Hi thank you for the response, I definitely do read books that don't have solutions. I do agree that I should be less reliant on solutions and more reliant on the knowledge of the subject and confirming the steps myself. cool vid!

@willthecat3861

Ай бұрын

Don't give up on requesting mathematicians (mathematics professors) to articulate how they 'do' mathematics... and expect to evaluate your understanding. IMO, many can't, and the majority don't want to. There is a very long tradition of 'hiding' the details, and engendering elitism... at least from Fermat and Gauss onward. If you really understand, and can do, high school mathematics... especially algebra... and you know how real numbers work... you should be able to... at least mostly understand the mathematical topics... and 'do' the 'average' associated homework problems. If you can't... get 'better' textbooks (by authors that want to 'explain' mathematics)... or... get better professors... or get a better university. Also... be aware that you are part of a system that pushes as many students out of mathematics as possible, yet doesn't mind taking the money, to do it.

@MathematicalToolbox

Ай бұрын

Hopefully between this video, and my original comment reply I answered all of your concerns!

Typical Physics texts contain answers to odd-numbered problems, and often hints for the more difficult ones. A lot of problems are of the form, "Consider situation 'S' (neglecting air resistance). Show that the equation of motion is ."

Learning math is hard. I can;t say I always do this, but when I do it works well for me. I try to carefully follow the examples in my book and notes. I then try to replicate them, when i'm stuck i go back and look at the example. Once you can do the examples right, I work on problems that i have solutions for. Once i'm getting them mostly right, i know i'm ready for other problems that i don't have solutions to. The idea is to slowly let go of the various types of scaffolding you're provided.

@willthecat3861

Ай бұрын

You mentioned "The idea is to slowly let go of the various types of scaffolding you're provided." You didn't mention, letting go of one's 'geometric crutches.' Which is another... IMO... non-sense phrase... promoted by the likes of Gauss... et al. There are few mathematicians, in history, to match Gauss. But far too many people, in history like him.

@MathematicalToolbox

Ай бұрын

Great input! I agree!

In this video I respond to another subscriber that is having difficulty with math books that do not contain solutions. Based off of my past experience studying mathematics, I believe this is due to this user's lack of understanding on how to study. My remedy to this situation is to ensure understanding of theorems, propositions, examples, proofs, etc. This should make most exercises much easier to solve. Additionally, you can still use and reference outside resources such as ChatGPT, textbooks, preliminary/supplementary reading books, online resources such as Reddit, Mathstackexchange, etc. This is the approach that I take, I do not mean to imply that this is the ONLY way to study or learn mathematics. Feel free to share your methodology down below. I hope this video was useful to not only the user that posed the question, but to anyone else that may have found themselves in a similar situation. Link to our Patreon: www.patreon.com/MathematicalToolbox Affiliate links: Stochastic Geometric Analysis by Calin: amzn.to/4cVpMy6

Great video MT. Nice tip on understanding theorems.

It's always easier to study mathematics with available solutions, but I find important to develop enough mathematical maturity to solve and prove (almost) everything which can be found in a textbook. There are lots of problems with solutions on the Internet, those are good when you are learning, by the other hand, it is much more important the early development of the ability to understand higher mathematics. Sure, math books are amazing, but mathematics is not literature, learning mathematics is a process that goes beyond books Liked your video, useful information

@MathematicalToolbox

Ай бұрын

Thank you for your input! Much appreciated!

The bit about abusing solutions needs to be talked about more everywhere. I see it talked about a lot, but it really needs to be said that figuring something out and then modifying your process is going to take you so much further in terms of being able to actually work through something you are presented with on the spot (in any subject). The key is to put in the repetitions before and after that point. If you invest the time in this, you will likely not have to spend much time fixing up your understanding of requisite concepts moving forward (saving time later!).

I think it's great to have a good, mature person, or group, to study with. This can enhance the learning experience. I know this isn't always an option though, sadly.

@stevenkies802

Ай бұрын

Discord groups, zoom clubs, reddit, etc. are always an option.

@willthecat3861

Ай бұрын

@@stevenkies802 There are a couple of 'well known' forums... and if you are willing to prostate yourself before the 'gods' that inhabit them... and admit you really are an idiot... they sometime will throw a few bread crumbs to you. I'm not saying there are not some very good mathematicians posting on those forums: there are. Just the same, and even though they know, and understand, mathematical definitions... they, don't have a poor understanding of what the term 'idiot' means, in the vernacular.

Thanks for the advice n motivation. Keep it up “Luffy” !!!

Well, in the USA, only solutions to odd numbered problems are generally given in math textbooks.

@MathematicalToolbox

Ай бұрын

In Europe (I recall that's where you're from), authors typically don't offer solutions?

@willthecat3861

Ай бұрын

Can't 'sell' a textbook (published for the university math course market) without... at least... some problems in it... that have no 'answers'. Many profs won't use it. (They can't assign homework problems from it.)

: I have a very specific problem i need help with : here are bunch of general study tips that everyone knows Goes to show that you should not try to learn from someone who is good at the subject, you need someone who is good at teaching.

@chpg6582

Ай бұрын

1) Mostly problems don't require a complex solution. If you follow advice you've heard, you will get great performance boost over your classmates that don't. It looks like you want some magic pill to solve problem, not a solution. 2) Author is asked to give his opinion on problem and he gives his opinion on problem. Moreover, he/his mates probably has struggled a lot while studying. So he might know some tips that a newbie doesn't know yet. That's why it is good to ask mathematic pro for advise too. It is always "practice to get good" with some glitter. What are you waiting for?

@professorquarter

Ай бұрын

This is a very generalized solution for learning proofs-based mathematics. This is NOT a video on how to study complex analysis or whatever. You honestly ought to be doing as he is discussing and also using more concrete worked out examples. ChatGPT is great for this and he suggests using it in the video. My preferred way to use chat is to have it poke holes in my work as its understanding of even fairly basic mathematics collapses when anything which is only implicitly involved comes into play.