Introduction to product-sum identities -- Number Theory 31

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  • Опубліковано 19 січ 2025

КОМЕНТАРІ • 14

  • @r.maelstrom4810
    @r.maelstrom4810 3 роки тому +4

    This level of sophistication was already developed, although without some of the formalizations here seen, by Euler in the XVIII century. Quite an achievement!

  • @karolakkolo123
    @karolakkolo123 3 роки тому +6

    Is our friend Good Place to Stop sick today?

  • @qzwxecrvtbynumi256
    @qzwxecrvtbynumi256 3 роки тому +9

    Does anyone know where I can find the syllabus for this course?

    • @captainsnake8515
      @captainsnake8515 3 роки тому

      Closest thing I could find was the course description on Randolph college’s math courses page: www.randolphcollege.edu/mathematics/curriculum/

  • @MyOneFiftiethOfADollar
    @MyOneFiftiethOfADollar 3 роки тому +1

    Your frequently donned tee shirt identity feels like product sum identity: (1+2+3+ ... + n)^2 = 1^3 + 2^3 + 3^3 + ... + n^3)

  • @darkmask4767
    @darkmask4767 3 роки тому +5

    28:06 good place to stop

  • @CglravgHRjsksgS
    @CglravgHRjsksgS 3 роки тому +1

    Can we have the products that turn into sums via the logarithm function. I saw it on one of your videos

  • @Blitnock
    @Blitnock 3 роки тому +6

    You know, Michael, you would have really made this lecture live more if you would have credited the people who found the q-binomial theorem. Andrews, Askey, and Roy (in "Special Functions") credit it to Cauchy (1843), Gauss (1866), and Heine (1847). Those are all names that your students should know and also indicates the significance of the theorem that three mathematicians such as these would discover it independently.
    This is meant as constructive criticism: you should include proper credits and a bit of history for what you teach. Students need to know that theorems don't come from nowhere; they are the work of human beings!

  • @SubtleForces
    @SubtleForces 2 роки тому

    The first theorem proof: I found it easy to follow, but I had 0 intuition about it. It is one of those things that seem very easy when you see it, but how did they come up with the idea in the first place? It makes me wonder how I could have had no clue whatsoever about how to approach it :-(

  • @angelwaters6474
    @angelwaters6474 3 роки тому

    Hi, are you going to go over norm maps in quadratic fields?

  • @rafael7696
    @rafael7696 3 роки тому

    Great video. But a miss olimpiad problems. Great work anyway.

  • @t7H2si0vß2
    @t7H2si0vß2 3 роки тому +3

    Rip dislike button.... not that I was going to press it anyways 😂