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

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Discussion Overview

The discussion revolves around recommendations for proof-based mathematics textbooks suitable for high school students, particularly those studying A-level mathematics. The focus includes topics such as logarithmic functions, trigonometry, differentiation, integration, and more, with an emphasis on understanding the proofs behind mathematical concepts.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant seeks a textbook that includes proofs for various mathematical properties and theorems relevant to A-level mathematics.
  • Another participant suggests "Basic Mathematics" by Lang as a suitable option.
  • Another recommendation includes calculus books by Spivak and Apostol for more depth and detail.
  • One participant proposes "Pre-calculus" by Axler, claiming it to be better than Lang's suggestion.

Areas of Agreement / Disagreement

Participants provide multiple competing suggestions for textbooks, indicating a lack of consensus on a single best option.

Contextual Notes

Participants have not discussed the specific strengths or weaknesses of each suggested book in detail, nor have they addressed how each book aligns with the curriculum or the specific needs of the student.

Who May Find This Useful

Educators and students interested in proof-based mathematics at the high school level, particularly those looking for resources that delve into the origins and proofs of mathematical concepts.

CornMuffin
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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
 
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Lang - Basic mathematics is exactly what you're looking for.
 
For more depth and detail, have you looked at the calculus books by Spivak and Apostol?
 
Maybe Axler, "Pre-calculus"? I found it better than Lang's Basic Mathematics.
 

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