Try These FIVE Things if You Are Getting Stuck in Mathematics
HTML-код
- Опубликовано: 2 авг 2024
- Today we are gonna talk about how to get "unstuck" in mathematics. These are not tips on how to study, but rather on how to save yourself from dropping the subject.
Affiliate links:
Mathematical Analysis by Binmore: amzn.to/4cbjaLP
Functional Analysis by Shima: amzn.to/4aNyaOY
How to Think about Analysis by Alcock: amzn.to/45bt1z7
Measure Theory by Malik et al: amzn.to/4c9SbQW
Principles of Mathematical Analysis by Rudin: amzn.to/4efmgQC
Solutions Manual to Principles of Mathematical Analysis by Kit Wing-Yu: amzn.to/3KAeOCg
Timestamps:
0:00 What this video is actually about
0:37 Textbooks
4:34 AI Chats
7:34 Tangent on solutions
9:38 Collaborate with others
11:07 Look for an Errata
13:50 Solutions Manual
16:39 Bonus
19:18 Outro 
Наука
Thank you!
Great vid again. Chatgpt is a gem for research and studying math and all other subjects found in college.
5:19 Ah yes, graduate school... where the grading scheme is as follows:
A - Acceptable
B - Barely get it
C - Can't figure it out
D - Don't come back
F - F outta here
Another resource I like is to use grad school refresher books for people who are going to be starting graduate school soon. These then to give you a lot of very concrete practice problems around the highlights of a subject and can be a good starting point. Going this route requires a time investment, but I have used that in the past.
@professorquarter this is a great suggestion!! Thank you for sharing!
Onto a more serious comment -- this is a highly valuable video and I hope it gets wide exposure.
I have tried to study math on "expert mode" many times, where I insist on doing all the problems in a text above my weight class (eg. straight to Baby Rudin for Analysis), in order, all alone, without checking any solutions, and without moving forward in the text until I finish all the problems in a section. I do it thinking that if I can't figure out what I'm stuck on, I won't be able to handle anything that comes later.
This attitude is rooted in toxic pride and an apparent misunderstanding of how one progresses through mathematics -- it has accomplished nothing of value. Meanwhile, here you are, talking about how you've done the exact opposite and yet understand mathematical concepts 2-3 years beyond anything I've ever studied.
I think there's a lot to unpack in your comment, and I think it deserves its own video, to be quite honest.
I 100% agree with you. A lot of members of the math community insist that we do things the way that they do them and that if you can't or won't, then you're dumb or wasting your time. As you say, this is toxic. Furthermore, this mentality is not wanted or acceptable here.
Many of us here in *this* community are learning math for fun and trying to learn math the same way a PhD. student would learn math will only lead to frustration.
I realized fairly early on that I could not do math as you say on 'expert mode'. This is not because I'm some 200IQ mathematician, but because I had (historically) and a low tolerance for suffering, and that low tolerance would lead me to quit a lot of things.
Yes, you can achieve a decent enough understanding without having to go on expert mode, despite what some would have you believe. I usually only pick out 5-10 exercises in any given problem set, and I *always* verify my answer.
As much as I talk about books on this channel, I still don't think I've done a good enough job of explaining how finding the right book for you can be life changing. It might not take 2-3 years to get to where I am. I would say learning analysis (or topology) is the best thing anyone interested in higher mathematics could do. There are a lot of really good, readable books on both of those subjects.
Thank you so much for sharing!
For a long time I have been struggling with a similar approach to studying mathematics. For me the underlying reason was this feeling that, otherwise, I won’t *remember* it well later and therefore would have trouble to deal and comprehend whatever is coming next. That I would have to read and study the subject again and use my time inefficiently.
Suffice it to say that *this* attitude is inefficient.
I am curious about your take on it.
In general, what I have experienced is that most books will test you on the content of the main part of the text, not the exercises themselves. So if you are dedicated to your subject (you might not even need to be, to be quite honest), you can study/memorize the definitions and the proofs of theorems/propositions.
Sometimes, the information in previous chapters is very heavily used in subsequent chapters, but oftentimes, it is assumed that you have a working familiarity with it. The only way to know for sure is to *try*. This is an issue I used to have and something that I saw in my wife when I was trying to share some concepts with her: the reluctance to try certain things. "Oh well, I know it won't work, so I'm not gonna try," nope. Try it anyway. There's also this feeling of almost fear. Perhaps this is due to a fear of failure. But in mathematics, I have become very good friends with the concept of failure. If I'm failing, it means I'm trying, and trying is always a good thing.
I would say that attempting to memorize the definitions and proofs of theorems/propositions has had the most impact on my feeling of having mastery or command of a subject. I've done this in my studies with measure theory. Now, I need to go back and do this with linear algebra as I always forget how to work with some of those ideas. 😂
Hope that helps!
Finding other books and a good study group are nice resources.
19:31 Membership part of the channel? On RUclips? I can't seem to find it.
I haven't published them here on RUclips yet. The memberships are pretty much ready to go, but I want to upload all the content I've already created before people give me their hard earned money. I have not gotten around to this yet. So sorry!
I am planning on uploading the same content on Patreon and RUclips. Currently, I have a book video on integral transforms and more than a few short discussions on books. I've got $1, $5, and $10 tiers on there. Thank you so much for considering supporting the channel.
patreon.com/MathematicalToolbox?Link
@@MathematicalToolbox Thank you!
Can Chatgpt not use something like Wolfram Alpha plugin to fact check it's answers and self correct itself?
I'm not 100% sure. This is a little advanced for me tbh. I've heard of people doing things like giving internet access to GPT, but I've never delved into any of this myself.
I don't know about the free version, but I know that ChatGPT plus allows you to use "Wolfram GPT" which will do all that kind of stuff for you.
It can but it's still not 100% trustworthy, because how plugins work is the model uses the plugin and then generates text from the whatever the tool produces So the eventual output is more reliable but not perfect. I still find chatgpt very useful for study. I treat it as a smart friend that I can discuss things with, ask questions etc, but make sure I check the answer carefully for myself.