Mathematical proofs are used to prove the correctness of formulas and assumed facts. Several basic procedures and ways of verifying mathematical correctness are in use, all of which follow a fixed scheme.

For the proof of the irrationality of the square root of 2 different proofs exist. This article explains the indirect proof variant in detail and introduces one of the possible short spellings in mathematical notation. Exercises with solutions consolidate what has been learned. 13 pages::

A4 • A4 duplex • US-Letter • US-Letter duplex

Computer algebra systems provide valuable services in checking calculated solutions. However, many programs have high resource requirements. The free, Python-based computer algebra system Sympy (WP article) runs on both new and old systems.

Learn more about the possibilities of modernizing an old computer with specialized lightweight free distributions: “Introduction to Free Software and Operating Systems”.

An overview article introducing widely used free typesetting systems and basic document types, with extensive link lists: „Free Typesetting Software for the Professional Document Preparation“, with a mini-introduction to basic technical (design) principles, including style sheets and style files.

Free software proves to be extremely flexible in importing and exporting mathematical typesetting elements and other file formats, word processors offer their own formula editors as well as the possibility to import math formulas in *the* standard format, in TeX (article sections):
“Classical Typesetting in Highest Quality for Writers and Scientists: TeX, LaTeX, LyX” •
“Free Text Editors and Recommended Reading on LaTeX, KOMA-Script & Co.”.

Miscellaneous

School mathematics: Detailed solutions to the first 27 text problems of “A first book in Algebra”, author Wallace C. Boyden, added, a textbook for beginners in algebra: Text problems with solutions, 10 pages (PDF, A4 format).

September 17, 2021

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