First year math major, text book recommendations please

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Background:
  • https://translate.google.pl/translate?sl=pl&tl=en&js=y&prev=_t&hl=en&ie=UTF-8&u=https%3A%2F%2Fwww.syllabus.agh.edu.pl%2F2018-2019%2Fen%2Fmagnesite%2Fstudy_plans%2Fstacjonarne-inzynieria-mechatroniczna%2Fmodule%2Frme-1-101-s-matematyka-1&edit-text=(mindless applying of 'algorithms' to solve an exercise)
  • https://translate.google.pl/translate?hl=en&sl=pl&tl=en&u=https%3A%2F%2Fwww.syllabus.agh.edu.pl%2F2018-2019%2Fen%2Fmagnesite%2Fstudy_plans%2Fstacjonarne-inzynieria-mechatroniczna%2Fmodule%2Frme-1-204-s-matematyka-2(the same)
  • Introduction to Linear Algebra - Gilbert Strang (this is a one big decomposition book. But thanks to it I'm able to somewhat understand PCA and SVM)
  • Introduction to Probability - Dimitri P. Bertsekas, John N. Tsitsiklis (halfway through)
in 2.5 month I start applied math major.

The first semester (in the center of a page, there are outlines of lectures):
  • https://translate.google.pl/translate?sl=pl&tl=en&js=y&prev=_t&hl=en&ie=UTF-8&u=https%3A%2F%2Fwww.syllabus.agh.edu.pl%2F2018-2019%2Fen%2Fmagnesite%2Fstudy_plans%2Fstacjonarne-matematyka%2Fmodule%2Fama-1-101-s-introduction-to-logic-and-set-theory&edit-text=
  • https://translate.google.pl/translate?hl=en&sl=pl&tl=en&u=https%3A%2F%2Fwww.syllabus.agh.edu.pl%2F2018-2019%2Fen%2Fmagnesite%2Fstudy_plans%2Fstacjonarne-matematyka%2Fmodule%2Fama-1-102-s-calculus-i
  • https://translate.google.pl/translate?hl=en&sl=pl&tl=en&u=https%3A%2F%2Fwww.syllabus.agh.edu.pl%2F2018-2019%2Fen%2Fmagnesite%2Fstudy_plans%2Fstacjonarne-matematyka%2Fmodule%2Fama-1-103-s-linear-algebra-with-geometry-i
Could you recommend textbooks for these three classes? And tell me whether it's a good idea to pick up some proof book in meantime (e.g. How to Prove It - Velleman) as preparation.
 
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If you are self-studying there's the MathisPower4U.com website with short videos on Calculus 1,2,3 Linear Algebra and Differential Equations covered as well as high school math in case you need to review something.

Bookwise:
- OpenStax Math (free, several books to choose from):

https://openstax.org/subjects/math

- Stewart for Calculus

https://www.amazon.com/dp/0538497815/?tag=pfamazon01-20

- Kiesler Calculus (using hyper-reals, non-standard but very insightful, did I mention free)

https://www.math.wisc.edu/~keisler/calc.html

https://www.math.wisc.edu/~keisler/foundations.pdf

- Proofs from the Book (inspired by Erdos and his belief that all the great proofs are in God's book)

https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK

https://www.amazon.com/dp/3662442043/?tag=pfamazon01-20