I need advice as to what math topic to study next

  • #1
I am a high schooler, I have studied a fair ammount of calculus probably up to about calc i level, I then skipped some stuff and did the vector calculus chapters in my calc book because it seemed interesting, I did grasp all the concepts, but I'll admit my integration techniques were not yet calc 3 level, I am weary to go back into calculus as a whole, I will be taking ap calc bc next year. I am about to finish the book "bert mendelson's intro to topology", It is great. I want to learn about differential topology, I ordered shilov's linear algebra book, do you think I can comprehend this with my knowledge, and then go on to look at differential topology? Or do you think I should just do more calculus.... thank you, any advice is appreciated
 

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  • #2
arildno
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Linear algebra is a very good choice for a new math topic. I'd even say: The very best topic for you right now. I
 
  • #3
Cool, can't wait to get started
 
  • #4
Jow
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I am in a similar situation. I've learnt some calculus on my own and am a bit stuck on what to do next. With regard to physics, I have been told that the next topics I should study are vector calculus, linear algebra, as well as ordinary and partial differential equations. If you, like me, are interested in physics then these topics are the next step.
 
  • #5
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Linear algebra is a very good choice for a new math topic. I'd even say: The very best topic for you right now. I
I agree. With that being said, I do not think Shilov is a good choice. A book like Lang or Axler is a better first exposure than Shilov.
 
  • #6
Jow, how much calculus have you learned? I'm Just curious because I've only gone up until like end of Calculus I stuff because I will be taking Calculus BC next year, and there are more interesting topics elsewhere in math. I do like physics and I've done a fair amount of vector calculus from a Calculus III textbook I got possession of, It is very interesting, probably one of the most interesting topics I have seen in Calculus so far, As long as you can grasp the concepts the math isn't overly difficult. I think I have a way to go until I can even think about differential equations. If you like abstract math you should look into topology, It is fairly accessible and if you go far enough in it also has very interesting applications in theoretical physics, and there are many basic books on the topic out there.
 
  • #7
chiro
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One recommendation for vector calculus is to read "Div Grad Curl and all That" for some intuition for this subject.
 
  • #8
Jow
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Jow, how much calculus have you learned? I'm Just curious because I've only gone up until like end of Calculus I stuff because I will be taking Calculus BC next year, and there are more interesting topics elsewhere in math. I do like physics and I've done a fair amount of vector calculus from a Calculus III textbook I got possession of, It is very interesting, probably one of the most interesting topics I have seen in Calculus so far, As long as you can grasp the concepts the math isn't overly difficult. I think I have a way to go until I can even think about differential equations. If you like abstract math you should look into topology, It is fairly accessible and if you go far enough in it also has very interesting applications in theoretical physics, and there are many basic books on the topic out there.

I have done a fair bit of Calculus, but it is hard to quantify how much by giving you what level I have taken up to because in Canada it is slightly different. I can give you the books I used however. I have worked through the entire Calculus for Dummies book as well as the textbook at my school for AP Calculus. Also, I used my cousin's Calculus textbook he had when taking it in first year university. I have also started to go through a books I got on differential equations. To be sure, I don't have a whole deal of knowledge in this matter, but I think once you have a good footing in Calculus you should be able to learn differential equations. Of course, as I said, I don't have a whole lot of experience on the matter, but from what I have seen this is my opinion. However, I do plan to learn vector analysis as well as some topology.
 

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