MATH 8610: Mathematics of Data Science

This spring, I’m teaching a graduate-level special topics course called “Mathematics of Data Science” at the Ohio State University. This will be a research-oriented class, and in lecture, I plan to cover some of the important ideas from convex optimization, probability, dimensionality reduction, clustering, and sparsity.

Click here for a draft of my lecture notes.

The current draft consists of a chapter on convex optimization. I will update the above link periodically. Feel free to comment below.

UPDATE #1: Lightly edited Chapter 1 and added a chapter on probability.

UPDATE #2: Lightly edited Chapter 2 and added a section on PCA.

UPDATE #3: Added a section on random projection.

UPDATE #4: Lightly edited Chapter 3. The semester is over, so I don’t plan to update these notes again until I teach a complementary special topics course next year.

UPDATE #5: As mentioned above, I’m teaching a complementary installment of this class this semester. I fixed several typos throughout, and I added a new section on embeddings from pairwise data.

UPDATE #6: Added a section on the clique problem.

UPDATE #7: Added a section on the Lovasz number.

UPDATE #8: Added a section on planted clique.

UPDATE #9: Added sections on maximum cut and minimum normalized cut.

UPDATE #10: Added a section on k-means clustering.

UPDATE #11: Started a chapter on compressed sensing.

UPDATE #12: Started a section on uniform guarantees.

UPDATE #13: Started a chapter on matrix analysis.

UPDATE #14: Started a section on matrix representations.

UPDATE #15: Started a section on spectral theory.

UPDATE #16: Added to the section on spectral theory.

UPDATE #17: Added more to the section on spectral theory.

UPDATE #18: Added even more to the section on spectral theory.

UPDATE #19: Finished the section on spectral theory and added a section on tensors.

UPDATE #20: Finished the section on tensors.

UPDATE #21: Added a section on random graphs.