Basic Mathematics by Shankar_1 Differential Calculus

Coronvirus is spreading all over the world now. It's a good time to go through the basic mathmatics by Shankar. There are 10 sessions in his book so I plan to document my learning progress in 10 blogs too. This is the first one - Differential Calculus. The first principle Chain rule derivativeproblem 1.2.2 D(1/x) … Continue reading Basic Mathematics by Shankar_1 Differential Calculus

Continue Shankar’s Lecture: Quantum Mechanics III: State of Momentum Formula/Postulate

Now comes to the most difficult portion for me. It took me three times watching the video to feel more comfortable of the theory of inferring the state of momentum of a quantum particle. In the previous session, Prof. Shankar demonstrated quantum particle's peculiarity can only be described in a sai/wave function, note not a … Continue reading Continue Shankar’s Lecture: Quantum Mechanics III: State of Momentum Formula/Postulate

Continue Shankar’s Lecture: Quantum Mechanics II: The Wave Function Normalization

Theory is developed based on experiments. I like the way Professor Shankar talked about how quantum mechanic physicists nailed the coffin of Newtonian physics by showing the famous double slit experiments. When they observed the interference phenomena, it's a natural and immediate attempt to try to explain by applying typical wave function using sin or … Continue reading Continue Shankar’s Lecture: Quantum Mechanics II: The Wave Function Normalization

Continue Shankar’s Lecture: Quantum Mechanics I: The key experiments and wave-particle duality

Following Professor's Shankar's Physics II was quite difficult, however, since I foresee quantum computing is going to be trending and hence need to pick up quantum computing skills, it's inescapable a task to return to Prof.Shankar's virtual class. There are three pillars leading to the quantum physics early 20th century. The very first is proposed … Continue reading Continue Shankar’s Lecture: Quantum Mechanics I: The key experiments and wave-particle duality

Linear Algebra Especially Eigenvector and Eigenvalue’s Application

It's fascinating to learn linear algebra knowing the enormous application in all kinds of verticals. From video games, neuron network to Google search, epidemic study and forensic detection. Thanks to 3Blue1Brown, we learn to look at matrix not as an abstract symbol, but a function/transformation of coordinate framework, carrying original data points to the new … Continue reading Linear Algebra Especially Eigenvector and Eigenvalue’s Application

Machine Learning by Andrew Ng_8 K-Means and PCA

Previous discussion is all about supervised learning, meaning there is a labeled or known output data pairs (x, y) for the algorithm to be trained. However, in real world, there are circumstances when intellectual creatures like human beings who can tell patterns without known data or first time. This is realized by another kind of … Continue reading Machine Learning by Andrew Ng_8 K-Means and PCA

Machine Learning by Andrew Ng_7 Support Vector Machine(SVM)

Another type of ML worth learning is SVM - support vector machine. The math behind is similar or derived from logistic regression with some mathematical substitution to get below: To be more concrete, it's main purpose is to achieve higher margin in terms of vector distance between data points and decision boundary Next, Kernel is … Continue reading Machine Learning by Andrew Ng_7 Support Vector Machine(SVM)