\( \newcommand{\blah}{blah-blah-blah} \newcommand{\eqb}[1]{\begin{eqnarray*}#1\end{eqnarray*}} \newcommand{\eqbn}[1]{\begin{eqnarray}#1\end{eqnarray}} \newcommand{\bb}[1]{\mathbf{#1}} \newcommand{\mat}[1]{\begin{bmatrix}#1\end{bmatrix}} \newcommand{\nchoose}[2]{\left(\begin{array}{c} #1 \\ #2 \end{array}\right)} \newcommand{\defn}{\stackrel{\vartriangle}{=}} \newcommand{\rvectwo}[2]{\left(\begin{array}{c} #1 \\ #2 \end{array}\right)} \newcommand{\rvecthree}[3]{\left(\begin{array}{r} #1 \\ #2\\ #3\end{array}\right)} \newcommand{\rvecdots}[3]{\left(\begin{array}{r} #1 \\ #2\\ \vdots\\ #3\end{array}\right)} \newcommand{\vectwo}[2]{\left[\begin{array}{r} #1\\#2\end{array}\right]} \newcommand{\vecthree}[3]{\left[\begin{array}{r} #1 \\ #2\\ #3\end{array}\right]} \newcommand{\vecfour}[4]{\left[\begin{array}{r} #1 \\ #2\\ #3\\ #4\end{array}\right]} \newcommand{\vecdots}[3]{\left[\begin{array}{r} #1 \\ #2\\ \vdots\\ #3\end{array}\right]} \newcommand{\eql}{\;\; = \;\;} \definecolor{dkblue}{RGB}{0,0,120} \definecolor{dkred}{RGB}{120,0,0} \definecolor{dkgreen}{RGB}{0,120,0} \newcommand{\bigsp}{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;} \newcommand{\plss}{\;\;+\;\;} \newcommand{\miss}{\;\;-\;\;} \newcommand{\implies}{\Rightarrow\;\;\;\;\;\;\;\;\;\;\;\;} \newcommand{\prob}[1]{\mbox{Pr}\left[ #1 \right]} \newcommand{\exval}[1]{\mbox{E}\left[ #1 \right]} \newcommand{\variance}[1]{\mbox{Var}\left[ #1 \right]} \)


Review: Linear Algebra, other math, computing

 


Goals

 

The review has two main purposes:

  1. We need to have certain core concepts from linear algebra at our finger tips so that our brain can wrap around the more interesting quantum concepts and not get bogged down in struggling with linear algebra.

  2. We are also going to review basic notions in math and computing. The main goal is to set the context for what we learn.
 

Note to CS, engg, and math students about physics:

  • No prior physics coursework is needed, except basic physics as learned in high-school.

  • There will be no physics homeworks nor any testing of physics.

  • We will describe physics to provide background and engage your curiosity.

  • If you come with an open mind to physics, you will find much that's interesting.

  • If you want to pursue physics on your own, we will provide a roadmap of books.
 

Note to math, engg, and physics students about computer science:

  • There will be no programming in the course. Nor will you need to understand much beyond what we review.

  • Do NOT think of the computing review as pointing out "Oh no, I don't have this background".

  • All we will need are the basic notions about how circuits work.
 

Note to CS, engg, and physics students about math:

  • While this is not a theorem-proof course, the material is definitely mathematical.

  • You might experience some notational unfamiliarity, which might cause you to feel anxious.

  • We will occasionally delve into more math than is needed for quantum computing but is essential for quantum mechanics. None of this will be tested.

  • The best thing you can do to avoid "math anxiety" is to work on the module problems and narrative-notes as early as possible, and as thorougly as possible.

  • You will be (pleasantly) surprised at how much your skill level will increase by the end of the semester.
 

To all students:

  • Because this is an interdisciplinary course, almost any particular topic or concept we do will be challenging for some, and easy for others. There's no avoiding this.

  • At no time should you let "They know this but I don't" get to you.

  • Instead, let's use the opportunity to learn from each other.

  • You are encouraged to meet up after class to pursue curiosity by interacting with your classmates.
 


How to review

 

The wrong way to do this review is to just read.

Instead:

  • Get your notebook out.
  • For every section: read and then write out a summary in your notebook, explaining it to yourself.
  • Add your own examples alongside mine. For example if I make an example vector \((2,3)\), you should make a different one.
  • Bottom line: if your written notes are much smaller than the size of the review, something's wrong.
Important: Do NOT skip any topic. The review is a minimal review.
 


The review

 

The review is organized into four sections.

Recommended order:

  1. Review of linear algebra (This page will link to others.)

  2. Review of key math concepts (Single page)

  3. Review of key computing concepts (Single page)

  4. A dash of physics (just for taste)
Ideally, you should complete the review as expeditiously as possible.


© 2022, Rahul Simha