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Hi guys i am looking to learn a decent amount of mathematics in quarantine time. I thought it would good time to study mathematics before I start University but I am not sure where to begin I wanna be really top notch when University starts. So if you guys could recommend books on the topic I have mentioned below along with maybe lecture notes. I am a high school student so please recommend something that I can understand but it also covers some pre University topics so I can be somewhat prepared. I also don't mind if a certain topic are mentioned together in a particular book I am just mentioning them seperately to give a better idea. I will be studying physic at University so if you feel there a certain topic missing here that I should know beforehand please feel free to mention it.

1) algebra

2) geometry

3) trigonometry

4) calculus

5) differential equations

6) vectors

7) Matrix

8) Set theory

9)complex numbers

10) analysis (very introductory I have never done it before)

Please do realise that I don't nee links or anything but simply the name of the book would do and maybe the author.

Thank you for all your help.

Shaun
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LonelyKraken249
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  • There have been many postings for each of the areas you list, for example, https://math.stackexchange.com/search?q=book+recommendation+algebra+, just search for the other areas and you will get a bunch of recommedations. – Moo Jun 10 '20 at 19:32
  • Sadly I have done a bit of research but not really found something that suits my need most of the recommendations are of book at a level I am not yet at to understand that's why I seeking help for a straight forward answer so that I am not confused a lot – LonelyKraken249 Jun 10 '20 at 19:35
  • Khans Academy gives you structure and content for free ;) – CoffeeArabica Jun 10 '20 at 19:46
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    I’m voting to close this because it is too broad. I feel like we could better help you if you isolated one topic you wanted to learn, explained what you already know about it, and listed what you think you’d like to learn and/or be able to do. – gen-ℤ ready to perish Jun 10 '20 at 19:47
  • Khan academy does and I do use for help but I need a book with the question and some explanation and graph in books are a lot more helpful so I am looking to study for books it's also fine if you don't have pdf or anything you don't have to link the book but at least the name and maybe author will be very helpful – LonelyKraken249 Jun 10 '20 at 19:48
  • @gen-zreadytoperish I understand what your try to say but it be difficult to mention each of those topics seperately and it did make the article too long. I understand your concern and I mentioned I have a high school knowledge of these topic so you can consider them very basic and I am looking for some book recommendations that will bring these up to a pre University level or at least provide an in depth view of the topic without making it to complicated cause my knowledge base is still not that high yet – LonelyKraken249 Jun 10 '20 at 19:52
  • Maybe some of the books I mention here. For example, among the books in the links is the School Mathematics Study Group volume Introduction to Matrix Algebra, – Dave L. Renfro Jun 10 '20 at 20:43
  • To those upvoting my comment: If you agree, then vote to close the question. Upvoting the comment doesn’t do anything. – gen-ℤ ready to perish Jun 10 '20 at 20:47
  • @DaveL.Renfro Thank you so much for linking this post. It was really helpful and I have understood a lot and I have certainly downloaded IM gelfand books as they are really and I am using currently. I really appreciate your help cause as you can see nobody else really helped – LonelyKraken249 Jun 11 '20 at 02:34

1 Answers1

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Since you're starting physics soon, and since you've hinted that the kinds of books that people strongly inclined towards math like are still too diffcult for you, I would suggest studying calculus from a book at a modest level of difficulty.

For this, I would recommend Calculus by Marsden and Weinstein, which can be downloaded for free from here: http://www.cds.caltech.edu/~marsden/volume/Calculus/

This textbook has useful quizzes at the beginning to tell you whether you need to take a lower-level course or not. It also has extensive review sections on algebra, analytic geometry and trigonometry.

If you do need to look at high school math again, one possibility is Basic Mathematics by Serge Lang.

Anonymous
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  • I have actually done basic mathematics by serge lang but i will definitely follow your advice and study calculus from this book – LonelyKraken249 Jun 12 '20 at 04:24
  • If you liked that book, then you can try Lang's First Course in Calculus as an alternative to Marsden and Weinstein. It's more concise than M/W, but probably requires more maturity and preparation. If you've read and understood Basic Mathematics, then you have sufficient preparation. See which one you like best and go with that one. – Anonymous Jun 12 '20 at 04:32
  • I have been using Paul online notes on calculus along with calculus lifesaver and Thomas calculus. Do you think these are good or will calculus by Marsden be better for studying – LonelyKraken249 Jun 12 '20 at 05:00
  • Of the three things you've mentioned, the only one I've seen is Thomas. I would say if you were just starting, I'd recommend Lang or Marsden over Thomas, which in later editions has become quite long and bloated. That being said, there isn't a huge difference, so the answer will depend on a couple of factors: (1) Are you enjoying the book by Thomas? (2) Have you advanced far enough in it that it no longer makes sense to make the effort of switching? I think it can slow you down if you try to use too many sources. – Anonymous Jun 12 '20 at 05:08
  • Well I haven't advanced that far yet since i am only using Thomas as secondary book for few extra questions so I will definitely switch to lang or Marsden and see how they feel. Thank you for your help and time – LonelyKraken249 Jun 12 '20 at 05:10
  • Okay, good. I like the third edition of Lang better than the first or the fifth. Have a look at the "Supplementary Exercises" at the end of Chapter 5 in Lang's third edition. These are the most interesting kinds of problems in basic calculus. – Anonymous Jun 12 '20 at 05:23
  • Well I have currently the fifth edition in PDF but I will try and find the third edition. But if you have the link to the pdf I would really appreciate if you could share it – LonelyKraken249 Jun 12 '20 at 05:46