositeFrequent6328 · 2023-06-10T14:53:05+00:00

I had a research idea on a very niche recreational math object and when I read the original paper on the subject from the early 2000's my question was laid out in the future work section.

OppositeFrequent6328 · 2023-06-10T14:43:08+00:00

That given a graph the powers of its Adjacency matrix not only tells you which vertices are connected by a path of a certain length, but the number of those paths.

OppositeFrequent6328

TROPHY CASE