Explaining Stanford's Applied Math PhD Qualification Exam (PART TWO)

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Have you ever wondered what’s on the Applied Math PhD Qualification Exam At Stanford?
Well this video is going over that! This is Part Two of Two, covering the computational section. Please like and subscribe for more videos!
Twitter: @jacobrintamaki
Link To Part One: • Explaining Stanford's ...
Link To Stanford Math PhD Qualifying Exam Syllabus: mathematics.stanford.edu/acad...
References:
- Larsson and Thomée, Partial differential equations with numerical methods, Springer.
- E, Li, and Vanden-Eijnden, Applied stochastic analysis, AMS.
- Mallat, A wavelet tour of signal processing, Academic Press.
Time-Stamps:
0:00 Introduction
1:13 Finite Methods (Difference, Element, Volume)
1:24 Finite Difference Methods
1:41 Laplace and Poisson
2:45 Heat Equation and Wave Equation
3:42 Elliptic Equation In Divergent Form
4:50 Finite Element Methods
6:11 Finite Volume Methods
7:09 Scalar Conservation Laws
7:56 Entropy Solution
9:14 Conservative Schemes
10:11 Godunov Scheme
10:59 Gradient Flow/Descent Methods
11:26 Gradient Flow
12:37 GD, SD, MBGD
14:24 Connection With Optimization
15:00 Hamiltonian Flow
15:35 Basic Symplectic Operators
16:42 Monte Carlo Methods
17:17 Metropolis Algorithm
19:00 Variance Reduction
19:35 Importance Sampling
21:02 The Euler-Maruyama Method
22:10 The Milstein Method
22:29 The Feynman-KAC Method
24:09 Wavelets
25:07 Multiresolution Scheme
25:41 Conjugate Mirror Filters
26:19 Orthogonal Wavelets
27:37 References
#math #phd #stanford #education

Опубликовано:

15 июл 2024

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Комментарии : 15

@jacobrintamaki 13 дней назад

Time-Stamps: 0:00 Introduction 1:13 Finite Methods (Difference, Element, Volume) 1:24 Finite Difference Methods 1:41 Laplace and Poisson 2:45 Heat Equation and Wave Equation 3:42 Elliptic Equation In Divergent Form 4:50 Finite Element Methods 6:11 Finite Volume Methods 7:09 Scalar Conservation Laws 7:56 Entropy Solution 9:14 Conservative Schemes 10:11 Godunov Scheme 10:59 Gradient Flow/Descent Methods 11:26 Gradient Flow 12:37 GD, SD, MBGD 14:24 Connection With Optimization 15:00 Hamiltonian Flow 15:35 Basic Symplectic Operators 16:42 Monte Carlo Methods 17:17 Metropolis Algorithm 19:00 Variance Reduction 19:35 Importance Sampling 21:02 The Euler-Maruyama Method 22:10 The Milstein Method 22:29 The Feynman-KAC Method 24:09 Wavelets 25:07 Multiresolution Scheme 25:41 Conjugate Mirror Filters 26:19 Orthogonal Wavelets 27:37 References

@abjohnson117 5 дней назад

Great video! As an Applied Math PhD student I think you explained all the concepts very succinctly at a level that a lot of people with some math background can understand. I think it would also be interesting to go through some problems from exams to apply some of these topics you've just explained very well. Thanks!

@jacobrintamaki 5 дней назад

Thank you for the comment! There are past exams online; I think this weekend I will make a video walking through them.

@emir2750 7 дней назад

Thank you for your clear explanations! I am a second year maths undergraduate student and thinking about these make me feel two things: (1) I feel like I might not be able to qualify for all of these in the rest 2 years I have in UG, (2) I feel motivated and want to work for these things starting now. We will see I guess xD

@Mcflush1 13 дней назад

Me as a ML PhD watching and listening along for fun. Great job

@MelodySparkleroni490 13 дней назад

me as a n international relations student watching and i feel the same way, very fun to follow along (although idk whats going on)

@jacobrintamaki 13 дней назад

what specifically did you not understand? I was kind of bad in this video for background (since usually you need a physics or a math degree to work up to this), but I still don't like having my videos be unintelligible.

@MelodySparkleroni490 13 дней назад

@@jacobrintamaki No no, l think you did a great job talking through concepts and explaining everything, l just don't have the prerequisite knowledge to keep up. If anything that goes to show you're a good orator

@sandygrungerson1177 10 дней назад

ML/AI/statistics/"data science"/etc is *not* science, it's a technical dead-end to keep the 120IQs occupied while the 140+'s do physics/maths. am i saying this to be offensive? no, you should be aware of the narrative traps created to corral or "tranche" you, just like all standardized testing.

@jamesrothwell1738 8 дней назад

Watched this whole mf and I got expelled from my senior year of high school lol I thought AP Calc BC was hard but I guess I just dipped my toe in the world of numbers…. But now I’m a refrigeration tech so I have no reason to dive in. So thank you for showing me some of what I would’ve ended up learning

@jacobrintamaki 8 дней назад

Two things: 1. I genuinely appreciate your comment. Thank you. 2. “But now I’m a refrigeration tech so I have no reason to dive in.” Don’t limit yourself like that. You’re clearly driven and curious. Keep going.

@jamesrothwell1738 8 дней назад

Watched this whole mf and I got expels from my senior year of high school lol I thought AP Calc BC was hard but I guess I just dipped my toe in the world of numbers…. But now I’m a refrigeration tech so I have no reason to dive in. So thank you for showing me some of what I would’ve ended up learning

@psychii678 13 дней назад

honestly this doesnt seem too difficult to pass, ive used most of the topics covered in CFD in undergrad

@psychii678 13 дней назад

the analytical section would probably be harder for me i guess

@jacobrintamaki 13 дней назад

@@psychii678 that's fair. I would say that this qual is in the mathematics department rather than MechE/Aero/Astro/CS, and is done on paper, so I wouldn't expect it to be incredibly involved as compared to industry sims.