#110 overall
Discrete Differential Geometry
Carnegie Mellon University
3 recommenders · 3 threads · recommended in 3 years, 2020–2025 · score 3.9
A graduate-level course by Keenan Crane at Carnegie Mellon on discrete differential geometry, the study of geometric concepts such as curvature, meshes, and differential operators using discrete representations suited to computer graphics and geometry processing. Course assignments, slides, notes, and lecture videos are publicly available.
Commenters call it an accessible route into advanced geometry topics, praising Crane for making them easy to follow and for the freely available videos and notes.
Science & Engineeringadvancedfreevideo lectures#discrete differential geometry#meshes#computer graphics#geometry processing#crane
Recommendations by year
20062026
Suddenly HN has decided that they're not visual learners anymore. Too bad, Keenan Crane from CMU has the best video course series on Discrete Differential Geometry:
https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1...
https://www.cs.cmu.edu/~kmcrane/Projects/DDG
If you’re looking for some great content that is completely unrelated, I’d recommend either Keenan Crane’s Discrete Differential Geometry course (https://www.cs.cmu.edu/~kmcrane/Projects/DDG/ and https://brickisland.net/DDGSpring2021/) or Peter Shirley’s Ray Tracing in a Weekend Series (https://raytracing.github.io/). The former is a little more math heavy/in-depth, whereas the latter is a little more abbreviated. Both are super fun and expose you to some really exciting and powerful ideas from Computer Graphics.
I'm not a CMU student, but keep my eyes peeled for new research / resources published by Keenan Crane [1]. He has a knack for making advanced topics very accessible.
Notably, this semester's DDG course has recently finished, and all assignments [2], slides [3], and notes [4] are available on the course website. Lecture videos for the second half of the course have been posted publicly online [5], presumably due to the coronavirus situation. Talk about silver linings!
I can also recommend the book by Edelsbrunner on Computational Topology, with corresponding course notes [6].
[1] Keenan Crane's website: http://www.cs.cmu.edu/~kmcrane/
[2] Assignments: http://brickisland.net/DDGSpring2020/assignments/
[3] Slides: http://brickisland.net/DDGSpring2020/category/slides/?order=...
[4] Course Notes: http://www.cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf
[5] Lectures: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1...
[6] https://www2.cs.duke.edu/courses/fall06/cps296.1/
Keep us posted about the lectures. I don't find a personal website of you. Then I would have bookmarked it.
There are so many awesome lectures from other CMU courses like Andy Pavlo's Database, Keenan Crane's Graphics courses.
I so hope CMU records their intro courses and put them out in public.
I'm a bit disappointed as I didn't see some of my favorites here :D One of them has already been mentioned, but I'll add it anyway.
- Harvard Stat 110: awesome and somewhat challenging lecture series on probability. It goes into all the probability basics, but also goes into problem solving skill very often, so the problem sets tended to be hard as I recall it. But the nice thing is that a lot of it you can find the solutions which are very well written -- and for the exams as well. Also, the lecturer Joe Blitzstein won best professor at Harvard if I'm not mistaken. https://www.youtube.com/playlist?list=PL2SOU6wwxB0uwwH80KTQ6...
- Statistical Rethinking by Richard Malkreath: man this one will make you relearn statistics. And with a heavy bayesian flavor, which if you hadn't had the chance to learn, will bend your mind as well. You will learn to build models that can describe a lot of situations in the real world, and estimate the parameters from data. Cool stuff if you ask me. https://www.youtube.com/watch?v=BYUykHScxj8&list=PLDcUM9US4X...
- Frank Harrel's Bioistatistics for biomedical reasearch: Frank Harrel is the go to guy to understand how to use data in clinical trials and diagnostics research. His book Regression Modeling strategies is a gem that every data scientist should read. This lecture series is aimed at biomedical researches, ie. people without a strong background in theoretical statistics. In the lectures he talks about the best practices and pitfalls you'll come accross when doing and reading research, and also explain some R code to do a better job. Harrel also wrote some very important R packages i.e. Hmisc and rms. https://www.youtube.com/@bbrcourse6203/videos
- calling bullshit in the era of big data: this is a last year course so it is very laid back in the discussions. I didn't go through the whole thing. But what I watched I remember it was really nice and thought provoking. https://www.youtube.com/watch?v=A2OtU5vlR0k&list=PLPnZfvKID1...
- statistical learning by Hastie and Tibshirani: these are the guys that wrote the two main books on statistical learning. If one wants to get into DS, this is the place to start. https://www.youtube.com/watch?v=LvySJGj-88U&list=PLoROMvodv4...
- Discrete Differential Geometry by Keenan Crane: ok, I didn't see the whole thing, because it was above my understanding. But the graphics and images are so eye catching I almost wanted to just sit there watching. I'm pretty sure this and his computer graphics lectures are aso engaging as hell and hidden gems of the internet. https://www.youtube.com/watch?v=mas-PUA3OvA&list=PL9_jI1bdZm...
Out of this list, the books I am familiar with, are great (Hilbert-Courant, Spivak, Korner's books). At the same time, even with extensive mathematical training, I haven't read them from start to finish. I wouldn't even like to say "read". For someone who's not used to mathematical reading, some of these books require careful study. That means generating examples to understand results (theorems), trying your own conjectures, proving things yourself etc. Over time, one becomes familiar with most/all the material in a book but the knowledge might have been acquired through various books (and courses) over time.
Also, mathematics is a massive field. The first question would be what kinds of mathematics would you like to get better at. There are great books in analysis. If you are starting out with a solid calculus knowledge, try Abbott's Understanding Analysis [1] or Duren's Invitation to Classical Analysis [2]. For asymptotic methods in PDEs, try Bender and Orszag [3] which is a wonderful book. But again, this might not be your cup of tea at all and there are more abstract or formal books like Rudin's.
If you want to approach fields without a lot of machinery, graph theory books by Bollobas are great (but difficult). See his Modern Graph Theory book [4] as an example.
For linear algebra, one of my favorites (but it was after I already learned the subject) is Trefethen's Numerical Linear Algebra book [5]. Another beautiful topic is at the intersection of linear algebra and combinatorics. See Babai and Frankl's lectures freely available online.
Then there are wonderful topics in geometry. A massive mountain to climb would be algebraic geometry. For one starting point, see [6]. Differential geometry (Spivak's multi-volume work or Needham's differential forms book) is another wonderful area. I would recommend Crane's discrete differential geometry course at Carnegie Mellon [7] if you want a concrete introduction.
You might want to demystify a topic you have heard about. E.g. Galois theory and the unsolvability of quintic equations. You could look at [8] which guides your way through wonderful problems.
We haven't even touched huge swathes of mathematics including anything topological or number theory. Even within the topics mentioned above, once you start, your journey will take a life of its own and you'll encounter multiple books and papers opening up new sub-fields.
The only approach that worked well for me in the past was to get completely consumed by what one topic one was studying. This meant not getting distracted by multiple topics. Once one enters the workforce, this is very hard (or at least has been for me). Without knowing someone, it's hard to recommend anything but the advantage with topics like graph theory and combinatorics is that one needs less machinery (as opposed to something like algebraic geometry). These fields lead you to interesting problems very rapidly and one can wrestle with them part-time.
[1] https://www.amazon.com/Understanding-Analysis-Undergraduate-...
[2] https://www.amazon.com/Invitation-Classical-Analysis-Applied...
[3] https://www.amazon.com/Advanced-Mathematical-Methods-Scienti...
[4] https://www.amazon.com/Modern-Graph-Theory-Graduate-Mathemat...
[5] https://www.amazon.com/Numerical-Linear-Algebra-Lloyd-Trefet...
[6] https://www.amazon.com/Algebraic-Geometry-Approach-Mathemati...
[7] https://www.cs.cmu.edu/~kmcrane/Projects/DDG/
[8] https://www.amazon.com/Through-Exercises-Springer-Undergradu...