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I've just finished A levels in maths, further maths and physics and intend on going to uni to do maths and physics joint but I feel that A levels haven't prepared me enough. So my plan is over the next 3 months to make my pre-calculus mathematics really good so that I will be able to easily go through harder calculus books in uni and not have any issues.

My plan is to cover

  • logic,
  • set theory,
  • pre-calculus maths - in full detail,
  • problem solving books.

The books I have or am going to read (I will try to cover everything but might not be able too):

  • Elementary symbolic logic,
  • Introduction to Set Theory, by Jech and Hrbacek,
  • An Introduction to Inequalities by Beckenbach and Bellman,
  • The Real Number System by Olmsted,
  • How to Solve It and The Art and Craft of Problem Solving,
  • Basic Mathematics by Lang,
  • Kiselev Geometry along with working through Euclid's Elements and The elements of Coordinate Geometry, by S. L. Loney, M.A. along with conics books 1-5,
  • Durell's Elementary Trigonometry and Advanced Trigonometry,
  • Precalculus: A Problem Solving Approach and
  • Stewart Precalculus.

My plan is to go through the logic and set theory book first and then use Basic Mathematics by Lang to springboard me into all the books which I will read in parallel with Lang's book.

Will this plan put me in a good position for university? Also, will it allow me to cover Apostol's and Spivak's Calculus? Any other recommendations or books to that are a must read? Please let me know or if you think I should definitely cover something. Again please let me know.

Tsundoku
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LEO
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  • Apostal? Do you mean Apostle's calculus? – math-physicist Jun 30 '23 at 16:59
  • Welcome to Mathematics Stack Exchange. Do you mean Apostol's? – J. W. Tanner Jun 30 '23 at 17:07
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    No one could read all those books in three months. I suggest starting with Lang and Polya's How to Solve It and maybe his Induction and Analogy in Mathematics. Perhaps Lang and one of the other two simultaneously. If you can do that in a summer you'll be well prepared. – Ethan Bolker Jun 30 '23 at 19:43
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    The Jech and Hrbacek book is WAY too advanced (and unnecessary) for you at this time. Also unnecessary is Olmsted's book. I would not worry about logic and set theory now (one typically picks up the necessary grammar-basics along the way in calculus and linear algebra, and then if necessary, take a formal "transition to advanced mathematics" type course if needed for further work). Beckenbach and Bellman's book is good, but a slight overkill for your purposes unless you like the topic. I recommend getting one of those comprehensive precalculus texts that are almost never (continued) – Dave L. Renfro Jun 30 '23 at 20:53
  • fully covered in typical classes (such as Cohen -- contents) and carefully work though all the final few chapters, focusing on topics such as: arithmetic and geometric sequences, partial fraction decompositions, polar coordinates, DeMoivre's Theorem, inverse trig functions and simplifying stuff like $\sin (\arctan x),$ rotation of coordinate systems, parametric equations, (continued) – Dave L. Renfro Jun 30 '23 at 20:54
  • being able to use elementary graph transformations (horizontal and vertical shifts, reflections about $x$-axis and/or $y$-axis, etc.) in connection with power functions and trig functions and exponential functions and logarithmic functions. – Dave L. Renfro Jun 30 '23 at 20:54
  • thankyou everyone for your comments i know this seems alot but tbh ive done quite abit of this in maths and further maths alevel i just want to get a solid understanding and foundation of the basics from seeing all the comments i will definitely revise my plan alot so thankyou to everyone who commented, tbh am board in my extended summer and i plan to put in alot of 3-6 hour study sessions in every day because i really like working on mathematics i find that lately i more enjoy working than bingeing youtube and netflix so am just gonna do math mostly tbh – LEO Jul 01 '23 at 14:16

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