Nice. I am a self-study-er so this is helpful advice. You definitely have to pick your battles and can't get lost in this autistic desire to linearly complete each book from cover to cover.
10:43 This is a common enough situation with books written in that era where, if you were taking a course that used such a text, you were a lot more likely to be at a university that built much of the introductory Analysis material directly into the Calculus sequence (using texts like Apostol or Spivak rather than, say, Stewart).
I've heard of those books, but I've actually never once made that connection. Awesome *analysis* !! I'm actually kind of mind blown right now, not gonna lie.
If you are hitting a subject cold, research the available textbooks from introductory Undergraduate level to Graduate level to get a handle on the starting point and what the advanced concepts are. If you have a strong technical background, you could start at the Junior/Senior level. Studying a subject from two different authors is enlightening: the subject matter is equivalent, but one gets two different views. This is a big help if you are doing a self-study. I'm working through two books on Microwave Engineering which cover "the same stuff", but each author has his own approach and sequence of topics.
When I was studying at university, I had to rush through the texbook and skip the parts that weren't covered by the professor for lack of time. So now that I'm studying on my own, I take my time and I'm very thorough. I try to only skip sections that I'm sure I'm not interested in, mainly the numerical methods and some applications. It is so great to be able to take a similar book on the subject, read the index, and see that you went through more than 80% of the content! I also think that being thorough pays off, both later in the book or when going deeper in the field through other books. Certainly, the thing that I do not suggest is to skip stuff just to get faster to the end of the book. But that's what seems to work best for me, I also understand the idea of "picking the right battle" and setting objectives that are realistically achievable with the limited amount of time, as well as skipping the parts that we find boring. The real solution would be to be immortal 😂
About being thorough, yes! That's something that other subscribers have mentioned before. It's something that even I have to work on. I do try to move through material quickly. It is often to my detriment as I leave behind some material or details. As one of the other subscribers mentioned, going through the material properly will save you time in the future from having to review material! A family member of mine is a nurse practitioner, and he said he wishes his superpower would be to be able to gain all of the information in a book by just touching it! I like the idea of being immortal, but it might have some unforseen consequences 🤣. Thank you for sharing!
@MathematicalToolbox thanks for your reply ... in the end everybody should do what works best for him! As for your family member, I understand his/her position, but I like the struggle, time and effort needed to learn. It's what make it so precious and rewarding!
The why unfortunately comes much later in math, because many many problems can be solved by the method of infinite series, and if you use this method you definitely want to know if your series solution converges.
It was difficult, or was it another reason? The content is definitely a little challenging the first time around. Although I did well in Cal II, I'll admit that I did not retain the information very well. It was to my detriment as series never go away. You will use most of what you learned in cal II again later!
It's easy to forget why you did all those convergence tests. Especially since, if I recall correctly, we didn't need them much in Calc 3 & LA/DE. They're crucial in the next level of coursework starting with introductory analysis, though.
Good advice. I always struggle with this. It's hard to know when you know something without an external check.
Nice. I am a self-study-er so this is helpful advice. You definitely have to pick your battles and can't get lost in this autistic desire to linearly complete each book from cover to cover.
10:43 This is a common enough situation with books written in that era where, if you were taking a course that used such a text, you were a lot more likely to be at a university that built much of the introductory Analysis material directly into the Calculus sequence (using texts like Apostol or Spivak rather than, say, Stewart).
I've heard of those books, but I've actually never once made that connection. Awesome *analysis* !! I'm actually kind of mind blown right now, not gonna lie.
If you are hitting a subject cold, research the available textbooks from introductory Undergraduate level to Graduate level to get a handle on the starting point and what the advanced concepts are.
If you have a strong technical background, you could start at the Junior/Senior level.
Studying a subject from two different authors is enlightening: the subject matter is equivalent, but one gets two different views. This is a big help if you are doing a self-study.
I'm working through two books on Microwave Engineering which cover "the same stuff", but each author has his own approach and sequence of topics.
When I was studying at university, I had to rush through the texbook and skip the parts that weren't covered by the professor for lack of time. So now that I'm studying on my own, I take my time and I'm very thorough. I try to only skip sections that I'm sure I'm not interested in, mainly the numerical methods and some applications. It is so great to be able to take a similar book on the subject, read the index, and see that you went through more than 80% of the content! I also think that being thorough pays off, both later in the book or when going deeper in the field through other books. Certainly, the thing that I do not suggest is to skip stuff just to get faster to the end of the book. But that's what seems to work best for me, I also understand the idea of "picking the right battle" and setting objectives that are realistically achievable with the limited amount of time, as well as skipping the parts that we find boring. The real solution would be to be immortal 😂
About being thorough, yes! That's something that other subscribers have mentioned before. It's something that even I have to work on. I do try to move through material quickly. It is often to my detriment as I leave behind some material or details. As one of the other subscribers mentioned, going through the material properly will save you time in the future from having to review material!
A family member of mine is a nurse practitioner, and he said he wishes his superpower would be to be able to gain all of the information in a book by just touching it! I like the idea of being immortal, but it might have some unforseen consequences 🤣.
Thank you for sharing!
@MathematicalToolbox thanks for your reply ... in the end everybody should do what works best for him! As for your family member, I understand his/her position, but I like the struggle, time and effort needed to learn. It's what make it so precious and rewarding!
Great analysis and insight into goals in reading math books. Very helpful video.Kudos👍
Most important question ... and one with which I always have trouble. Another question: When to stop collecting materials and when to begin studying!
HAHAHA great question. I usually stop buying books when I find another hobby to spend money on. MTG, Gunpla, martial arts, etc.
Very helpful. 👍
Nice talk.
Definitely lost the why at the end of calc 2 whith all the series convergence tests
The why unfortunately comes much later in math, because many many problems can be solved by the method of infinite series, and if you use this method you definitely want to know if your series solution converges.
It was difficult, or was it another reason? The content is definitely a little challenging the first time around. Although I did well in Cal II, I'll admit that I did not retain the information very well. It was to my detriment as series never go away. You will use most of what you learned in cal II again later!
It's easy to forget why you did all those convergence tests. Especially since, if I recall correctly, we didn't need them much in Calc 3 & LA/DE. They're crucial in the next level of coursework starting with introductory analysis, though.
Thank you
First 😂😂😂
Sorry i Always found these comments a bit silly, but this time I couldn't help making one 😁
I'll be honest, I do it too sometimes! Thank you very much!