Toxic Study Habits and Mindsets In Mathematics

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Күн бұрын

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@hubomba 6 ай бұрын

I have an undergrad in Math with some grad level sprinkled in and frankly Baby Rudin never made sense to me. The argument is navigating the obscurity of the text will make you better at Analysis, but for the time spent on the artificial difficulty of the text you could have gotten through the same content quicker and moved onto more advanced subjects. Rudin is also horrendous for training any intuition about the subject which is very important, Pugh is an example of an author who does that well without sacrificing rigor. Skimming what other departments are doing as time passes it looks like more of them are dumping Rudin for other options which is somewhat vindicating. You hit the nail on the head that most people who give that advice most likely don't actually do it or are parroting it to sound smart and get mathstackexchange or reddit internet points.

@walter274 6 ай бұрын

I haven't read Pugh, but i heard it was good. I have a friend that is connected to Penn, so i was skimming Penn's webpage and can across the Econ department, and Pugh is the Analysis book they want their students to be comfortable with.

@TranquilSeaOfMath 6 ай бұрын

But aren't internet points and sounding smart what it's all about? 🙄 I'm being facetious of course. I do wonder what drives some textbook choices. Ideally, we would choose the best for our audiences. That probably doesn't always happen though; unfortunately. I don't always like the books and materials used in other sections of courses I have taught at the undergrad level, but I have kept them. Thank you for sharing your insight and experience.

@MathematicalToolbox 6 ай бұрын

@hubomba I've never heard of Pugh before. Thank you for sharing! Thank you for your input about Rudin. I have not heard/seen anyone say anything bad about it. Very enjoyable to read, too! Felt like I was reading a review. 😁

@Edward-zw9ld 6 ай бұрын

Goals are critical, great vid.

@MathematicalToolbox 6 ай бұрын

Indeed! Thanks again!

@TranquilSeaOfMath 6 ай бұрын

Nice discussion. I believe understanding what prerequisites are needed will help people develop a plan to work toward the level they want to achieve. I'm not sure that many people realize how specialized the study of mathematics can get. In education theory, it is discussed like it's a river. In my experience, it's like an ocean!

@walter274 6 ай бұрын

Twenty years ago, when i was an undergrad I can across the book Advanced Calculus a Differntial Forms Approach by Edwards. It looked really cool and i could kind of get it, i had just finished calc 3 and linear algebra when i found the book. I came across the book for 30 on ebay two weeks ago and grabbed it. I made a plan, just like you mentioned. I'm doing multivariable calc out of Adams and Essex, Linear Algebra out of Strang, proofs out of Chartrand, and Real Analysis out of Abbot. Then I'm going to go through Edwards. I hope to be on Edwards in 12 to 15 months.

@TranquilSeaOfMath 6 ай бұрын

@@walter274 Sounds like a great journey. Best wishes. Cheerful Calculations! 🧮

@ClumpypooCP 6 ай бұрын

Interesting video man, have not seen anyone else talk about this. I really like your style, but I wish you were more interested in algebra since that is where my mathematical interests lie … the stuff you are interested in is literally the complete opposite of me 😂

@MathematicalToolbox 6 ай бұрын

Thank you for the nice words! I apologize for my lack of interest in algebra! I am lacking a sufficient background in algebra and geometry, so I try to stick to what I know. I've got several books that I've used lightly, that may be of use to you if you need a book recommendation or two. I will get to algebra and geometry at some point, just not sure when. Hopefully you enjoy the content enough to stick around :D

@ClumpypooCP 6 ай бұрын

@@MathematicalToolbox no problem man, yeah you have a really chill presentation style and speak on topics that no one else does. Keep it up

@Mathematica702 6 ай бұрын

As far as ‘appreciation’, you study whatever pleases you, and enjoy the process. There is nothing to achieve, nothing to become, for a real connoisseur, beyond whatever’s enjoyable, or interesting.

@ethann3887 6 ай бұрын

This video was informative on what to be aware of, I'm currently about to go into undergrad maths myself. Can I ask what's you background in mathematics ? You seem very knowledgeable.

@MathematicalToolbox 6 ай бұрын

I'm happy to help! My formal background in mathematics consists of a minor in applied mathematics. After university, I've delved into many subjects (at various levels of understanding): integral equations, stochastic calculus, analysis, measure theory, functional analysis, etc.

@noJobProgrammer 6 ай бұрын

Having calculus and linear algebra as background, what would be the shortest path to get into stochastic calculus at an average level?

@walter274 6 ай бұрын

I don't know Stochastic Calculus, so take what i'm saying with a pebble of salt, but i would think some probability would be useful. I have a bizzare recomendation for that. Don't get Ross's intro to probabiity book. Get his Probability and Statistics books for Engineers, and his Probability Models book. Together they cover the same maerial as the intro book, and you can find solutions manuals online. Or so i've heard :) The excersises are often duplicated. You can get both used for like 10 each. That said there are many good probability books out there, not just ones by Ross.

@MathematicalToolbox 6 ай бұрын

It depends on what you mean by "average level." You can use the book mentioned in the video. The blue book by Professor Calin. No probability is required, just calculus. The prerequisites from probability are given in the second chapter. I would consider having some probability and learning stochastic calculus using a book that assumes probability to be an average level. This is because the subject usually requires measure theoretic probability. Measure theoretic probability would be at the advanced level, I would say. You can use something like Blitzstein and Hwang, or Carol Ash's Probability Tutoring Book, or Lefebvre for probability. There are dozens of really good probability books. Then, you can use something like Klebaner, Durrett, Shreve, etc. to learn the subject. So, the shortest path at an average level could be Calculus I -> Calculus II & Linear Algebra -> Probability -> Stochastic Calculus

@MonkeyDLuffy-gd6se 6 ай бұрын

Hey hopefully you've been doing well. I was wondering on your opinion on rather toxic habits some mathematicians/tutors have. I am in my first year and i really struggled second semester, a lot of it is because I love to self study and when I do it is almost a must to atleast have some solutions to exercises. Now for a lot of books this is no problem to find solution pdfs but for some self-made syllabi from professors then it gets a lot harder (having to compare exercises from different books etc.) When i told my tutor (remember this is a second semester first yearh undergrad) she basically said that at this point you ought to "know" how to solve the problems. I find this a not so nice response since in general it is just better to have solutions so you can verify and see if you forgot a detail that might make the proof invalid etc. What is your opinion on this?

@MathematicalToolbox 6 ай бұрын

Thank you. I've been doing well. Yourself? As far as finding solutions to problems when there is no solutions manual, you can check out my last video (in case you haven't already). I talk about all the different things you can try when stuck. As far as forgetting stuff or not having learned stuff in a certain order, who cares. Just learn it again or learn it now. It's probably because you were not exposed to it, didn't learn it properly the first time, or didn't put in the effort to memorize it, or you just don't use that math often. It's really not a big deal. I have to go back and verify my understanding of vector spaces, linear independence, etc. pretty often tbh. I would be concerned with a pattern of negativity coming from a tutor like this. It could be just an isolated incident, though. You could say something like, "It's okay, that's why you're here. Explain it to me." I would have taken it as an opportunity to offer you more tutor time, hahaha. I still use solutions all the time, but I study for fun. You, as a university student, might want your understanding to be a little bit better than mine, though. If you are going to use solutions heavily, I suggest you use them in a healthy way. E.g. don't get stuck on problem 1 and go looking for a solution after 15 minutes. Chances are you need to go back and verify your understanding of the definitions, theorems, examples, etc. There have been several times when I was struggling with an exercise, just to find a solution, and it was pretty much an exact step by step as one of the examples! I hope that helps. I'll probably do a video on this. Thank you and good luck in your studies. Feel free to reach out whenever!