I've been doing similar for about a year. My target is to learn the math needed to make 3d games, so basically algebra, geometry, calculus and linear algebra.
I started with brilliant.org, and while I liked the level of polish in the interactive lessons, I found the lesson structure to be out of sequence, often referring to things that haven't been covered yet. They didn't seem to have put as much thought into pedagogy as Math Academy as described in TFA.
So I gave up on that and instead have been shipping several kilograms of dead tree across the pacific in the form of The Art Of Problem Solving series of textbooks. They are great, the lesson structure and building up of complex ideas from first principles is outstanding. They will humble you though, as the exercises are tough. They're also quite expensive but IMHO worth it.
Math Academy does look interesting, If I was not halfway through my series I would probably take a look. But I do enjoy having reference books on hand. Many times I've jumped back to brush up on a topic that has slipped from memory.
I solve my exercises with the most low tech solution possible, but I like the freedom it gives me to try new approaches, and nothing beats the latency between idea to ink on paper.
edit: also wanted to add that I've enrolled Chat GPT4 as my tutor. Contrary to many other's experiences that I've read, I find it to generally be very good at reasoning in this level of mathematics. It's helped me many times when I've gotten stuck. And on the occasions where it bullshitted its way to an incorrect answer, I always challenge it if I don't understand, and we ultimately find out if it hallucinated something (rare, can usually be fixed by restating the problem), or I gave it the wrong input to start with (unfortunately more common than I'd like)
I'm in that camp and can suggest a few recommendations in order of:
https://d3dcoder.net/ -- The DX12 book is the latest edition. The books have several chapters at the beginning covering 3d transformations.
https://foundationsofgameenginedev.com/ -- The first installation, Mathematics. This will cover a lot more ground and derive things from first principles while not being overly formal.
Are you using any of the stuff you're learning for whatever practical 3d game-making things you're working on? Just curious how it's working out, you've picked a pretty broad foundation as a starting point.
I took a brief detour late last year to study "Linear Algebra: Theory, Intuition, Code", and to my surprise it stuck pretty well. The author said the pre-reqs were just "basic high school math", but I'm glad I had recently done lots of algebra and geometry, as the difference between that and some vague memories of stuff I did 30 years ago in school is pretty wide.
I haven't started any 3d game projects yet. For that, my plan is to do the webgpufundamentals.org course first. Scanning the TOC, I think I would be able to attempt it from what I learned from the linear algebra book.
That said, I'm doing AOPS Intermediate Algebra at the moment, and the Precalc text covers more advanced trig and matrix stuff, so I'm thinking it would be good to finish at least to there before starting to apply the knowledge.
As a Mathematician who worked in Theoretical Physics for a bit, I'm happy to hear that there's people out there interested in the area.
Maths often get a bad rep, but at their core they are probably the most interesting thing to learn, on par with music in my opinion.
I encourage anyone interested in Mathematics (regardless of your level) to check out Roger Penrose's The Road to Reality. I know it's technically a physics book, even though Penrose was originally a Mathematician, but trust me, he explains things in a way that open up your mind, even for seasoned veterans. He begins with basic calculus, but ends up covering Groups, Topology, Complex Analysis, Differential Geometry, etc etc etc.
This post couldn't be any more timely. I dropped out of school years ago (16 years ago to be exact) to take care of my sick mother when she was dying.
I never went back. I just started working.
I am happy to report I am back in school and will be FINALLY finishing my Computer Science degree but I have a very long 4 years ahead of me. Math is going to be hard.
What is encouraging is the thrill of when I get the answer right and most importantly knowing HOW I got there. It's (almost) better than sex.
This is inspiring to me, as I'm in a similar boat and while I'm pretty okay at my job in practical terms, I often feel as if I lack a certain mathematical foundation. May I ask how old you are, whether you are enrolled in a full-time course (w/ much younger other students, I suppose?) and how that has been for you?
It's also based on an underlying knowledge graph, connecting concepts across various subjects like maths, machine learning, physics, etc. You can check the graph for transformer here: https://afaik.io/nebula?category=brickset&id=VLlOnZLl&mode=d... (only available on desktop...
Basically, it frees you from learning maths from scratch and just learning the prerequisites required to grasp the concept, and there are free resources attached.
Don't get me wrong, I can totally relate to the desire to relearn maths. One of the reasons that I'm building this tool is for me to relearn physics and know how to get there with my maths and cs background. I just feel in this specific scenario there might be more effective ways to learn in depth and have fun at the same time.
I find the concept of "underlying knowledge graph" interesting. What does it mean?
I assume it means such a graph connects the topics together as "pre-requisites". To understand A you need to already understand B and C, and to understand B you need to understand D and ... etc.
But the thing about such a graph is that really it must be a tree, not just a directed graph. Why? Because there cannot be cycles in it. If to understand A you need to understand B, and to understand B you would need to understand A, you could never understand either of them. Right?
"underlying knowledge graph" is a directed acyclic graph (DAG), based on prerequisite relations among topics. So you are right that there cannot be cycles but it's not a tree either because a tree (technically) only allows one parent.
I will recommend a couple great channels for Math:
1. https://www.youtube.com/@SawFinMath : She is a great Professor that walks through problems/solutions one step at a time, so that you can follow along. Has a bunch of Under Graduate course playlists like discrete math, calculus, (abstract or linear) algebra, statistics. highly recommended for the great pacing and solving a lot of problems live.
2. https://mathispower4u.com/ : Another professor who takes an open math textbook (free), and makes a course out of it. Its a little bit more difficult because of denser "pure math" material, but in return, you basically cover everything that a college usually would. He has courses like discrete math, calculus, graph theory, trigonometry, statistics, algebra, geometry etc. Also solves a lot of problems live.
I haven't really tried it, but apparently there is https://www.myopenmath.com/index.php which is sort of like exercism in that you follow along a textbook and solve problems. If someone has tried this, maybe they can share their experience.
When I went back to school for CS, I used this book https://a.co/d/7hlRdnK to relearn math. I couldn’t recommend it more.
It starts with algebra and works through calculus. There is a pretest before every section, so you know what you need to focus on and what you can skip.
People here mention KhanAcademy and AOPS series for self learning. I've used both when relearning Math as an adult. But there is one more resource which is absolutely terrific: Henry Sinclair Hall's books. Not only they are good (way better than the aforementioned ones), but being published in the 19th century, they are in public domain now and can be downloaded from the Internet Archive free of charge: https://archive.org/search?query=creator%3A%22Hall%2C+H.+S.+...
And, also, How to Prove it by Velleman is a must read.
Math Academy is much more dense and on-point that Khan's. You don't have to sit through 15 minutes of video when 2 minutes worth of text explanation does it.
It uses spaced repetition for topics that you aren't good at, and for recently learned subjects.
The topic dependency tree and automatic progressing to "unlocked" topics is obvious in retrospect, but here it's done very cleanly and unobtrusively.
The initial evaluation test is worth its weight in gold. It eliminates the need to grind through things that you already know, but still covers any gaps.
I had kids on Khan for few weeks and it was a hassle. The pace was too slow, too much time sunk into trivialities and they were bored most of the time. With Math Academy they sit down, they do their 20-30 min of focused hands-on effort and they are done for the day.
I did a year and a half ago before getting too busy with work. I found it to be a bit spartan, but still the most efficient tool for math study I've used.
I was a math major long ago, so it was more a case of relearning than initial learning for me but the built-in SRS helped a lot and so did the granularity of the lessons. It's head and shoulders above Brilliant, IMO.
If it didn't exist or I couldn't afford it, I'd probably go the OpenCourseWare approach. https://ocw.mit.edu/
It's really good for its goals. I've used it for a few months and was really happy with the results. The spaced repetition aspect worked perfectly. The courses are still being worked on - already 99% there with quality, but you can report any issues and they get fixed. Just keep in mind that the target is largely students, (at least at the moment) so the aim is mastery of the subject - if you're interested in learning the concept but not actually doing a lot of practice of using it, then it may not be the right service. And there are magic internet points / leaderboards if gamification is something that works for you.
The exercise sizes are also very small almost all the time. That means instead of a whole topic at the time and figuring out where you left the last time, you can do as much as you want at a time and not be restricted by artificial "chapters".
I have been doing the Math for ML course and would recommend.
I have UK A level math but not Further Math, so up to basic calculus. But I forgot most of it and so Math Academy has me going through a lot of the Math Foundation units along the way.
I was initially put off by the monthly price, as it is quite steep. The clincher is that about a year before starting Math Academy I had gone through the Open University’s MST124/125 textbooks (covering the same stuff as Foundations). Except even after a year I’d already forgotten most of it.
Math Academy learning feels much more robust, since it includes spaced reviews and regular tests. I record things in Anki but it’s useful to have regular practice questions too. I also use ChatGPT to spell out things and find it works well at this level.
Some things I’d like Math Academy to have:
- ability to skip lessons (I don’t want to spend ages going over symbolic integration again)
- a reference page to track unlocked material, maybe with Anki integration
- fewer multiple choice questions and more in depth problems
- proof-based math. I’m told this is coming but the degree-level courses have missed their estimated due dates.
I will definitely finish Math for ML and then do linear algebra and multivariate calculus. You’d still need a good textbook to do them rigorously, but I think Math Academy sets you up well.
It's very good. I've tried it after hesitating a bit because of the price tag compared to Khan Academy — no regrets.
K.A. is great and I still use with my kid, but M.A. is more condensed and to the point for my needs. I was properly guided through the first program choices according to my profile, and the diagnostic exam you start with was perfect to highlight what I actually need to work on given my limited time.
Explanations and courses are super condensed, with the right amount of example and pedagogy that clicks for me.
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I started with brilliant.org, and while I liked the level of polish in the interactive lessons, I found the lesson structure to be out of sequence, often referring to things that haven't been covered yet. They didn't seem to have put as much thought into pedagogy as Math Academy as described in TFA.
So I gave up on that and instead have been shipping several kilograms of dead tree across the pacific in the form of The Art Of Problem Solving series of textbooks. They are great, the lesson structure and building up of complex ideas from first principles is outstanding. They will humble you though, as the exercises are tough. They're also quite expensive but IMHO worth it.
Math Academy does look interesting, If I was not halfway through my series I would probably take a look. But I do enjoy having reference books on hand. Many times I've jumped back to brush up on a topic that has slipped from memory.
I solve my exercises with the most low tech solution possible, but I like the freedom it gives me to try new approaches, and nothing beats the latency between idea to ink on paper.
edit: also wanted to add that I've enrolled Chat GPT4 as my tutor. Contrary to many other's experiences that I've read, I find it to generally be very good at reasoning in this level of mathematics. It's helped me many times when I've gotten stuck. And on the occasions where it bullshitted its way to an incorrect answer, I always challenge it if I don't understand, and we ultimately find out if it hallucinated something (rare, can usually be fixed by restating the problem), or I gave it the wrong input to start with (unfortunately more common than I'd like)
https://d3dcoder.net/ -- The DX12 book is the latest edition. The books have several chapters at the beginning covering 3d transformations.
https://foundationsofgameenginedev.com/ -- The first installation, Mathematics. This will cover a lot more ground and derive things from first principles while not being overly formal.
https://www.mathfor3dgameprogramming.com/ -- A lot more formal than most game/graphics math books, and goes into more depth, particularly on the linear algebra.
I haven't started any 3d game projects yet. For that, my plan is to do the webgpufundamentals.org course first. Scanning the TOC, I think I would be able to attempt it from what I learned from the linear algebra book.
That said, I'm doing AOPS Intermediate Algebra at the moment, and the Precalc text covers more advanced trig and matrix stuff, so I'm thinking it would be good to finish at least to there before starting to apply the knowledge.
What's the scope of The Art of Problem Solving? How far does the series go?
- Prealgebra
- Intro to Algebra
- Intro to Counting & Probability
- Intro to Geometry
- Intro to Number Theory
- Intermediate Algebra
- Intermediate Counting & Probability
- Precalculus
- Calculus
Maths often get a bad rep, but at their core they are probably the most interesting thing to learn, on par with music in my opinion.
I encourage anyone interested in Mathematics (regardless of your level) to check out Roger Penrose's The Road to Reality. I know it's technically a physics book, even though Penrose was originally a Mathematician, but trust me, he explains things in a way that open up your mind, even for seasoned veterans. He begins with basic calculus, but ends up covering Groups, Topology, Complex Analysis, Differential Geometry, etc etc etc.
And, on parallel, check out John Baez's guide on how to learn Maths and Physics: https://math.ucr.edu/home/baez/books.html
I love all of Baez's pages and work, he does some really interesting mathematics: https://math.ucr.edu/home/baez/
I'm also a big fan of Tai-Danae Bradley's work: https://www.math3ma.com/
Anyway, I hope people find these recommendations interesting or useful...
I never went back. I just started working.
I am happy to report I am back in school and will be FINALLY finishing my Computer Science degree but I have a very long 4 years ahead of me. Math is going to be hard.
What is encouraging is the thrill of when I get the answer right and most importantly knowing HOW I got there. It's (almost) better than sex.
However, I start a math course that meets two days a week in person soon.
I look relatively young with a hat on, that will keep me from feeling insecure about my appearance. I'm bald as Dwayne Johnson.
Remains to be seen but I won't let anything stand in my way of finishing. Just going to put my head down and do the work. Not socialize.
It's also based on an underlying knowledge graph, connecting concepts across various subjects like maths, machine learning, physics, etc. You can check the graph for transformer here: https://afaik.io/nebula?category=brickset&id=VLlOnZLl&mode=d... (only available on desktop...
Basically, it frees you from learning maths from scratch and just learning the prerequisites required to grasp the concept, and there are free resources attached.
Don't get me wrong, I can totally relate to the desire to relearn maths. One of the reasons that I'm building this tool is for me to relearn physics and know how to get there with my maths and cs background. I just feel in this specific scenario there might be more effective ways to learn in depth and have fun at the same time.
I assume it means such a graph connects the topics together as "pre-requisites". To understand A you need to already understand B and C, and to understand B you need to understand D and ... etc.
But the thing about such a graph is that really it must be a tree, not just a directed graph. Why? Because there cannot be cycles in it. If to understand A you need to understand B, and to understand B you would need to understand A, you could never understand either of them. Right?
It may be a tree. But it must be a DAG (directed acyclic graph).
1. https://www.youtube.com/@SawFinMath : She is a great Professor that walks through problems/solutions one step at a time, so that you can follow along. Has a bunch of Under Graduate course playlists like discrete math, calculus, (abstract or linear) algebra, statistics. highly recommended for the great pacing and solving a lot of problems live.
2. https://mathispower4u.com/ : Another professor who takes an open math textbook (free), and makes a course out of it. Its a little bit more difficult because of denser "pure math" material, but in return, you basically cover everything that a college usually would. He has courses like discrete math, calculus, graph theory, trigonometry, statistics, algebra, geometry etc. Also solves a lot of problems live.
I haven't really tried it, but apparently there is https://www.myopenmath.com/index.php which is sort of like exercism in that you follow along a textbook and solve problems. If someone has tried this, maybe they can share their experience.
It starts with algebra and works through calculus. There is a pretest before every section, so you know what you need to focus on and what you can skip.
https://www.amazon.com/dp/0521017076
Maths: A Student's Survival Guide: A Self-Help Workbook for Science and Engineering Students 2nd Edition by Jenny Olive
ISBN-10: 0521017076 ISBN-13: 978-0521017077
How about some free resources like Khan Academy?
Has anyone tried that course? Is it any good?
Math Academy is much more dense and on-point that Khan's. You don't have to sit through 15 minutes of video when 2 minutes worth of text explanation does it.
It uses spaced repetition for topics that you aren't good at, and for recently learned subjects.
The topic dependency tree and automatic progressing to "unlocked" topics is obvious in retrospect, but here it's done very cleanly and unobtrusively.
The initial evaluation test is worth its weight in gold. It eliminates the need to grind through things that you already know, but still covers any gaps.
I had kids on Khan for few weeks and it was a hassle. The pace was too slow, too much time sunk into trivialities and they were bored most of the time. With Math Academy they sit down, they do their 20-30 min of focused hands-on effort and they are done for the day.
I was a math major long ago, so it was more a case of relearning than initial learning for me but the built-in SRS helped a lot and so did the granularity of the lessons. It's head and shoulders above Brilliant, IMO.
If it didn't exist or I couldn't afford it, I'd probably go the OpenCourseWare approach. https://ocw.mit.edu/
The exercise sizes are also very small almost all the time. That means instead of a whole topic at the time and figuring out where you left the last time, you can do as much as you want at a time and not be restricted by artificial "chapters".
I have UK A level math but not Further Math, so up to basic calculus. But I forgot most of it and so Math Academy has me going through a lot of the Math Foundation units along the way.
I was initially put off by the monthly price, as it is quite steep. The clincher is that about a year before starting Math Academy I had gone through the Open University’s MST124/125 textbooks (covering the same stuff as Foundations). Except even after a year I’d already forgotten most of it.
Math Academy learning feels much more robust, since it includes spaced reviews and regular tests. I record things in Anki but it’s useful to have regular practice questions too. I also use ChatGPT to spell out things and find it works well at this level.
Some things I’d like Math Academy to have:
- ability to skip lessons (I don’t want to spend ages going over symbolic integration again)
- a reference page to track unlocked material, maybe with Anki integration
- fewer multiple choice questions and more in depth problems
- proof-based math. I’m told this is coming but the degree-level courses have missed their estimated due dates.
I will definitely finish Math for ML and then do linear algebra and multivariate calculus. You’d still need a good textbook to do them rigorously, but I think Math Academy sets you up well.
K.A. is great and I still use with my kid, but M.A. is more condensed and to the point for my needs. I was properly guided through the first program choices according to my profile, and the diagnostic exam you start with was perfect to highlight what I actually need to work on given my limited time.
Explanations and courses are super condensed, with the right amount of example and pedagogy that clicks for me.