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Aleph 0
Canada
Приєднався 5 кві 2018
Thanks for stopping by! Aleph 0 is a channel devoted to bringing pure mathematics into the hands of learners. If you'd like to sign up for the Aleph 0 newsletter to receive weekly learning resources in math, see the signup link below:
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Twitter: 00aleph00
Email Newsletter Signup: docs.google.com/forms/d/1vbFngpXPJ80iCn90Z5ihlOsocX8qGI8DlyWxvUPj6bM/edit
Twitter: 00aleph00
How to learn machine learning as a complete beginner: a self-study guide
A step-by-step roadmap of how to learn machine learning as a beginner.
If you'd like to sign up for the Aleph 0 math / machine learning newsletter, fill out the form here: forms.gle/Rt1f5StAj3yZtakE6
------------
BOOK RECOMMENDATIONS
Grokking Deep Learning by Andrew Trask
The 100-page Machine Learning Handbook by Andriy Burkov
Deep Learning with PyTorch by Laura Mitchell, Sri Yogesh K, and Vishnu Subramanian
1a. FEED-FORWARD NEURAL NETWORKS
Chapter 1 of Book by Michael Nielsen: neuralnetworksanddeeplearning.com/chap1.html
Grokking Deep Learning (Chapters 2,3)
The 100-page Machine Learning Handbook (Chapter 3.1, 3.2, Chapter 6)
1b. GRADIENT DESCENT / BACKPROPAGATION
Grokking Deep Learning (Chapters 4,6)
Chapter 2 of Book by Michael Nielsen:
neuralnetworksanddeeplearning.com/chap2.html
2. CONVOLUTIONAL NEURAL NETWORKS
Two videos by Computerphile:
Blurs and filters: ua-cam.com/video/C_zFhWdM4ic/v-deo.html&ab_channel=Computerphile
Edge detection: ua-cam.com/video/uihBwtPIBxM/v-deo.html&ab_channel=Computerphile
Intro to CNNs: ua-cam.com/video/py5byOOHZM8/v-deo.html&ab_channel=Computerphile
Deep Learning with PyTorch (Chapter 5)
3. RECURRENT NEURAL NETWORKS
Grokking Deep Learning (Chapters 11 and 12)
Video by Serrano Academy: ua-cam.com/video/UNmqTiOnRfg/v-deo.html&ab_channel=Serrano.Academy
Stat Quest: ua-cam.com/video/AsNTP8Kwu80/v-deo.html&ab_channel=StatQuestwithJoshStarmer
4. AUTOENCODERS
Deep Learning with Pytorch (Chapter 6).
Video playlist by Digital Sreeni:
ua-cam.com/play/PLZsOBAyNTZwb-uK_a6ywrU3t0hy80G5QP.html
5. REINFORCEMENT LEARNING
Deep Learning with Pytorch (Chapter 9).
6. ATTENTION
Blog post by Jay Alammar: jalammar.github.io/illustrated-transformer/
Lecture by Stanford Online: ua-cam.com/video/XfpMkf4rD6E/v-deo.html&ab_channel=StanfordOnline
Intro: (0:00)
Three book recommendations: (0:53)
Feed-Forward Neural Networks: (2:06)
Convolutional Neural Networks: (4:12)
Recurrent Neural Networks: (5:21)
Autoencoders: (6:36)
Reinforcement Learning: (7:20)
Attention: (7:54)
General Tips: (9:06)
If you'd like to sign up for the Aleph 0 math / machine learning newsletter, fill out the form here: forms.gle/Rt1f5StAj3yZtakE6
------------
BOOK RECOMMENDATIONS
Grokking Deep Learning by Andrew Trask
The 100-page Machine Learning Handbook by Andriy Burkov
Deep Learning with PyTorch by Laura Mitchell, Sri Yogesh K, and Vishnu Subramanian
1a. FEED-FORWARD NEURAL NETWORKS
Chapter 1 of Book by Michael Nielsen: neuralnetworksanddeeplearning.com/chap1.html
Grokking Deep Learning (Chapters 2,3)
The 100-page Machine Learning Handbook (Chapter 3.1, 3.2, Chapter 6)
1b. GRADIENT DESCENT / BACKPROPAGATION
Grokking Deep Learning (Chapters 4,6)
Chapter 2 of Book by Michael Nielsen:
neuralnetworksanddeeplearning.com/chap2.html
2. CONVOLUTIONAL NEURAL NETWORKS
Two videos by Computerphile:
Blurs and filters: ua-cam.com/video/C_zFhWdM4ic/v-deo.html&ab_channel=Computerphile
Edge detection: ua-cam.com/video/uihBwtPIBxM/v-deo.html&ab_channel=Computerphile
Intro to CNNs: ua-cam.com/video/py5byOOHZM8/v-deo.html&ab_channel=Computerphile
Deep Learning with PyTorch (Chapter 5)
3. RECURRENT NEURAL NETWORKS
Grokking Deep Learning (Chapters 11 and 12)
Video by Serrano Academy: ua-cam.com/video/UNmqTiOnRfg/v-deo.html&ab_channel=Serrano.Academy
Stat Quest: ua-cam.com/video/AsNTP8Kwu80/v-deo.html&ab_channel=StatQuestwithJoshStarmer
4. AUTOENCODERS
Deep Learning with Pytorch (Chapter 6).
Video playlist by Digital Sreeni:
ua-cam.com/play/PLZsOBAyNTZwb-uK_a6ywrU3t0hy80G5QP.html
5. REINFORCEMENT LEARNING
Deep Learning with Pytorch (Chapter 9).
6. ATTENTION
Blog post by Jay Alammar: jalammar.github.io/illustrated-transformer/
Lecture by Stanford Online: ua-cam.com/video/XfpMkf4rD6E/v-deo.html&ab_channel=StanfordOnline
Intro: (0:00)
Three book recommendations: (0:53)
Feed-Forward Neural Networks: (2:06)
Convolutional Neural Networks: (4:12)
Recurrent Neural Networks: (5:21)
Autoencoders: (6:36)
Reinforcement Learning: (7:20)
Attention: (7:54)
General Tips: (9:06)
Переглядів: 49 947
Відео
The shocking connection between complex numbers and geometry.
Переглядів 90 тис.2 місяці тому
A peek into the world of Riemann surfaces, and how complex analysis is algebra in disguise. Secure your privacy with Surfshark! Enter coupon code ALEPH for an extra 3 months free at surfshark.deals/ALEPH. Help fund future projects: www.patreon.com/aleph0 An equally valuable form of support is to simply share the videos. SOURCES and REFERENCES for Further Reading: This video is a quick-and-dirty...
What is a hole?
Переглядів 81 тис.5 місяців тому
An introduction to the fundamental group, a key concept in algebraic topology. This video is sponsored by Brilliant. To try it out for free for 30 days, head to brilliant.org/Aleph0/. The first 200 people to sign up will get 20% off a yearly subscription. Help fund future projects: www.patreon.com/aleph0. An equally valuable form of support is to simply share the videos. A HUGE thank you to Wal...
What is algebraic geometry?
Переглядів 205 тис.8 місяців тому
Algebraic geometry is often presented as the study of zeroes of polynomial equations. But it's really about something much deeper: the duality between abstract algebra and geometry. Help fund future projects here: www.patreon.com/aleph0 An equally valuable form of support is to simply share the videos. A HUGE HUGE thank you to Faisal Al-Faisal for working with me on the script and storyboard fo...
The unsolvable problem that launched a revolution in set theory
Переглядів 158 тис.Рік тому
An introduction to the Continuum Hypothesis - a problem in set theory that cannot be proved correct or incorrect. Help fund future projects: www.patreon.com/aleph0 An equally valuable form of support is to simply share the videos. A HUGE thank you to Luciano Salvetti, a graduate student at the University of Toronto in set theory, for helping me make this video! MUSIC CREDITS: The song is “Takin...
The bridge between number theory and complex analysis
Переглядів 197 тис.2 роки тому
How the discoveries of Ramanujan in 1916, combined with the insights of Eichler and Shimura in the 50's, led to the proof of Fermat's Last Theorem. Help fund future projects: www.patreon.com/aleph0 An equally valuable form of support is to simply share the videos. SOURCES and REFERENCES for Further Reading! This video is a quick-and-dirty introduction to modular forms and elliptic curves. But a...
Algebraic number theory - an illustrated guide | Is 5 a prime number?
Переглядів 162 тис.2 роки тому
This video is an introduction to Algebraic Number Theory, and a subfield of it called Iwasawa Theory. It describes how prime numbers factor in infinite towers of number rings. Help fund future projects: www.patreon.com/aleph0 An equally valuable form of support is to simply share the videos. Minor corrections: at 4:58: I should have said "closed under addition and *subtraction*" instead of "clo...
How to self study pure math - a step-by-step guide
Переглядів 1,8 млн2 роки тому
This video has a list of books, videos, and exercises that goes through the undergrad pure mathematics curriculum from start to finish. REAL ANALYSIS Book: “Understanding Analysis” by Stephen Abbott. Videos: Lectures by Francis Su (ua-cam.com/play/PL0E754696F72137EC.html) LINEAR ALGEBRA Book: “Linear Algebra Done Right” by Sheldon Axler Videos: Sheldon Axler’s Playlist (ua-cam.com/play/PLGAnmvB...
What is the square root of two? | The Fundamental Theorem of Galois Theory
Переглядів 258 тис.2 роки тому
This video is an introduction to Galois Theory, which spells out a beautiful correspondence between fields and their symmetry groups. SOURCES and REFERENCES for Further Reading! This video is a quick-and-dirty introduction to Galois theory. But as with any quick introduction, there are details that I gloss over for the sake of brevity. To learn these details rigorously, I've listed a few resour...
The Insolvability of the Quintic
Переглядів 178 тис.3 роки тому
This video is an introduction to Galois Theory, which spells out a beautiful connection between fields and their Galois Groups. Using this, we'll prove that the quintic has no general formula in radicals. SOURCES and REFERENCES for further reading! As with any quick introduction, there are details that I gloss over for the sake of brevity. If you’d like to learn these details more rigorously, I...
The derivative isn't what you think it is.
Переглядів 692 тис.3 роки тому
The derivative's true nature lies in its connection with topology. In this video, we'll explore what this connection is through two fields of algebraic topology: homology and cohomology. SOURCES and REFERENCES for Further Reading! In this video, I give a quick-and-dirty introduction to differential forms and cohomology. But as with any quick introduction, there are details that I gloss over for...
Elliptic Curves and Modular Forms | The Proof of Fermat’s Last Theorem
Переглядів 262 тис.3 роки тому
Elliptic curves, modular forms, and the Taniyama-Shimura Conjecture: the three ingredients to Andrew Wiles’ proof of Fermat’s Last Theorem. This is by far the hardest video I've ever had to make: both in terms of learning the content and explaining it. So there a few questions I don't have answers for. If you're up for it, feel free to answer these as a UA-cam comment or on Twitter (@00aleph00)...
Poincare Conjecture and Ricci Flow | A Million Dollar Problem in Topology
Переглядів 322 тис.4 роки тому
How do we use Riemannian Geometry and Surgery Theory to crack a million-dollar problem in topology? Ricci flow, that's how. In this video, we tackle the only Millennium Prize Problem that's been solved so far, and find the deep mathematics uncovered in the process. Official Problem Statement: www.claymath.org/millennium-problems/poincaré-conjecture Follow me! Twitter: 00aleph00 Inst...
Navier Stokes Equation | A Million-Dollar Question in Fluid Mechanics
Переглядів 450 тис.4 роки тому
The Navier-Stokes Equations describe everything that flows in the universe. If you can prove that they have smooth solutions, you'll win a million dollars. Official Problem Statement: www.claymath.org/millennium-problems/navier–stokes-equation A very informative talk by Dr. Edriss Titi: ua-cam.com/video/VH4oawCiHPU/v-deo.html Follow me! Twitter: 00aleph00 Instagram: 00...
Stokes' Theorem on Manifolds
Переглядів 173 тис.4 роки тому
Stokes' Theorem is the crown jewel of differential geometry. It extends the fundamental theorem of Calculus to manifolds in n-dimensional space. This video aims to give an intuitive discussion of Stokes' Theorem, without the complicated equations and formalism. For those interested in the details, here's a thorough treatment of the topic: arxiv.org/abs/1604.07862 (Be warned, this rabbit hole go...
I didn't understood a sh** about the firt page of the first book. Not my level at all 😂
Now I have something to do for the next 4 to 6 years 😂
I LOVE YOU LUCIANO
Nice animation
This is an excellent video, with wonderful graphics that really make the ideas behind Galois theory come to life. There's only one thing that threw me. At around 7:42, you state that Aut F is "a little too big", so we restrict our attention to Aut F/Q. I spent a good hour trying to figure out what could possibly be in Aut F but not in Aut F/Q. At the end of it, I proved to myself that any field automorphism of any field containing Q must fix Q, so it ended up being an hour well spent. It doesn't detract from the main point you're making there, which is essentially, "this is the notation we use", and when we have Q<K<F, it's nice to have consistent notation for comparing Aut F/Q, Aut F/K, and Aut K/Q. Making the subfield Q explicit is a little bit like writing integers as n/1, just to make them look like the other rationals, perhaps for calculating mediants or something.
Oh no, the Clay Institute took him away! (Abrupt video ending)
you forgot step 1. Be a genius.
I have one question: In the last example, why are the even powers of zeta not conjugates over Q with zeta?
I wouldnt recommend this linear algebra book. Determinants are a major part in almost every field connected to linear algebra, for example functional analysis, cryptography, numerical mathemathics, algebraic number theory, linear differential equations in multiple variables, and the list keeps going. Learning them early on and getting a feeling for it is in my opinion quite important. And sure, you can teach linear algebra without them, but so you can do a lot of things. But these tools were developed for a very specific reason, so dont take them away..
Thank you. That was excellent
Thank you!
I'm currently in my second year of marketing and realized i enjoy solving math problems more than studying marketing ( i love marketing but the thing is that when studying math, i lose track of time. Whereas when studying marketing which i love doing, i just find it hard to lose track of time like when studying math). Currently thinking of majoring in math after graduating marketing but i don't know if it's worth it or not 😭
2:18
IMHO it makes no sense to wait so much to learn about Algebraic Topology, it's a fairly easy subject and already viable after Point Set Topology and Group Theory/Abstract Algebra, but it paves the way to readily understand several applications in both Complex Analysis and Differential Geometry!
complete beginner?
skill issue
No sé absolutamente nada sobre matemáticas, (solo sumar, dividir y multiplicar) de ahí más nada, ya que perdí 4to y 5to año por la cuarentena, de igual manera nunca es tarde
Thank you for immersing such a thoughtful insight into me
Huh?
What a wonderful way of teaching. Bravo!
Man, your video is fascinating. What an age to live in
I think this is one of the videos that got me to switch from physics to maths. Thank you!
Good video bhai. You have good boxing technique here but remember to return your hand to your face so you don't get countered! I wish you the best of luck in your upcoming fight!!
Sir please provide lectures on sieve theory
Well, I don't know why I have studied some commutative algebra though, but I really can't understand some popularizations like this or even some books, which really phrases what the algebraic geometry is
thanks for the nice video and the literature list. perfect 🙂
Thank youuu. I am interested in maths but I have a very different life so I can't just go and study it. But self learning guide is what I needed so far because that's what I was doing. Found some books and was checking youtube to learn it but this video will be so helpful. Thank you so much❤❤
I got my degree in pure math next year, but i just found this video :(
So it’s a neat twist on a binary system ? Just 1,0
Great video explained very well ❤
neat to see Dhruv's name again in an unexpected place
Man i love doing pure meth.
God the first “equally” spaced circle of 5ths that’s used a couple times drove me nuts 😂
Hands down the best introduction to algebraic geometry and rings I’ve seen on UA-cam! 👏🏼
What car do you have? It looks really sleek and clean. If it’s a Tesla could you specify which model? Thanks.
Group theory is already Greek to me.
Coming back to this video when I understand it properly
Idiotic garbage content. Adblocker totally justified.
Check out the math sorcerer
Great video
There is an absolute truth in math, but we haven't reached it yet
难怪看代数几何里面都是抽象的证明, 人都看懵逼了, 感谢这个视频. 后面介绍的数都翻烂了, 厉害❤
How in the name of fuck does GRH tell you about class numbers
Ah I see, it bounds the number of ideals you have to check
You saved me 10 days of reading through proofs and many books to get this intuitivly 🤣 For some reasons books ussually skip this intuitive part and its most important part for some of us :(
loved it!
The Axler book is quite Bourbakian. If teachers run around shouting `down with determinants' one ends up with students that can neither do calculations nor solve problems.
i came here because another video said that the quintic hypersurface was cause for why there are additional dimensions, that somehow a 3 dimensional shape proved there were 5 dimensions instead of 4, and i get here and all i see is ramblings of methed out mathematicians... does any of this actually correspond to the natural world? like does any of this actually exist somewhere outside your mind?
this is why handing out hard drugs in a math class is a bad idea...
Yes Humans… this is a beautiful argument. Ceasefire NOW… Everything is Connected 🎈🪬🇺🇸🛸🐇🛰️🪤🛼🧣🚀
Real Analysis in 2nd year and Differential Geometry in 3rd year? I wonder what university you went to 😂 great video though, I'll be especially diving into Complex Analysis using your resources, thank you!