# Posts by Tag

## Crouzeix’s divergence free basis for the Navier-Stokes equation

This is the solution (long read) to a Chapter 11 exercise of the book by Brenner and Scott (Brenner & Scott, 2008). Personally I really like this problem...

## Amateur mathematician studies Quantum Field Theory part 2: Maxwell equations

In the first part, we reviewed a brief history of the mathematics of the Quantum Field Theory (not exhaustively, but enough to get the idea). In this part, w...

## Amateur mathematician studies Quantum Field Theory part I

Translating the language of physicists to the language of mathematicians.

## iFEM project: implementing the hierarchical basis for linear finite elements

This note walks through the construction of the stiffness matrix for the finite element approximation of Poisson equation in 2D using the hierarchical basis...

## Galerkin Transformer: A One-Shot Experiment at NeurIPS 2021

A newbie’s journey of submitting his first ML paper to a top conference.

## Vectorization tricks for cell arrays in MATLAB

How to write elegantly fast code to handle cell array with different length vector at each row.

## Notes on 130C: Stochastic Processes

This notes contains some of the notes I used in UC Irvine Math 130C course.

## Notes on the history of trace theorems on a Lipschitz domain

Some detective work on the trace lemmata (and the converse one) for the Sobolev spaces.

## Winter 2019 Math 10 Final Project Kaggle in-class Competition

In the course project, groups of three students will work together to create regression/classifiers for an in-class Kaggle prediction competition. The compet...

## Some constructions related to Helmholtz decomposition

Using Poincare lemma to construct vector field explicitly for Helmholtz decomposition.

Since Google+ is finally to be shut down by Google as of Feb 1, 2019, aside from migrating G+’s social bookmarking functionality to Medium.com and Pocket app...

## Equivalence between Sobolev norm and Sobolev-Slobodeckij norm for integer-order spaces

This short post explores the equivalence between Sobolev norm and Sobolev-Slobodeckij norm for $W^{s,p}(\Omega)$ when $s$ is an integer.

## Deriving the expression of the Lorentz force using the language of a mathematician

This is a continuation of my previous “complaining” post on the language difference of mathematician vs physicists regarding the same thing.

## Random notes about physicists’ obsession with Einstein notations

I took a quantum physics class on Coursera this year and I found that the Mathematical language spoken by the two communities, math vs physics, are quite dif...

## Several explicit constructions of the Helmholtz decomposition

Here we present two approaches to construct Helmholtz decompositions.

## An identity for the continuous integral solution of the conservation law

This is an exercise in Evans, Partial Differential Equations (1st edition), page 164, problem 13.

## Kernels of a bounded operator’s extension

This is a post recording my answer to a question on Math StackExchange1 with some references in L. Tartar’s book2. https://math.stackexchange...

## Proof of the coercivity for Robin boundary problem

This is an exercise for finite element method most likely. Our question is:

## How to impose boundary condition for 2-dimensional curl-curl weak problem

First about the appropriate boundary condition we would like to impose: The cross product(scalar-$\mathrm{curl}$) in $\mathbb{R}^2$ is done by we embed a vec...

## An example on the limiting case of Sobolev embedding

Sobolev embedding When $p=n$

## Use a reverse method of characteristics to get the trajectories equation

This is an exercise in Evans, Partial Differential Equations (2nd edition), Chapter 10 Conservation laws.

## Discontinuous Galerkin method for linear advection equation

PDE This was the first project after I switched to a PhD program in computational math. The goal of the project is to study the Discontinuous Galerkin (DG) f...

## Amateur mathematician studies Quantum Field Theory part 2: Maxwell equations

In the first part, we reviewed a brief history of the mathematics of the Quantum Field Theory (not exhaustively, but enough to get the idea). In this part, w...

## Amateur mathematician studies Quantum Field Theory part I

Translating the language of physicists to the language of mathematicians.

## iFEM project: implementing the hierarchical basis for linear finite elements

This note walks through the construction of the stiffness matrix for the finite element approximation of Poisson equation in 2D using the hierarchical basis...

## Galerkin Transformer: A One-Shot Experiment at NeurIPS 2021

A newbie’s journey of submitting his first ML paper to a top conference.

## Vectorization tricks for cell arrays in MATLAB

How to write elegantly fast code to handle cell array with different length vector at each row.

## Notes on the history of trace theorems on a Lipschitz domain

Some detective work on the trace lemmata (and the converse one) for the Sobolev spaces.

## Equivalence between Sobolev norm and Sobolev-Slobodeckij norm for integer-order spaces

This short post explores the equivalence between Sobolev norm and Sobolev-Slobodeckij norm for $W^{s,p}(\Omega)$ when $s$ is an integer.

## Several explicit constructions of the Helmholtz decomposition

Here we present two approaches to construct Helmholtz decompositions.

## Kernels of a bounded operator’s extension

This is a post recording my answer to a question on Math StackExchange1 with some references in L. Tartar’s book2. https://math.stackexchange...

## How to impose boundary condition for 2-dimensional curl-curl weak problem

First about the appropriate boundary condition we would like to impose: The cross product(scalar-$\mathrm{curl}$) in $\mathbb{R}^2$ is done by we embed a vec...

## An example on the limiting case of Sobolev embedding

Sobolev embedding When $p=n$

## Discontinuous Galerkin method for linear advection equation

PDE This was the first project after I switched to a PhD program in computational math. The goal of the project is to study the Discontinuous Galerkin (DG) f...

## Crouzeix’s divergence free basis for the Navier-Stokes equation

This is the solution (long read) to a Chapter 11 exercise of the book by Brenner and Scott (Brenner & Scott, 2008). Personally I really like this problem...

## iFEM project: implementing the hierarchical basis for linear finite elements

This note walks through the construction of the stiffness matrix for the finite element approximation of Poisson equation in 2D using the hierarchical basis...

## Galerkin Transformer: A One-Shot Experiment at NeurIPS 2021

A newbie’s journey of submitting his first ML paper to a top conference.

## Notes on the history of trace theorems on a Lipschitz domain

Some detective work on the trace lemmata (and the converse one) for the Sobolev spaces.

## Equivalence between Sobolev norm and Sobolev-Slobodeckij norm for integer-order spaces

This short post explores the equivalence between Sobolev norm and Sobolev-Slobodeckij norm for $W^{s,p}(\Omega)$ when $s$ is an integer.

## Several explicit constructions of the Helmholtz decomposition

Here we present two approaches to construct Helmholtz decompositions.

## An identity for the continuous integral solution of the conservation law

This is an exercise in Evans, Partial Differential Equations (1st edition), page 164, problem 13.

## Kernels of a bounded operator’s extension

This is a post recording my answer to a question on Math StackExchange1 with some references in L. Tartar’s book2. https://math.stackexchange...

## Proof of the coercivity for Robin boundary problem

This is an exercise for finite element method most likely. Our question is:

## How to impose boundary condition for 2-dimensional curl-curl weak problem

First about the appropriate boundary condition we would like to impose: The cross product(scalar-$\mathrm{curl}$) in $\mathbb{R}^2$ is done by we embed a vec...

## Use a reverse method of characteristics to get the trajectories equation

This is an exercise in Evans, Partial Differential Equations (2nd edition), Chapter 10 Conservation laws.

## Discontinuous Galerkin method for linear advection equation

PDE This was the first project after I switched to a PhD program in computational math. The goal of the project is to study the Discontinuous Galerkin (DG) f...

## Crouzeix’s divergence free basis for the Navier-Stokes equation

This is the solution (long read) to a Chapter 11 exercise of the book by Brenner and Scott (Brenner & Scott, 2008). Personally I really like this problem...

## Amateur mathematician studies Quantum Field Theory part 2: Maxwell equations

In the first part, we reviewed a brief history of the mathematics of the Quantum Field Theory (not exhaustively, but enough to get the idea). In this part, w...

## Amateur mathematician studies Quantum Field Theory part I

Translating the language of physicists to the language of mathematicians.

## iFEM project: implementing the hierarchical basis for linear finite elements

This note walks through the construction of the stiffness matrix for the finite element approximation of Poisson equation in 2D using the hierarchical basis...

## Galerkin Transformer: A One-Shot Experiment at NeurIPS 2021

A newbie’s journey of submitting his first ML paper to a top conference.

## Notes on the history of trace theorems on a Lipschitz domain

Some detective work on the trace lemmata (and the converse one) for the Sobolev spaces.

## Some constructions related to Helmholtz decomposition

Using Poincare lemma to construct vector field explicitly for Helmholtz decomposition.

## Several explicit constructions of the Helmholtz decomposition

Here we present two approaches to construct Helmholtz decompositions.

## Kernels of a bounded operator’s extension

This is a post recording my answer to a question on Math StackExchange1 with some references in L. Tartar’s book2. https://math.stackexchange...

## Proof of the coercivity for Robin boundary problem

This is an exercise for finite element method most likely. Our question is:

## How to impose boundary condition for 2-dimensional curl-curl weak problem

First about the appropriate boundary condition we would like to impose: The cross product(scalar-$\mathrm{curl}$) in $\mathbb{R}^2$ is done by we embed a vec...

## An example on the limiting case of Sobolev embedding

Sobolev embedding When $p=n$

## Funny moments of using the GitHub Copilot

My experience of using the GitHub copilot as a computational mathematician.

## Galerkin Transformer: A One-Shot Experiment at NeurIPS 2021

A newbie’s journey of submitting his first ML paper to a top conference.

## Build a budget 3090 deep learning workstation Bonus: How to get a MacOS keyboard layout on Linux (Ubuntu, Fedora, etc)

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

## Build a budget 3090 deep learning workstation Part Three: undervolt an RTX GPU on Ubuntu

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

## Build a budget 3090 deep learning workstation Part Two: use GPU only for CUDA not for display

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

## Build a budget 3090 deep learning workstation Part One: assembling and GPU bent

Assembling of a deep learning workstation with RTX 3090 + 10850k, and how to deal with the bent of the heavy 3090 card.

## Build a budget 3090 deep learning workstation Part Zero: random tidbits

A random newbie’s story on building an RTX 3090 workstation.

## Vectorization tricks for cell arrays in MATLAB

How to write elegantly fast code to handle cell array with different length vector at each row.

## Finally switched to Jekyll with Mathjax!

I finally decided to migrate various of my old writing in my faculty website at UC Irvine (deactivated as of Oct 2020) a static website generator Jekyll. App...

## MATLAB finally updated its array compatibility to match Python

Matlab finally embraces (partially) the way matrix manipulation should be Starting in MATLAB R2016b with the addition of implicit expansion, some combinatio...

## Winter 2019 Math 10 Final Project Kaggle in-class Competition

In the course project, groups of three students will work together to create regression/classifiers for an in-class Kaggle prediction competition. The compet...

## Getting ready for Math 10: intro to ML

I created an introductory machine learning class for math undergrad who has no previous exposure to programming back in Winter 2019 quarter. This post will t...

## Galerkin Transformer: A One-Shot Experiment at NeurIPS 2021

A newbie’s journey of submitting his first ML paper to a top conference.

## Build a budget 3090 deep learning workstation Bonus: How to get a MacOS keyboard layout on Linux (Ubuntu, Fedora, etc)

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

## Build a budget 3090 deep learning workstation Part Three: undervolt an RTX GPU on Ubuntu

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

## Build a budget 3090 deep learning workstation Part Two: use GPU only for CUDA not for display

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

## Build a budget 3090 deep learning workstation Part One: assembling and GPU bent

Assembling of a deep learning workstation with RTX 3090 + 10850k, and how to deal with the bent of the heavy 3090 card.

## Build a budget 3090 deep learning workstation Part Zero: random tidbits

A random newbie’s story on building an RTX 3090 workstation.

## Winter 2019 Math 10 Final Project Kaggle in-class Competition

In the course project, groups of three students will work together to create regression/classifiers for an in-class Kaggle prediction competition. The compet...

## Getting ready for Math 10: intro to ML

I created an introductory machine learning class for math undergrad who has no previous exposure to programming back in Winter 2019 quarter. This post will t...

## Amateur mathematician studies Quantum Field Theory part 2: Maxwell equations

In the first part, we reviewed a brief history of the mathematics of the Quantum Field Theory (not exhaustively, but enough to get the idea). In this part, w...

## Amateur mathematician studies Quantum Field Theory part I

Translating the language of physicists to the language of mathematicians.

## Some constructions related to Helmholtz decomposition

Using Poincare lemma to construct vector field explicitly for Helmholtz decomposition.

## Deriving the expression of the Lorentz force using the language of a mathematician

This is a continuation of my previous “complaining” post on the language difference of mathematician vs physicists regarding the same thing.

## Random notes about physicists’ obsession with Einstein notations

I took a quantum physics class on Coursera this year and I found that the Mathematical language spoken by the two communities, math vs physics, are quite dif...

## Several explicit constructions of the Helmholtz decomposition

Here we present two approaches to construct Helmholtz decompositions.

## How to impose boundary condition for 2-dimensional curl-curl weak problem

First about the appropriate boundary condition we would like to impose: The cross product(scalar-$\mathrm{curl}$) in $\mathbb{R}^2$ is done by we embed a vec...

## Funny moments of using the GitHub Copilot

My experience of using the GitHub copilot as a computational mathematician.

## Galerkin Transformer: A One-Shot Experiment at NeurIPS 2021

A newbie’s journey of submitting his first ML paper to a top conference.

## Build a budget 3090 deep learning workstation Bonus: How to get a MacOS keyboard layout on Linux (Ubuntu, Fedora, etc)

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

## Build a budget 3090 deep learning workstation Part Three: undervolt an RTX GPU on Ubuntu

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

## Build a budget 3090 deep learning workstation Part Two: use GPU only for CUDA not for display

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

## Build a budget 3090 deep learning workstation Part One: assembling and GPU bent

Assembling of a deep learning workstation with RTX 3090 + 10850k, and how to deal with the bent of the heavy 3090 card.

## Build a budget 3090 deep learning workstation Part Zero: random tidbits

A random newbie’s story on building an RTX 3090 workstation.

## Crouzeix’s divergence free basis for the Navier-Stokes equation

This is the solution (long read) to a Chapter 11 exercise of the book by Brenner and Scott (Brenner & Scott, 2008). Personally I really like this problem...

## iFEM project: implementing the hierarchical basis for linear finite elements

This note walks through the construction of the stiffness matrix for the finite element approximation of Poisson equation in 2D using the hierarchical basis...

## Vectorization tricks for cell arrays in MATLAB

How to write elegantly fast code to handle cell array with different length vector at each row.

## Notes on the history of trace theorems on a Lipschitz domain

Some detective work on the trace lemmata (and the converse one) for the Sobolev spaces.

## Proof of the coercivity for Robin boundary problem

This is an exercise for finite element method most likely. Our question is:

## Discontinuous Galerkin method for linear advection equation

PDE This was the first project after I switched to a PhD program in computational math. The goal of the project is to study the Discontinuous Galerkin (DG) f...

## Crouzeix’s divergence free basis for the Navier-Stokes equation

This is the solution (long read) to a Chapter 11 exercise of the book by Brenner and Scott (Brenner & Scott, 2008). Personally I really like this problem...

## iFEM project: implementing the hierarchical basis for linear finite elements

This note walks through the construction of the stiffness matrix for the finite element approximation of Poisson equation in 2D using the hierarchical basis...

## Galerkin Transformer: A One-Shot Experiment at NeurIPS 2021

A newbie’s journey of submitting his first ML paper to a top conference.

## Proof of the coercivity for Robin boundary problem

This is an exercise for finite element method most likely. Our question is:

## How to impose boundary condition for 2-dimensional curl-curl weak problem

First about the appropriate boundary condition we would like to impose: The cross product(scalar-$\mathrm{curl}$) in $\mathbb{R}^2$ is done by we embed a vec...

## Discontinuous Galerkin method for linear advection equation

PDE This was the first project after I switched to a PhD program in computational math. The goal of the project is to study the Discontinuous Galerkin (DG) f...

## Winter 2019 Math 10 Final Project Kaggle in-class Competition

In the course project, groups of three students will work together to create regression/classifiers for an in-class Kaggle prediction competition. The compet...

## Getting ready for Math 10: intro to ML

I created an introductory machine learning class for math undergrad who has no previous exposure to programming back in Winter 2019 quarter. This post will t...

## An identity for the continuous integral solution of the conservation law

This is an exercise in Evans, Partial Differential Equations (1st edition), page 164, problem 13.

## Proof of the coercivity for Robin boundary problem

This is an exercise for finite element method most likely. Our question is:

## Use a reverse method of characteristics to get the trajectories equation

This is an exercise in Evans, Partial Differential Equations (2nd edition), Chapter 10 Conservation laws.

## Funny moments of using the GitHub Copilot

My experience of using the GitHub copilot as a computational mathematician.

## Shortcut to git commit and push in Visual Studio Code

Use VSCode task to streamline the workflow of building a site and push the changes to GitHub.

Install wgo.js in the Jekyll blog and load it on demand using a toggle in preamble.

## How to use a custom Jekyll plugin on Github pages

GitHub pages allows Jekyll version only to be 3.9, let us find a way around it.

## Getting ready for Math 10: intro to ML

I created an introductory machine learning class for math undergrad who has no previous exposure to programming back in Winter 2019 quarter. This post will t...

## Build a budget 3090 deep learning workstation Bonus: How to get a MacOS keyboard layout on Linux (Ubuntu, Fedora, etc)

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

## Build a budget 3090 deep learning workstation Part Three: undervolt an RTX GPU on Ubuntu

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

## Build a budget 3090 deep learning workstation Part Two: use GPU only for CUDA not for display

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

## Build a budget 3090 deep learning workstation Part One: assembling and GPU bent

Assembling of a deep learning workstation with RTX 3090 + 10850k, and how to deal with the bent of the heavy 3090 card.

## Build a budget 3090 deep learning workstation Part Zero: random tidbits

A random newbie’s story on building an RTX 3090 workstation.

## Ubuntu

Install wgo.js in the Jekyll blog and load it on demand using a toggle in preamble.

## How to use a custom Jekyll plugin on Github pages

GitHub pages allows Jekyll version only to be 3.9, let us find a way around it.

## Build a budget 3090 deep learning workstation Bonus: How to get a MacOS keyboard layout on Linux (Ubuntu, Fedora, etc)

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

## Build a budget 3090 deep learning workstation Part Three: undervolt an RTX GPU on Ubuntu

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

## Build a budget 3090 deep learning workstation Part Two: use GPU only for CUDA not for display

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

## Shortcut to git commit and push in Visual Studio Code

Use VSCode task to streamline the workflow of building a site and push the changes to GitHub.

Install wgo.js in the Jekyll blog and load it on demand using a toggle in preamble.

## How to use a custom Jekyll plugin on Github pages

GitHub pages allows Jekyll version only to be 3.9, let us find a way around it.

## Finally switched to Jekyll with Mathjax!

I finally decided to migrate various of my old writing in my faculty website at UC Irvine (deactivated as of Oct 2020) a static website generator Jekyll. App...

## Notes on the history of trace theorems on a Lipschitz domain

Some detective work on the trace lemmata (and the converse one) for the Sobolev spaces.

## Proof of the coercivity for Robin boundary problem

This is an exercise for finite element method most likely. Our question is:

## An example on the limiting case of Sobolev embedding

Sobolev embedding When $p=n$

## iFEM project: implementing the hierarchical basis for linear finite elements

This note walks through the construction of the stiffness matrix for the finite element approximation of Poisson equation in 2D using the hierarchical basis...

## Vectorization tricks for cell arrays in MATLAB

How to write elegantly fast code to handle cell array with different length vector at each row.

## MATLAB finally updated its array compatibility to match Python

Matlab finally embraces (partially) the way matrix manipulation should be Starting in MATLAB R2016b with the addition of implicit expansion, some combinatio...

## Vectorization tricks for cell arrays in MATLAB

How to write elegantly fast code to handle cell array with different length vector at each row.

## Finally switched to Jekyll with Mathjax!

I finally decided to migrate various of my old writing in my faculty website at UC Irvine (deactivated as of Oct 2020) a static website generator Jekyll. App...

## MATLAB finally updated its array compatibility to match Python

Matlab finally embraces (partially) the way matrix manipulation should be Starting in MATLAB R2016b with the addition of implicit expansion, some combinatio...

## Amateur mathematician studies Quantum Field Theory part 2: Maxwell equations

In the first part, we reviewed a brief history of the mathematics of the Quantum Field Theory (not exhaustively, but enough to get the idea). In this part, w...

## Amateur mathematician studies Quantum Field Theory part I

Translating the language of physicists to the language of mathematicians.

## Galerkin Transformer: A One-Shot Experiment at NeurIPS 2021

A newbie’s journey of submitting his first ML paper to a top conference.

## Shortcut to git commit and push in Visual Studio Code

Use VSCode task to streamline the workflow of building a site and push the changes to GitHub.

Install wgo.js in the Jekyll blog and load it on demand using a toggle in preamble.

## How to use a custom Jekyll plugin on Github pages

GitHub pages allows Jekyll version only to be 3.9, let us find a way around it.

## Funny moments of using the GitHub Copilot

My experience of using the GitHub copilot as a computational mathematician.

## Winter 2019 Math 10 Final Project Kaggle in-class Competition

In the course project, groups of three students will work together to create regression/classifiers for an in-class Kaggle prediction competition. The compet...

## Funny moments of using the GitHub Copilot

My experience of using the GitHub copilot as a computational mathematician.

## Shortcut to git commit and push in Visual Studio Code

Use VSCode task to streamline the workflow of building a site and push the changes to GitHub.

## Notes on the history of trace theorems on a Lipschitz domain

Some detective work on the trace lemmata (and the converse one) for the Sobolev spaces.

## Notes on 130C: Stochastic Processes

This notes contains some of the notes I used in UC Irvine Math 130C course.

## Galerkin Transformer: A One-Shot Experiment at NeurIPS 2021

A newbie’s journey of submitting his first ML paper to a top conference.

## Galerkin Transformer: A One-Shot Experiment at NeurIPS 2021

A newbie’s journey of submitting his first ML paper to a top conference.