Ethan Zell
Ethan Zell
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Math PhD Students Hunt for Errors in False Proofs. Try it Yourself!
We test Michigan PhD students on "false proofs" to see if they can spot the errors. Try them yourself and then watch them take a crack at each!
*Small hints were allowed.
*Annaliese wanted to note that she is not ~technically~ in the PhD program; she is doing her Masters.
Переглядів: 1 050

Відео

Calculus 1: Antiderivatives and the Indefinite Integral
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Our live video lecture on 4/16/2020 for Math 115 at the University of Michigan.
Calculus 1: Fundamental Theorem of Calculus
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Our live video lecture from 4/13/2020 for MATH 115 at the University of Michigan.
Calculus 1: Defining the Integral
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Our live video lecture from 4/9/2020 for MATH 115 at the University of Michigan.
Calculus 1: Properties of the Definite Integral
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(Not live) video lecture for MATH 115 at the University of Michigan.
Calculus 1: Motivation for the Integral
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Our live video lecture from 4/8/2020 for MATH 115 at the University of Michigan.
Calculus 1: Related Rates Examples
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Our live video lecture from 3/26/2020 for MATH 115 at the University of Michigan.
Calculus 1: Applications to Marginality
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Our live video lecture from 3/25/2020 for MATH 115 at the University of Michigan.
Calculus 1: Optimization and Modeling
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Our live video lecture from 3/18/2020 for MATH 115 at the University of Michigan.
Calculus 1: Optimization and Mean Value Theorem Review
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Our live video lecture from 3/16/2020 for MATH 115 at the University of Michigan.
Interviewing International Math PhD Students Part 1
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International math PhD students at the University of Michigan answer questions about their new lives in the US!
Interviewing International Math PhD Students Part 2
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International math PhD students at the University of Michigan answer questions about their new lives in the US!
Limit of Lp Norms of a Function
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Here, we tackle a suggested problem which deals with the limit of Lp norms of a measurable, complex-valued function, f. My intended audience is advanced undergraduates or incoming graduate students with some analysis experience. Made by Ethan Zell With thanks to Ben Hayes and Francesco Di Plinio Book Reference: Real and Complex Analysis by Rudin Note: I'm making these videos to make studying fo...
What Happens When a Function is Injective and Entire?
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An injective (one-to-one) and entire (analytic everywhere) function must be linear. Here, we show why. My intended audience is advanced undergraduates or incoming graduate students with some analysis experience. Made by Ethan Zell With thanks to Ben Hayes Book Reference: Complex Analysis by Ahlfors Note: I'm making these videos to make studying for my qualifying exams more enjoyable. Please let...
Convergence Criterion
Переглядів 5075 років тому
We work through a criterion for convergence which is useful in analysis (and even beyond). My intended audience is advanced undergraduates or incoming graduate students with some analysis experience. Made by Ethan Zell With thanks to Ben Hayes and Francesco Di Plinio Book Reference: Real and Complex Analysis by Rudin Note: I'm making these videos to make studying for my qualifying exams more en...
Complex Analysis: Tricky Sum Problem
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Complex Analysis: Tricky Sum Problem
A Necessary and Sufficient Condition for Lp and Lq Inclusion
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A Necessary and Sufficient Condition for Lp and Lq Inclusion
A Weird Lebesgue Integral
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A Weird Lebesgue Integral
Tricky Maximum Modulus Application
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Tricky Maximum Modulus Application
Schwarz Lemma Application
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Schwarz Lemma Application
Conformal Maps: Two Quick Examples
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Conformal Maps: Two Quick Examples
Rouches Theorem Example
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Rouches Theorem Example
Complex Analysis: Uniform Convergence on Compact Sets
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Complex Analysis: Uniform Convergence on Compact Sets
Complex Polynomials: Example Using the Fundamental Theorem of Algebra
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Complex Polynomials: Example Using the Fundamental Theorem of Algebra

КОМЕНТАРІ

  • @zeferreira8805
    @zeferreira8805 Рік тому

    4:22 exactly what I was looking for... Thank you! Greetings from Portugal 🙂

  • @ferolimen
    @ferolimen Рік тому

    I didn't know your UA-cam channel, I found this video very enjoyable :), thanks! And by the way, I found also this exercise kind of difficult, one might think that the solution is easier.

  • @n4d3m4gn3t
    @n4d3m4gn3t Рік тому

    Fantastic video.

  • @jiyeonlee5452
    @jiyeonlee5452 2 роки тому

    Thanks so much!

  • @ummwho8279
    @ummwho8279 2 роки тому

    Ethan, I may be wrong but I noticed at 7:12 I don't think you took the p-th root of the second term, ie the one that becomes the measure. Or am I wrong?

    • @ethanzell4073
      @ethanzell4073 2 роки тому

      I think it's ok. The Holder conjugate of q/p is q/(q-p). You can see that the norm for the function that is identically 1 is the q/(q-p) norm and so in the following line it has exponent (q-p)/q on the outside.

  • @markmarkus808
    @markmarkus808 2 роки тому

    Very helpful. Thx

  • @pablomerehidalgo
    @pablomerehidalgo 3 роки тому

    It's amazing that I found one of my former classmates in this vídeo. Congratulations Andrés! You made it!

  • @carlosgruss7289
    @carlosgruss7289 3 роки тому

    Great video, thanks :)

  • @mohammadabdulla8601
    @mohammadabdulla8601 3 роки тому

    I really wish there were more of these videos. Great work.

  • @d.m.2343
    @d.m.2343 3 роки тому

    math4ai3 check

  • @user-qy3vs7px4y
    @user-qy3vs7px4y 3 роки тому

    Thank you Dr . Can I chat with you

  • @salonimandloi812
    @salonimandloi812 3 роки тому

    Very good explanation 👍😊 thank you sir...

  • @khaledqaraman
    @khaledqaraman 3 роки тому

    So helpful... Thanks

  • @douglasstrother6584
    @douglasstrother6584 3 роки тому

    The Smith Chart used in RF/Microwave Engineering is an example of a Möbius Transformation. arxiv.org/pdf/1201.4068.pdf

  • @user-zh1uz3nq7r
    @user-zh1uz3nq7r 4 роки тому

    From iraq to you Thanks for that

  • @BehnamEsmayli
    @BehnamEsmayli 4 роки тому

    Q1)For positive real numbers, square root is ALWAYS a positive quantity. So, root of 4 is +2 and never -2. The confusion comes from x^2=4 ==> x=+/-2 and the incorrect/lazy way some instructors do it by writing x^2=4 ==> x= oot{4} ==> x= +/-2 which should instead be x=+/- oot{4}. Q2) OMG! Why isn't everyone shouting out the simple refutation that "what is $x$ many times if $x$ is not an integer?!" Because something is written down on a page does not mean it is valid in to begin with. Since we intend to take d/dx we must consider x being non-integer.

  • @seungaaaaaaaaa
    @seungaaaaaaaaa 4 роки тому

    Thank you Ethan!!

  • @esmamaysan2909
    @esmamaysan2909 4 роки тому

    Thank you for the vidéo just continue and go ahead

  • @MathGirlEducation
    @MathGirlEducation 4 роки тому

    Love this! I think the input should be -1/3 instead of 1/3? Either way, it doesn't change the bound since we take the modulus. Edit: Actually, I realized that I was using a different fractional transform, (i-z)/(i+z), which is a negative version of the Cayley transform.

    • @ethanzell4073
      @ethanzell4073 4 роки тому

      Glad you liked it! I wish I could make more of these, but graduate school is now in full swing.

  • @ethanzell4073
    @ethanzell4073 5 років тому

    Edit: In the statement of Holder's inequality, I do need that f, g are measurable even though that is (kind of) implied by the conclusion.

  • @eetuhalme8207
    @eetuhalme8207 5 років тому

    Great work! I'm learning real analysis myself and it's nice to see well presented problems on it in video form. Subscribed for more and have good luck studying for prelims :)

    • @ethanzell4073
      @ethanzell4073 5 років тому

      Thanks! Lmk if there are any analysis problems you'd like to see :)

    • @eetuhalme8207
      @eetuhalme8207 5 років тому

      @@ethanzell4073 I would be intrested on seeing why ||f||p goes to ||f||∞ when p goes to ∞. For example when f is complex measurable on X and μ is positive Borel measure on X. I think you have to assume that ||f||r < ∞ for some r ≥ 0. And thanks alot :)

    • @ethanzell4073
      @ethanzell4073 5 років тому

      @Eetu Halme, sounds fun! I'll take a look at that.