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MMM – Memos on Math/Music: This site lists memos on music and math by the site owner.
The music will be listed as mp3 files. Those files have a portrait of the composer as an eye-catcher:
e.g., J. S. Bach’s music on periodic instrumentation has the following portrait,
whereas modern interpretation of J.S. Bach’s music has the following portrait.
Many thanks from the site owner to MuseScore https://musescore.com/ without which he can never create mp3 files.
The math will be listed as PDF files. Some of them are typed using conventional word processors, and others are in LaTeX. Those files have “Girl with a Pearl Earring” by Johannes Vermeer as an eye-catcher: see below.
The site owner would like to express his appreciation to his cousin and the spouse (of the cousin) for suggesting that he should set up a site to list his “achievement” so far.
To view the content, click the URL line for each index below.
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Index for the work by J. S. Bach
https://wordpress.com/post/mathmusic52.com/2030
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Index for memo on mathematics
https://wordpress.com/post/mathmusic52.com/2038
Index for the work by D. Scarlatti
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RV 580: A. Vivaldi “Concerto in B minor”, L’estro armonico, Op.3, No. 10
Created using MuseScore.
Tuned with A = 415 Hz.
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BWV 1006: J. S. Bach “Violin Partita No. 3″ in E major”
Created using MuseScore.
Tuned with A = 415 Hz.
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BWV 1005: J. S. Bach “Violin sonata No. 3” in C major
Created using MuseScore.
Tuned with A = 415 Hz.
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Groups of order p^2
Let p be a prime number. Then it is known that every group of order p2 is abelian. The following is a proof which does not resort to contradiction.
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BWV 1004: J. S. Bach “Violin Partita No. 2″ in D minor”
Created using MuseScore.
Tuned with A = 415 Hz.
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BWV 1003: J. S. Bach “Violin sonata No. 2” in A minor
Created using MuseScore.
Tuned with A = 415 Hz.
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BWV 1002: J. S. Bach “Violin Partita No. 1” in B minor
Created using MuseScore.
Tuned with A = 415 Hz.
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BWV 1001: J. S. Bach “Violin Sonata No. 1” in G minor
Created using MuseScore.
Tuned with A = 415 Hz.
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On SL (2, Z) and SL (2, Z / NZ)
The classical groups are one of the major sources of interest in algebra and topology. When one replaces the field of real numbers by the ring of integers or the ring of integers mod N, they are still of interest in algebra.
Here we consider the relationship between SL (2, Z) and SL (2, Z / NZ).
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A detailed proof of the correspondence theorem
The correspondence theorem is one of the isomorphism theorems in algebra valid for both pairs (a group and its normal subgroup) and (a commutative ring and its ideal). Unfortunately, not many textbooks on algebra (or group theory or ring theory, for that matter) offer a detailed proof. Thus, this article may be of some use to students of mathematics.
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MMM 