Seeking advice about learning more math

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  • #36
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I don't recommend learning your school syllabus ahead of time because that could mean you get very bored in class. I know from personal experience because I learned to read before I went to school and my first year was terrible because I had nothing to do. It's not something I would recommend to anyone.

Rather than doing something like that, I would recommend using a more advanced book like Spivak at the same time as you learn calculus. That way, you won't get ahead of time. Regarding linear algebra, you could do the same thing if you ever do it in college, using a book like Axler. But that all depends how you like abstract math. You may not like it.

Luckily, linear algebra has little overlap with calculus so it shouldn't affect it very much.

This is the book I will be given next year. Is this a quality book?
 

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  • #37
verty
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This is the book I will be given next year. Is this a quality book?

I think it must be good because Finney is the same author of probably my favourite calculus book, Thomas & Finney 9th edition, the one with the blue lighthouse on the cover. And with many authors like that, they wouldn't have been tired writing the book, so I think it'll be just fine.
 
  • #38
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I think it must be good because Finney is the same author of probably my favourite calculus book, Thomas & Finney 9th edition, the one with the blue lighthouse on the cover. And with many authors like that, they wouldn't have been tired writing the book, so I think it'll be just fine.
So you think I should get the more advanced book in addition?
 
  • #39
fresh_42
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So you think I should get the more advanced book in addition?
If you buy Spivak, Greub or similar books, they will either become your standard source to look up things and a good basis to deepen your knowledge, or you will sell them in the near future on ebay or amazon. Will say, even if you decide, that they are still too difficult or time consuming by now, they will still be a good purchase for tomorrow, or you followed a different path in the meantime. That's a risk you must assess.

In the above thread there are many good advises and, yes, contradicting ones, because they show you possible alternatives. Don't get frustrated by stuff that you find too difficult and don't learn ahead of classes. The books on openstax and maybe the pdf about proofs are all meant for the transition high school -> college and they should not be a problem for you. Greub and Spivak are textbooks for those who study mathematics, or at least the basics of mathematics, as e.g. a meteorologist would do. If you really are interested in a subject, then there is no problem learning it. If it costs you energy to sit down, read and learn it, then you are not really interested and no advise on earth can change this.
 
  • #40
verty
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So you think I should get the more advanced book in addition?

I think for your final year you should try to do the best you can in school and another book could be a distraction. You want the best marks so you get into your desired university. What I meant was, when you are in university you might have to do calculus again, and then you could use a more advanced book if you wanted so that it would offset the tendency to become lazy. The same goes for linear algebra, you could use a more difficult book if you find you already know it. But like I said, I don't see the value in studying ahead of time but since you may choose math, I thought it would be useful to have a look at some abstract math to see what it is like.
 
  • #41
mathwonk
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