Background: Math Essentials: Undergraduate 100-level calculus. 300 or 400 level linear algebra course that includes singular value decomposition. I used Gilbert Strang's Linear Algebra and Its Applications back in early antiquity. It is still in print. There are great lectures by Strang at MIT's Open Courseware

• CIS520 - Machine Learning. Ben Taskar or Lyle Ungar
  This is the course to take on macahine learning. Not easy.
• CIS521 - Artificial Intelligence. Ben Taskar or Lyle Ungar
  Standard intro to AI; mot much machine learning.
• CIS620 - (Advanced) Artificial Intelligence
  Differs from year to year
• EE674 - Information Theory
  Santosh Venkatesh. Strong, extremely well taught, but not easy introduction to information theory. challenging.
• MATH360,361 - Elementary Analysis/Advanced Calculus
  Andy Schein writes: I view 360 as a hurdle that must be overcome in order to prepare for 361. 361 is a real gem of a course introducing the Jacobian, the Hessian, constrained optimization with Lagrange multipliers, advanced integration theory and other things you have probably seen in papers or courses but didn't know where to learn about. There is a 500 level version of this course which I attempted to audit at one point, but was made to feel unwelcome as an auditor by the particular professor that semester. I have heard conflicting reports about whether the 500 level version is too much harder than the 300 level version. The 300-level version is quite manageable with a steady stream of homework's to complete. I wish I had taken/audited this series my second year. Students with engineering degrees from countries other than the U.S. may have already seen enough of this material. U.S. Computer Science students on the other hand are often weak on continuous mathematics.
• STAT511 - Statistics for Business and Economics Lawrence Brown
  The most useful course at Penn on Statistics (and probably on ML as well). This is an applied Statistics course that will help you analyze data sets and give a strong foundation in the concepts of Statistics. Many people take the probability course before it STAT 510.
• STAT520 - Econometrics
  Regression. Good stat course; not just for economists.
• STAT530 - Probability J. Michael Steele
  People with a mathematical bent love Steele's courses. Those who lack a math orientation complain that it is too fundamental and not sufficiently applied to be of use to most CS majors.
• STAT550/551 - Mathematical Statistics
  This is a core course in the Statistics Ph.D. program at Wharton. It should only be taken by those with advanced calculus or analysis background (e.g. MATH360/361) and at least a 100 level background in statistics and probability.

Much of this was written by Andy Schein, and is becoming a little dated; feel free to email me for current recommendations.

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ungar@cis.upenn.edu