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Calculus Suggestion for a proof-based math text book for high school

  1. Oct 22, 2015 #1
    I am currently teaching the pure mathematics II component of A-level mathematics which consist of the following subjects: Logarithmic/exponential functions, trigonometry, differentiation, integration (including integration by parts, and trig substitution), numerical approximation of roots of a function, vectors, differential equations, complex numbers.

    My student asked me for a math book which goes through the proof of some of the properties, identities, equations and theorems or it's origin discussed in class. I often go through proofs in class, but the book that we use hardly ever have proofs.

    Do you have any suggestion for a proof-based math book suitable for a curious, and above average high school math student.

    Thank you
  2. jcsd
  3. Oct 22, 2015 #2
    Lang - Basic mathematics is exactly what you're looking for.
  4. Oct 23, 2015 #3


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    For more depth and detail, have you looked at the calculus books by Spivak and Apostol?
  5. Nov 16, 2015 #4
    Maybe Axler, "Pre-calculus"? I found it better than Lang's Basic Mathematics.
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