5 ms·

Notes for courses taken at Harvard (2015-2019)

168 points by E-Reverance 6y ago

ipunchghosts 6y ago
From the authors website... "These notes are of pretty poor quality, since with I was lost with high probability when I wrote them"
- E-Reverance 6y ago
  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/ https://dec41.user.srcf.net/notes/
  - shuckles 6y ago
    Arun Debray has notes from his undergraduate and graduate programs in mathematics here: https://web.ma.utexas.edu/users/a.debray/lecture_notes/ https://web.ma.utexas.edu/users/a.debray/lecture_notes/
    - E-Reverance 6y ago
      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.
      - shuckles 6y ago
        You could presumably email Arun and re-compile: "If you want to look over the .tex source for any of these notes, please send me an email."
  - enugu 6y ago
    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.
  - emmanueloga_ 6y ago
    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 https://en.wikipedia.org/wiki/Academic_term#United_Kingdom
- E-Reverance 6y ago
  (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/ https://dongryulkim.wordpress.com/notes/course_notes/
- tkgally 6y ago
  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.
a1pulley 6y ago
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 :-)
- E-Reverance 6y ago
  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/ https://dongryulkim.wordpress.com/notes/course_notes/
andi999 6y ago
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?
- 0xdeadb00f 6y ago
  Perhaps they're shorter modules than usual? That does seem pretty intense to me
xendop 6y ago
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 http://abel.math.harvard.edu/pamphlets/courses.html
E-Reverance 6y ago
The mod probably should put back the word math in the title
- 0xdeadb00f 6y ago
  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).
  - pc86 6y ago
    "There are four physics courses, so having 'Math courses' in the title is pedantically incorrect, so I will remove it."
gadders 6y ago
Anyone seen something like this for medicine? I'd look to show my daughter that wants to be a medic...
- nosianu 6y ago
  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.
  - gadders 6y ago
    Fair point about not googling but personal recommendations still have a place.
scscsc 6y ago
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.
- WalterBright 6y ago
  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.
  - lukeramsden 6y ago
    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. [0] https://paircast.io/ https://paircast.io/
  - deleted 6y ago
    [deleted]
  - zerr 6y ago
    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.
    - WalterBright 6y ago
      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 :-/
Zealotux 6y ago
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.
- aesyondu 6y ago
  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.
  - Zealotux 6y ago
    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?
    - ivan_ah 6y ago
      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_preview.pdf https://minireference.com/static/excerpts/noBSmath_v5_previe... Concept map: https://minireference.com/static/conceptmaps/math_concepts.pdf 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.pdf https://minireference.com/static/excerpts/noBSLA_v2_preview.... Concept map: https://minireference.com/static/conceptmaps/linear_algebra_concepts.pdf 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.
- vansul 6y ago
NPDW 6y ago
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). http://dec41.user.srcf.net/notes http://dec41.user.srcf.net/notes
- ruang 6y ago
  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.
  - NPDW 6y ago
    He, infamously, wrote these notes realtime in lectures.
    - montalbano 6y ago
      To add, here is an interesting resource on how one might go about doing that using Vim and LaTeX: https://castel.dev/post/lecture-notes-1/ https://castel.dev/post/lecture-notes-1/
      - necrotic_comp 6y ago
        This is fantastic. Writing notes has always been a bugbear of mine, because 1) my handwriting is terrible and 2) writing notes takes me out of the lecture. It seems like this is more than fast enough to keep up with the lecture and have something to review properly after the lecture is over.
      - part1of2 6y ago
        >> These lecture notes — including figures — are made while attending the lecture and have not been edited afterwards. This is truly incredible to me.
makach 6y ago
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.
vincentchu 6y ago
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.
- strikelaserclaw 6y ago
  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.

168 points by E-Reverance 6y ago

From the authors website... "These notes are of pretty poor quality, since with I was lost with high probability when I wrote them"

E-Reverance 6y ago
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/ https://dec41.user.srcf.net/notes/
- shuckles 6y ago
  Arun Debray has notes from his undergraduate and graduate programs in mathematics here: https://web.ma.utexas.edu/users/a.debray/lecture_notes/ https://web.ma.utexas.edu/users/a.debray/lecture_notes/
  - E-Reverance 6y ago
    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.
    - shuckles 6y ago
      You could presumably email Arun and re-compile: "If you want to look over the .tex source for any of these notes, please send me an email."
- enugu 6y ago
  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.
- emmanueloga_ 6y ago
  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 https://en.wikipedia.org/wiki/Academic_term#United_Kingdom
E-Reverance 6y ago
(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/ https://dongryulkim.wordpress.com/notes/course_notes/
tkgally 6y ago
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.

a1pulley 6y ago

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 :-)

E-Reverance 6y ago
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/ https://dongryulkim.wordpress.com/notes/course_notes/

andi999 6y ago

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?

0xdeadb00f 6y ago
Perhaps they're shorter modules than usual? That does seem pretty intense to me

xendop 6y ago

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 http://abel.math.harvard.edu/pamphlets/courses.html

E-Reverance 6y ago

The mod probably should put back the word math in the title

0xdeadb00f 6y ago
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).
- pc86 6y ago
  "There are four physics courses, so having 'Math courses' in the title is pedantically incorrect, so I will remove it."

gadders 6y ago

Anyone seen something like this for medicine? I'd look to show my daughter that wants to be a medic...

nosianu 6y ago
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.
- gadders 6y ago
  Fair point about not googling but personal recommendations still have a place.

scscsc 6y ago

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.

WalterBright 6y ago
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.
- lukeramsden 6y ago
  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. [0] https://paircast.io/ https://paircast.io/
- deleted 6y ago
  [deleted]
- zerr 6y ago
  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.
  - WalterBright 6y ago
    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 :-/

Zealotux 6y ago

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.

aesyondu 6y ago
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.
- Zealotux 6y ago
  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?
  - ivan_ah 6y ago
    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_preview.pdf https://minireference.com/static/excerpts/noBSmath_v5_previe... Concept map: https://minireference.com/static/conceptmaps/math_concepts.pdf 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.pdf https://minireference.com/static/excerpts/noBSLA_v2_preview.... Concept map: https://minireference.com/static/conceptmaps/linear_algebra_concepts.pdf 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.
vansul 6y ago

NPDW 6y ago

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). http://dec41.user.srcf.net/notes http://dec41.user.srcf.net/notes

ruang 6y ago
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.
- NPDW 6y ago
  He, infamously, wrote these notes realtime in lectures.
  - montalbano 6y ago
    To add, here is an interesting resource on how one might go about doing that using Vim and LaTeX: https://castel.dev/post/lecture-notes-1/ https://castel.dev/post/lecture-notes-1/
    - necrotic_comp 6y ago
      This is fantastic. Writing notes has always been a bugbear of mine, because 1) my handwriting is terrible and 2) writing notes takes me out of the lecture. It seems like this is more than fast enough to keep up with the lecture and have something to review properly after the lecture is over.
    - part1of2 6y ago
      >> These lecture notes — including figures — are made while attending the lecture and have not been edited afterwards. This is truly incredible to me.

makach 6y ago

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.

vincentchu 6y ago

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.

strikelaserclaw 6y ago
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.