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There are some great notes on Mathematics taken from a former student at Cambridge (now doing a PhD at Harvard).
They are ridiculously good quality and lecturers had to ask Dexter to take down notes a term at a time to ensure students weren't skipping lectures.
The notes cover a lot more than what a standard student would do over 3 years undergrad + 1 year graduate (masters).
> lecturers had to ask Dexter to take down notes a term at a time to ensure students weren't skipping lectures
This is just... Stupid. Instead of admitting what a poor job you're doing, you're trying to suppress a student, unpaid student, that did a better job than you. (the you is of course the lecturer)
Anecdote: I was a professor of Computer Science from 2004 to 2006, for two years. I was teaching Compilers. I was 25 years old when I started, and Compilers was the worst possible course to teach. I was paid the miserable sum of 1,600 eur per year, which is why the usual "university mafia" wasn't interested in putting someone else in that position (it happened at the end of my second year anyway, when the course was assigned to a full-time professor).
I didn't want my students to pay $150 for the book, as this was Italy in early 2000s and students didn't have a lot of money (probably true today), so I created a big handout book that they could download and print, free of charge, and released it with a Creative Commons license. Or you could order the printed version on Lulu (although, for some reason, this one had to have an "all rights reserved") [0].
Anyway, at some point a professor in the Math department threatened me because students were using my handout to study regular expressions, and it was (in his mind) hurting the sales of the book they were using for his course; that book was of course authored by the professor, and he was making some money from it. How shameful.
Oh, yes: of course I ignored the threats.
[0]: https://www.lulu.com/en/ca/shop/simone-brunozzi/dispense-lab...
> I was paid the miserable sum of 1,600 eur per year, which is why the usual "university mafia" wasn't interested in putting someone else in that position
> Anyway, at some point a professor in the Math department threatened me because students were using my handout to study regular expressions, and it was (in his mind) hurting the sales of the book they were using for his course; that book was of course authored by the professor, and he was making some money from it. How shameful.
It sounds like you missed a potential revenue stream here haha! The fact that the math professor was mad about it meant that you had a potential market!
Also, aren't regex just documented everywhere on the internet? Maybe not in Italian...
Everything is on the internet - it doesn't eliminate the need from students to have a textbook of sorts.
While I have nothing but great things to say about my time at university, I always found it comical how grounded they were in their traditions.
Even under lockdown they refuse to record lectures, forcing the student to make sure they attended their 9am Saturday lecture, or miss the lecture and most definitely not understand any future lectures.
This becomes even more comical when you realise the lecturer is just reciting their own lecture notes and writing out the equations on the blackboard (not whiteboard of course!). However, I will always admire Professor Tim Gowers for teaching an entire Analysis course with no lecture notes and coming up with all of the proofs on the spot.
These are great. I wonder why he didn't just handwrite the notes. These are much better, but they seem like they would take a long time unless you can type latex quickly.
He, infamously, wrote these notes realtime in lectures.
To add, here is an interesting resource on how one might go about doing that using Vim and LaTeX:
That's a great endorsement for marketing his notes as an accessible alternative to a Canmbridge education. Sad that the professors are so jealous and petty.
It may not seem obvious to everyone, but the value is taking the notes (helps learning significantly), not reading them without context after the fact.
People who are interested in learning a subject without attending lectures would be better served by a textbook in the field.
I kept my notes from college. They're pretty much useless today because there's no context.
If I had had the foresight to bring along a cassette recorder, that would have been the context. But I didn't, and neither did anyone else. Of course, there's no way I could have afforded the large number of cassette tapes, either, so the point is moot.
It's too bad all those lectures are lost to history.
It's interesting to me that no one had a cassette recorder in class. When I was working on my degree in the mid 90s nearly everyone had a recorder on their desk while they were taking notes. I didn't record every class or even every lecture, I focused mostly on the topics/lectures where I had difficulties. If I 'got it' I usually recorded over that tape.
I may even have a box of them somewhere around here in the barn.
> It's interesting to me that no one had a cassette recorder in class.
Not too surprising given that a cassette tape in the 70's cost several dollars (equivalent to maybe $20 today). It was so expensive it simply didn't occur to people to record such things.
It's like photos. The cheapest 35mm photo cost a buck an image, and this was for slides, not prints. It's why photos of my college career are nearly non-existent. And movie film - forget about it.
> I may even have a box of them somewhere around here in the barn.
I recommend digitizing them. Cassettes don't last forever, and you'll probably enjoy hearing them again.
I'd say it depends on the lecturer and how the lecture is held. Some read it specifically for the notes to be taken. And it is assumed that students would learn from these notes afterwards, which are much more concise compared to textbooks.
My notes were usually just copying whatever the prof wrote on the blackboard while lecturing. It was usually all I could do to keep up.
But reading the notes later would cause me to recollect what was said, and so the notes were very useful. Unfortunately, enough time has passed that I've forgotten what was said, and only have the notes.
It's like watching a sitcom with the sound turned off :-/
Maybe a "Paircast[0] for lecture notes"-type application could help with this. Records audio, maybe even transcribing it (if high enough quality), while also tracking how the notes relate to the audio across the time of the lecture.
As for lectures in the past, it is a shame we may have lost them, as it seems to me (purely speculatively) that the lectures from the 70s and 80s seemed to make a whole different class of programmers to the ones of today. Or maybe it was the tinkering and not the lectures, who knows.
But there is a lot of value in possibility to look what's being done at other courses after you finished yours.
If Dongryul would add the latex files to the repo and use more descriptive folder names, I suspect that he'd see some pull requests come in to fix errata. If the coursework started at an undergraduate level, I would have been happy to help :-)
There are some undergraduate courses like Math 55a. For a list with descriptive names, they are on his old website https://dongryulkim.wordpress.com/notes/course_notes/
Does anyone have adequate resources to share on learning Math "from scratch"? I must shamefully admit that anything beyond the basic symbols is entirely foreign to me.
The sources and advice linked below are helpful. Given that we have no idea what level "from scratch" means, or your preferred learning style, I'm upvoting Khan academy on the basis of their map/pathway/dependency graph. Shows how topics build on each other and gives you a framework.
The other piece of general advice is to define what it means to learn math. You only learn math by solving problems with it. Do the exercises. The theory is only there to enable you to do the exercises/problem sets.
preferably on paper and pencil (yes even for sets of differential equations where you have to track 14 complex variables over multiple steps and you fuck up your answer because you mis-copied an exponent on line 12 of 35 lines. It is slow and difficult on paper, and that is an advantage when you are learning).
[Warning Advice from a Beginner]
I started self learning Maths (number theory) this year from scratch I am extremely slow but I am progressing. My advice is take a textbook of the kind of maths you want to learn and skip the theory jump straight to the exercises do them and compare the answers, if your answers are wrong then read the theory. Also when doing exercises you can reference the theory but don't read the theory alone.
One thing that will block you is notation, if you are a coder Math As Code [0] is great way to decode the advanced Mathematical symbols, It helped me start reading math:
This[0] was posted up on here a while ago - has some good book recommendations for teaching yourself maths (assuming you remember some basics from school[1]).
I got a few of them and whilst they may have gathered some dust... They seem great! Also obliged to recommend Khan Academy and the 3Blue1Brown youtube channel - but they are probably best for fun/inspiration
[0] 'Mathematics for the adventurous self-learner' -https://www.neilwithdata.com/mathematics-self-learner
[1] If I knew zero maths I'd probably check out the basics on Khan Academy or maybe get a tutor
It might help to clarify what type of Math you want to learn. E.g., right now I'm learning discrete math to improve my understanding of algorithms.
You're right, I'm a developer so anything that could help me with algorithms is welcomed. I also have a growing interest in 3D so I suppose linear algebra?
I have two books you might be interested in (written by me).
If you want to review math fundamentals (high school math), the No Bullshit Guide to Mathematics will be good for you—condensed material for adult learners. Preview: https://minireference.com/static/excerpts/noBSmath_v5_previe... Concept map: https://minireference.com/static/conceptmaps/math_concepts.p...
For linear algebra, check No Bullshit Guide to Linear Algebra. Preview: https://minireference.com/static/excerpts/noBSLA_v2_preview.... Concept map: https://minireference.com/static/conceptmaps/linear_algebra_...
You can find them in print on the amazons and in digital form on gumroad.
Oh and as a general tip: make sure to do some problems while studying/reviewing. It's super important to put things into action, otherwise it's very easy to read and think you understand despite not having integrated the new knowledge. A few problems here and there though, and you can make very fast progress and remember things in the long term. As they say, math is not a spectator sport.
From the authors website...
"These notes are of pretty poor quality, since with I was lost with high probability when I wrote them"
That does raise the question though as to why the notes have garnered enough attention to necessitate such a comment from the author. Maybe it isn't a good idea to use these notes as reference, but they are of some value. At the very least it is interesting to see that such a large repository of notes of this form exists. The only other collection that is similar to this that I know of is https://dec41.user.srcf.net/notes/
It is the first time I hear about "Michaelmas" and "Lent" terms [1]. Why not using simple ordinal names?
1: https://en.wikipedia.org/wiki/Academic_term#United_Kingdom
Arun Debray has notes from his undergraduate and graduate programs in mathematics here: https://web.ma.utexas.edu/users/a.debray/lecture_notes/
Dumb question:
Is there a way to make the margins wider (preferably free)? This may sound odd but I dislike moving my eyes horizontally, and I'd like to take advantage of the notes you've recommended somehow.
Thanks for linking to such a great resource. I am somewhat awed by how much he has learned in his undergrad years.
Also, thanks to other posters too. The two other notes sites are also great.
(Full context for those who are encountering this)
"These are live-TeXed notes for the courses I took/am taking at Harvard. Typing up my notes with a computer is mostly inspired by this site (which is also a good resource). The purpose of writing up these notes is primarily to use as a reference for myself, and I advise great caution to those trying to learn actual math from them. Brackets indicate that you must be extra cautious when consulting them. If you find anything wrong (mathematically wrong claims or even typos) please notify me by email." https://dongryulkim.wordpress.com/notes/course_notes/
At a glance, they look pretty good to me. If I had taken notes of that quality when I was a graduate student in mathematics forty years ago, maybe I would have become a mathematician after all.
This is not how I make notes. This is way beyond my note-taking skills and I cannot say anything else than I am deeply impressed!
High quality notes is of highest value to yourself, or others, as has been proven many times before. My favourite example is the notes taken by Marcel Grossmann, used by Albert Einstein.
The mod probably should put back the word math in the title
Mods changing titles and links has always seemed sort of arbitrary to me. Most of the time I don't see the use (I understand it can be useful, but the times I've seen it done it usually hasn't).
"There are four physics courses, so having 'Math courses' in the title is pedantically incorrect, so I will remove it."
You can take 11 modules in one semester? How do you do that? Even assuming they are all 2h per week, do you have to look at the academic calender (or timetable) and try to find all courses which dont overlap?
Perhaps they're shorter modules than usual? That does seem pretty intense to me
Anyone seen something like this for medicine? I'd look to show my daughter that wants to be a medic...
There is tons and tons of great content on sites like Youtube (search for what you want: anatomy, neurology, physiology, organic chemistry, biochemistry, genetics, statistics,...) or courses on edx or Coursera (mostly free without the useless "certificates"). Never mind even more sites Google will show you.
Some of it dumbed down, but lots of it is from professionals and lecturers for actual medical students. I won't post examples because there really is so much that it's useless for me to do so, apart from pointing out the sites I used myself.
On another note, I continue to be amazed by the fact that so often I see people asking in forums instead of Google. It shows how important humans are to humans, no matter what service machines will offer, or how great recorded content is, live content from/with an actual human will be preferred to a large degree.
Just yesterday in some forum somebody asked a question to find a certain novel. I copy-pasted his exact question into Google and found the novel immediately. This is quite common. Is this a topic of discussion at companies like Google? No matter the automation, a lot of humans are very reluctant to interact with the machine(s). It seems to me this is quite an obstacle for companies on the business of putting machines in front of customers instead of humans.
Fair point about not googling but personal recommendations still have a place.
Seems like a solid resource. In case others were wondering which courses were what - there's an index here http://abel.math.harvard.edu/pamphlets/courses.html
This is an impressive course load ... looks like he started by taking Math 55 freshman year, reputedly the hardest freshman math course in the country.
I'm not 100% certain, but i believe he ranked pretty highly in IMO (maybe a gold medalist). A Lot of those caliber guys take grad level courses in sophomore year so I'm sure math 55 isn't as tough for them.