Lesson 1.2 : Maps
Lesson 1.3 [Video] : Commute, Identity Morphism
Lesson 1.4 [Video] : Identity Law (Set Endomorphism), Associativity Law
Lesson 1.5 : [Video] Category of Sets (Concrete Category)
Number of Set Mappings:
Music and math: The genius of Beethoven – Natalya St. Clair:
Music = Math
This “Butterfly Lovers Violin Concerto” (梁山伯与祝英台: 梁祝 小提琴协奏曲 ) composed 50 years ago by 2 Chinese music students, now played so lovely by a Japanese lady violinist: 诹访内晶子 (Akiko Suwanai), who is the current user of the violin ”Dolphin”, one of the top 3 violins in the world made by Antonio Stradivarius
Only in the kingdom of Music (the other one is Mathematics) where human political hatred does not exist between countries due to past wars: Japan and China, Germany and the Allied Nations, … Just only yesterday China President Xi and Japan PM Abe both showed awkward “poker face” hand-shake at the APEC Beijing meeting; contrast to the 20th century’s greatest mathematician David Hilbert from Nazi Germany was welcome in America to chair the inauguration of the International Congress of Mathematics.
If more students love Math and Music, the world of tomorrow will be more peaceful.
Watch 諏訪內晶子 -《梁祝小提琴協奏曲》 Butterfly Lovers Violin Concerto. Notice her 1714 ‘magical’ violin is the treasure gift “Dolphin Stradivarius”, once owned and played by the virtuoso Jascha Heifetz (1901–1987).
The legendary love story is the Chinese version of “Romeo & Juliet“:
If you want your kids to grow up with Math talent, start young in Music, be it playing a simple drum or flute, later then at age 4 or 5 progressing to piano or violin, along the way pick up musical theory…
Notice that great mathematicians (or Physicists the close cousins of Math) are often music talented, but the converse not true! Einstein performed violin with an orchestra formed by a group of Nobel Prize Physicists; never heard Mozart or Langlang (朗朗) or any great musicians proved any Math Conjectures.
Music trains the abstract thinking mind, good for mastering the most abstract subjects like Abstract Algebra or ‘Abstract’ Physics (Quantum Physics).
Prof Alice Chang Sun-Yung (University of Princeton, Geometric Analysis)
“Math is a language like music. To learn it systematically, it is necessary to master small pieces & gradually add another piece & then another… In a sense, Math is like the classical Chinese language – very polished, very elegant. Sitting in a good math lecture is like sitting in a good opera. Everything comes together.”