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| − | <b>HH2 | + | <b>Gradient descent, how neural networks learn | Deep learning, chapter 2 |
| − | </b><br>BB2 | + | </b><br>Home page: http://www.3blue1brown.com/ Brought to you by you: http://3b1b.co/nn2-thanks And by Amplify Partners. For any early-stage ML startup founders, Amplify Partners would love to hear from you via 3blue1brown@amplifypartners.com To learn more, I highly recommend the book by Michael Nielsen http://neuralnetworksanddeeplearning.com/ The book walks through the code behind the example in these videos, which you can find here: http://github.com/mnielsen/neural-networks-and-deep-learning MNIST database: http://yann.lecun.com/exdb/mnist/ Also check out Chris Olah's blog: http://colah.github.io/ His post on Neural networks and topology is particular beautiful, but honestly all of the stuff there is great. And if you like that, you'll *love* the publications at distill: http://distill.pub/ |
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Revision as of 13:59, 14 September 2020
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Getting Started
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Math is the hidden secret to understanding the world | Roger Antonsen
Unlock the mysteries and inner workings of the world through one of the most imaginative art forms ever -- mathematics -- with Roger Antonsen, as he explains how a slight change in perspective can reveal patterns, numbers and formulas as the gateways to empathy and understanding. I am a logician, mathematician, computer scientist, author, public speaker, science communicator, and artist. You can find me at the University of Oslo, where I teach Logical Methods as an Associate Professor at the Department of Informatics in the research group Analytical Solutions and Reasoning (ASR), otherwise at UC Berkeley, California and ICERM at Brown University, where I am a Visiting Scholar. I am also engaged in various forms of science communication and outreach, which you may read about below. My academic interests are logical calculi, proof theory, mathematical logic, complexity theory, automata, combinatorics, philosophy of mathematics, visualizations, and mathematical art, but I am interested in most topics related to mathematics, computer science, art, and philosophy.
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Mathematics is the sense you never knew you had | Eddie Woo | TEDxSydney
In this illuminating talk, high school mathematics teacher and YouTube star Eddie Woo shares his passion for mathematics, declaring that "mathematics is a sense, just like sight and touch" and one we can all embrace. Using surprising examples of geometry, he encourages everyone to seek out the patterns around us, for "a whole new way to see the world". A public high school teacher for more than 10 years, Eddie Woo gained international attention when he posted videos of his classroom lessons online, to assist an ill student. His YouTube channel, WooTube, has more than 200,000 subscribers and over 13 million views. Eddie believe that mathematics can be embraced and even enjoyed by absolutely everybody. He was named Australia's Local Hero and was a Top 10 Finalist in the Global Teacher Prize for his love of teaching mathematics. This talk was given at a TEDx event using the TED conference format but independently organized by a local community. Learn more at https://www.ted.com/tedx
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How you can be good at math, and other surprising facts about learning | Jo Boaler | TEDxStanford
You have probably heard people say they are just bad at math, or perhaps you yourself feel like you are not “a math person.” Not so, says Stanford mathematics education professor Jo Boaler, who shares the brain research showing that with the right teaching and messages, we can all be good at math. Not only that, our brains operate differently when we believe in ourselves. Boaler gives hope to the the mathematically fearful or challenged, shows a pathway to success, and brings into question the very basics of how our teachers approach what should be a rewarding experience for all children and adults. Jo Boaler is a professor of mathematics education at Stanford and the co-founder of YouCubed, which provides resources and ideas to inspire and excite students about mathematics. She is also the author of the first massive open online course on mathematics teaching and learning. Her book Experiencing School Mathematics won the Outstanding Book of the Year award for education in Britain. A recipient of a National Science Foundation "early career award"' she was recently named by BBC as one of the eight educators changing the face of education. This talk was given at a TEDx event using the TED conference format but independently organized by a local community. Learn more at http://ted.com/tedx
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Love and Math an interview with Edward Frenkel
UC Professor of mathematics Edward Frenkel describes the relationship of Love and Mathematics, calls for a more modern way of teaching math in schools, and talks of the principles and people that have advanced our understanding of Math as a window onto reality. Edward Frenkel is a professor of mathematics at the University of California, Berkeley, which he joined in 1997 after being on the faculty at Harvard University. He is a member of the American Academy of Arts and Sciences, a Fellow of the American Mathematical Society, and the winner of the Hermann Weyl Prize in mathematical physics. Frenkel has authored three books and over eighty scholarly articles in academic journals, and he has lectured on his work around the world. His YouTube videos have garnered over 4 million views combined. Frenkel’s latest book Love and Math was a New York Times bestseller and has been named one of the Best Books of the year by both Amazon and iBooks. It is being translated into 16 languages. Frenkel has also co-produced, co-directed and played the lead in the film Rites of Love and Math (2010).
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Mathematics Ontology
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The Map of Mathematics
The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.
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Mind Map of Maths
LarryLemonMaths
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Mathematics for Machine Learning | M. Deisenroth, A Faisal, and C. Ong .. Companion webpage ...
Scalar, Vector, Matrix & Tensor
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How Data travels in Deep Neural Networks | Scalar vs Vector vs Matrix vs Tensor
This video titled "How Data travels in Deep Neural Networks | Scalar vs Vector vs Matrix vs Tensor" explains the role of Tensors in TensorFlow, What exactly are tensors as well as Characteristics of tensors. How Data travels in Deep Neural Networks? A comparison of Scalar vs Vector vs Matrix vs Tensor. SUPPORT ME on Patreon: http://www.patreon.com/theaiuniversity
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Why Linear Algebra ? Scalars, Vectors, Tensors
NPTEL-NOC IITM Lecture - 03
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Transformation properties of scalars, vectors and tensors
This video is on the basics of scalars, vectors and tensors and their transformation properties.
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Scalar, Vector, Matrix, Tensor, Matrix Transpose
Deep Shallownet Topics to cover based on: Deep Learning An MIT Press book Ian Goodfellow and Yoshua Bengio and Aaron Courville http://www.deeplearningbook.org/
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Scalars
a single number. For example weight, which is denoted by just one number.
Vectors
are an array of numbers. The numbers are arranged in order and we can identify each individual number by its index in that ordering. We can think of vectors as identifying points in space, with each element giving the coordinate along a different axis. In simple terms, a vector is an arrow representing a quantity that has both magnitude and direction wherein the length of the arrow represents the magnitude and the orientation tells you the direction. For example wind, which has a direction and magnitude.
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What is a vector? - David Huynh
Physicists, air traffic controllers, and video game creators all have at least one thing in common: vectors. But what exactly are they, and why do they matter? David Huynh explains how vectors are a prime example of the elegance, beauty, and fundamental usefulness of mathematics. Lesson by David Huynh, animation by Anton Trofimov.
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Matrices
A matrix is a 2D-array of numbers, so each element is identified by two indices instead of just one. If a real valued matrix A has a height of m and a width of n, then we say that A in Rm x n. We identify the elements of the matrix as A_(m,n) where m represents the row and n represents the column.
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The Applications of Matrices | What I wish my teachers told me way earlier
Zach Star This video goes over just a few applications of matrices that may give you some insight into how they can be used in the real world. Linear algebra was never explained well to me in school and I had very little motivation to learn matrices at the time so hopefully this helps you if you're in a similar situation. Also note there are so many applications there's just no way to fit them into one video but here you'll find some of my favorite instances of when they come up. Support the Channel: http://www.patreon.com/zachstar Google PageRank Algorithm: http://youtu.be/qxEkY8OScYY Mathematics Used to Solve Crime: http://youtu.be/-cXBgHgX5UE
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Multiplying Matrices - Example 1
Multiplying Matrices - Two examples of multiplying a matrix by another matrix are shown. For more free math videos, visit http://PatrickJMT.com
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How to organize, add and multiply matrices - Bill Shillito
When you're working on a problem with lots of numbers, as in economics, cryptography or 3D graphics, it helps to organize those numbers into a grid, or matrix. Bill Shillito shows us how to work with matrices, with tips for adding, subtracting and multiplying (but not dividing!). Lesson by Bill Shillito, animation by The Leading Sheep Studios.
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Tensors
In mathematics, a tensor is an algebraic object that describes a (multilinear) relationship between sets of algebraic objects related to a vector space. Objects that tensors may map between include vectors and scalars, and, recursively, even other tensors. Tensors can take several different forms – for example: scalars and vectors (which are the simplest tensors), dual vectors, multi-linear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system. Wikipedia
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What's a Tensor?
Dan Fleisch briefly explains some vector and tensor concepts from A Student's Guide to Vectors and Tensors
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Tensors Explained Intuitively: Covariant, Contravariant, Rank
Tensors of rank 1, 2, and 3 visualized with covariant and contravariant components. My Patreon page is at http://www.patreon.com/EugeneK
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3blue1brown
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But what is a Neural Network? | Deep learning, chapter 1
Home page: http://www.3blue1brown.com/ Brought to you by you: http://3b1b.co/nn1-thanks Additional funding provided by Amplify Partners Full playlist: http://3b1b.co/neural-networks Typo correction: At 14 minutes 45 seconds, the last index on the bias vector is n, when it's supposed to in fact be a k. Thanks for the sharp eyes that caught that! For those who want to learn more, I highly recommend the book by Michael Nielsen introducing neural networks and deep learning: http://goo.gl/Zmczdy There are two neat things about this book. First, it's available for free, so consider joining me in making a donation Nielsen's way if you get something out of it. And second, it's centered around walking through some code and data which you can download yourself, and which covers the same example that I introduce in this video. Yay for active learning! http://github.com/mnielsen/neural-networks-and-deep-learning I also highly recommend Chris Olah's blog: http://colah.github.io/ For more videos, Welch Labs also has some great series on machine learning: http://youtu.be/i8D90DkCLhI http://youtu.be/bxe2T-V8XRs For those of you looking to go *even* deeper, check out the text "Deep Learning" by Goodfellow, Bengio, and Courville. Also, the publication Distill is just utterly beautiful: http://distill.pub/ Lion photo by Kevin Pluck
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Explained
Siraj Raval
Gilbert Strang (MIT) - Linear Algebra
Fourier Transform (FT), Fourier Series, and Fourier Analysis
Joseph Fourier showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. Joseph was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and vibrations. The Fourier transform and Fourier's law of conduction are also named in his honor. Fourier is also generally credited with the discovery of the greenhouse effect.
- Fourier Transform (FT) decomposes a function of time (a signal) into its constituent frequencies. This is similar to the way a musical chord can be expressed in terms of the volumes and frequencies of its constituent notes. Fourier Transform | Wikipedia
- Fourier Series is a periodic function composed of harmonically related sinusoids, combined by a weighted summation. The discrete-time Fourier transform is an example of Fourier series. For functions on unbounded intervals, the analysis and synthesis analogies are Fourier Transform and inverse transform. Fourier Series | Wikipedia
- Fourier Analysis the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier Analysis | Wikipedia
Math Mistakes | Matt Parker
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The Greatest Maths Mistakes | Matt Parker | Talks at Google
When math goes wrong, things can get expensive. Or absolutely hilarious. For this talk we invited YouTube personality (Numberphile, standupmaths), math communicator, comedian, and one third of the Festival of the Spoken Nerd, Matt Parker, to share his favorite math mistakes from his new UK #1 bestseller, "Humble Pi - A Comedy of Maths Errors". Matt exposes errors on the Two Pound Coin, very specific rules for trains operating in Switzerland, and how simple unit conversion slip ups can cost billions of dollars. He also discusses the infamous 256th level of Pac-Man and answers audience questions about more hilarious mathematical failures. Get the book here: http://goo.gl/G4kqw6
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What Happens When Maths Goes Wrong? - with Matt Parker
Most of the time, the maths in our everyday lives works quietly behind the scenes, until someone forgets to carry a '1' and a bridge collapses or a plane drops out of the sky.
Subscribe for regular science videos: http://bit.ly/RiSubscRibe Matt's book "Humble Pi" available now: https://geni.us/9nPhpn3 Matt Parker is a stand-up comedian and mathematician. He appears regularly on TV and online: as well as being a presenter on the Discovery Channel. His YouTube videos have been viewed over 37 million times. Previously a high-school mathematics teacher, Matt visits schools to talk to students about maths as part of Think Maths and he is involved in the Maths Inspiration shows. In his remaining free time, Matt wrote the books Things To Make and Do in the Fourth Dimension and Humble Pi: A Comedy of Maths Errors. He is also the Public Engagement in Mathematics Fellow at Queen Mary University of London. This talk was filmed in the Ri on 1 March 2019.
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