Sanjeev Arora on rethinking the graduate algorithms course
[Below is a guest post from Sanjeev Arora on his redesign of the traditional graduate algorithms course to be a better match for today’s students. –Boaz]
For the last two years I have tried new ideas in teaching algorithms at the graduate level. The course is directed at first year CS grads, but is also taken by grads from related disciplines, and many advanced undergrads. (Links to course homepage, and single file with all course materials.)
The course may be interesting to you if, like me, you are rethinking the traditional choice of topics. The following were my thoughts behind the redesign:
- The environment for algorithms design and use has greatly changed since the 1980s. Problems tend to be less cleanly stated (as opposed to “bipartite matching” or “maximum flow”) and often involve high-dimensional and/or noisy inputs. Continuous optimization is increasingly important.
- As the last theory course my students (grad or undergrad) might take for the rest of their lives, it should somewhat fill in holes in their undergraduate CS education: information/coding theory, economic utility and game theory, decision-making under uncertainty, cryptography (anything beyond the RSA cryptosystem), etc.
- Programming assignments need to be brought back! CS students like hands-on learning: an algorithm becomes real only once they see it run on real data. Also, computer scientists today —whether in industry or academia—rely on subroutine libraries and scripting languages. A few lines in Matlab and Scipy can be written in minutes and run on datasets of millions or billions of numbers. No JAVA or C++ needed! Algorithms education should weave in such powerful tools. It is beneficial even for theory students play with them.
Sample programming assignments: (a) (compression via SVD) given a 512 x 512 grayscale image, treat it as a matrix and take its rank k approximation via SVD, for k=15, 30,45,60. Use mat2gray in matlab to render this new matrix as a grayscale image and see what k suffices for realistic recovery. (b) You are given S&P stock price data for 10 years. run online gradient descent to manage a portfolio (Lecture 16), and report what returns you get with various parameter settings.
Students are allowed to do a final project in lieu of a final, and many choose to apply algorithms to some real world problem they are interested in. Sample projects are also listed on the course page.
I welcome your comments, suggestions, and links to other relevant course materials on the web!