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Document integrity: “Practical Application of Cryptographic Checksums”, with an introduction to applied cryptography.
Referenced in: “Künstliche Intelligenz - Ethik und Recht”, Hoeren/Pinelli (Hrsg.), 2022, footnote 49 on page 11, Verlag C.H. Beck, (book review by Roland Kemper) • “M2M-Geschäfte, Vertragsschluss und vertragliche Struk­tu­ren im automatisierten E-Procurement”, Dajana Mohr, Tectum Verlag 2022, footnote 283 on page 72, PDF sample  •  German legal magazine JuristenZeitung, 18.09.2020, “Daten im Rechtsverkehr – Überlegungen für ein allgemeines Datenvertragsrecht” (footnote 14, page 881), Thomas Hoeren and Stefean Pinelli, Verlag Mohr Siebeck  •  Wikipedia article “Checksum” (EN) • Wikipedia article “Prüfsumme”  • 
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Scientific typesetting: “Free Typesetting Software for the Professional Document Preparation”
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Introduction to the indirect proof: “Proof of the Irrationality of the Square Root of 2”
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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. 12 pages::

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

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, in English)..

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