E-book, Non-Fiction, Other


A website providing a free, advanced basic high school math textbook in PDF format. Starting from Peano's Axioms, develops the natural number system, the integers, rationals, reals and complex numbers. Provides complete explicit proofs of basic theorems such as the Fundamental Theorem of Arithmetic and the Fundamental Theorem of Algebra. Gives explicit calculations of pi and e (the base of natural logarithms) from first principles. Gives explicit constructions of exponential, logarithmic and trig tables. The book is completely self-contained. The author welcomes comments on specific sections. The current version addresses Curriki review comments on section 1.2, dated 05/27/11.


  • Mathematics > General
  • Education > General

Education Levels:

  • Grade 11
  • Grade 12
  • Higher Education
  • Graduate
  • Undergraduate-Upper Division
  • Undergraduate-Lower Division


high school math Peano’s Axioms Natural Numbers Integers Fractions Reals Complex Numbers Proofs



Access Privileges:


License Deed:

Creative Commons Attribution Non-Commercial No Derivatives


This resource has not yet been aligned.
Curriki Rating
On a scale of 0 to 3
On a scale of 0 to 3

This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 3, as of 2011-05-27.

Component Ratings:

Technical Completeness: 3
Content Accuracy: 3
Appropriate Pedagogy: 2

Reviewer Comments:

This book represents a monumental effort by a mathematician to construct a self-contained textbook in real mathematics for an audience of non-mathematicians. The text is maintained as a digital file accessible to all on the Internet, a notably heroic and public-spirited achievement. The text starts with the Peano axioms and proceeds to construct all the number sets rigorously. All results are proved using the usual standards of mathematical proof; yet the text is intended for amateurs! This is quite an undertaking. Unfortunately the author frequently fails to explain himself clearly. Even professional mathematicians will have trouble following some of his arguments, and the readers are not professionals. (for instance, Section 1.2 - Positional Systems - is pretty opaque). The book would benefit from a good editor.

Not Rated Yet.

Non-profit Tax ID # 203478467