"Aggressively taking the least shortcuts possible is the fastest shortcut." - [Hackernews user 127](https://news.ycombinator.com/item?id=37358559)
"The only way to learn mathematics is to do mathematics" - [Paul Halmos](https://en.wikipedia.org/wiki/Paul_Halmos)
Excellent process from [uwaterloo](https://uwaterloo.ca/centre-for-teaching-excellence/catalogs/tip-sheets/self-directed-learning-four-step-process)
1. Assess readiness
2. Set learning goals
3. Engage in the process
4. Evaluate learning
My basic plan is to attempt to give myself the equivalent of an MSc program in AI/ML/Data Science, with all the associated mathematical and computer science foundations and filling in any prerequisite knowledge or areas where I am super rusty using primarily on-line resources.
This I will do by self-directed study, documenting this process to form a set of notes on the topics under question. To enhance my own ability to stay motivated and evaluate my own learning I have decided to "[[A few points about learning in public|learn in public]]" and make some or all of my notes available online. The goal is to iteratively become more rigorous as my skills improve so I hope to go back and refine or improve old material over time.
The goals of this activity are:
1. To provide focus and structure to this activity to help me stay committed
2. To study deeply into areas I am interested in
3. To have a sound and broad mathematical background to my work
4. To get really good at AI and machine learning from both a practical and theoretical point of view
## First steps
I have begun this process by completing a couple of on-line courses on [deeplearning.ai]([https://www.deeplearning.ai](https://www.deeplearning.ai/)) and starting some background study, making my algebra less rusty and then doing the [Maths for AI and Machine Learning](https://www.deeplearning.ai/courses/mathematics-for-machine-learning-and-data-science-specialization/) specialization by deeplearning.ai on Coursera.
I’m pulling together a [[self study syllabus|self-study syllabus]] and am considering taking some online university maths courses to help to maintain motivation.
## Philosophy of studying maths
My approach to maths is that maths is three things:
1. A body of knowledge that has been built up over thousands of years by some of the most amazing people. It is a privilege to study it and I aspire one day to make some small contributions
2. a set of skills used by mathematicians to discover this knowledge
3. a language used to communicate this knowledge to others
With that in mind, I want to not only learn more maths, but also to improve my fluency with and understanding of the language as well as improve my ability to use the skills practically. So I'm going to work in 4 streams in parallel:
1. from the ground up to improve the rigour of my understanding of basic concepts, trying to prove/derive every important result myself along the way
2. forwards from my current understanding doing lots of problems to work on my practical skills to enhance my practical abilities and increase my knowledge even when my foundational understanding hasn't quite caught up yet
3. on my ability to *communicate* maths by writing notes, getting fluent with Latex, getting better at using other mathematical tools such as Maxima, Geogebra etc. I will bias towards opensource tools wherever practically possible and try to make source files etc available where I can.
4. on practical programming/visualization/data science stuff that applies these abilities to real world problems
## On Hard Work
Check out [You are studying maths wrong](https://www.youtube.com/watch?v=CEg9Q2hY2ks) and remember there are _no shortcuts whatsoever_ in maths. The point of solving practise problems is not to get the answer to the problem it is to become a mathematician. (See the below about 1m in).
## If you come across these notes
Firstly, hi. Secondly please note the following limitation. I am only learning maths, not a teacher, professor or some other kind of expert. These are my personal notes which I'm providing here as I learn in the hope that they are an aid to study for others. Although I am doing my best to make them accurate _they will definitely contain gaps, errors, misunderstandings etc from small typos to unintentional grave errors_. By all means use them if you find them helpful for learning, but [[#On Hard Work|do your own work]] and verify everything contained within here so you give yourself a chance to avoid mistakes I have made and get good. Additionally, specifically don't just copy anything and hand it in for any sort of assignment or homework and think that's ok. That is _not ok_ for several reasons:
1. I will get things wrong
2. you don't have my permission to do so, and they're my notes so under copyright law I get to say that
3. it would be a _serious_ violation of academic integrity. It may not seem like it to you, but your personal integrity is one of the most precious assets you have. Once lost it is practically impossible to ever be regained. Just don't go there - not even in small ways, not even if you're sure no one will find out.
4. You will be cheating yourself out of the chance of ever doing the work required to get good. _The opportunity to do the work is the golden ticket to understanding that everyone has in their possession_. If you just copy someone else's work (including mine) you are just throwing that chance away. If you think by reviewing someone else's work you are going to get the depth of understanding you would get by doing the work yourself you are just deceiving yourself. The way maths works is that everything builds on everything else. If you don't understand one piece the whole jenga tower of your understanding will fall. Tldr: Do the work and understanding will come. Take the easy route and it will come back to bite you later.
With that out of the way, I really hope these are helpful as I have done the best that I can. Feel free to email me at [email protected]
if you have any questions or comments. In particular if you notice errors I would love to hear about them and fix them.