From the part on "Intro Classes" --<p>"The introductory courses for math majors are MAT 215: Single Variable Analysis, MAT 217: Linear Algebra, and MAT 218: Multivariable Analysis. Like the great majority of math courses at Princeton, these three courses are theoretical and proof-based. [...] These three are usually the first math classes that math majors take at Princeton. However, the math department is very flexible in allowing advanced freshmen to skip some or all of these courses."<p>MAT 215 is classical analysis (epsilon-delta, differentiability, etc.). Its own course page (<a href="https://www.math.princeton.edu/undergraduate/course/mat215" rel="nofollow">https://www.math.princeton.edu/undergraduate/course/mat215</a>) advises regular students considering taking the course:<p>"Typically students have a 5 on the BC calculus exam together with a math SAT score of at least 750."<p>The concept of being so advanced as a freshman that you <i>skip</i> this class is pretty amazing to me. I know those folks are out there, but skipping honors analysis really brings it home.<p>I struggled through another Ivy's version of Honors Analysis for math majors (out of baby Rudin) as a beginning grad student.
For those interested in the "Probability and Statistics" portion of the guide, Princeton recently created a certificate program in statistics and machine learning that has some more updated information on courses: <a href="http://sml.princeton.edu/" rel="nofollow">http://sml.princeton.edu/</a><p>I'm pursuing the certificate right now and the courses have been great so far. Princeton's known for having a rather theory-heavy approach in their quantitative classes but I've found a good balance with applications in some of the classes (COS 424, COS 402).
The intro courses have changed slightly. Now, there is the 215-217 track (analysis + linear algebra) and the 216-218 track (basically honors version). Most math majors take the latter.<p>The algebra introductory courses have different numbers, and are now 345-346 instead of 322-323. There is now an advanced graph theory class (477) that follows the introductory one. Also, there is a theoretical machine learning class (COS 511) and the algorithms/complexity graduate sequence (COS 522-523) may be relevant as well.<p>I will probably update these changes on the website sometime in the near future...
I've always liked Tim Gowers' welcome to incoming students to the Cambridge Mathematical Tripos program. Lots of great tips on learning/studying math, asking intelligent questions, etc.<p><a href="https://gowers.wordpress.com/2011/09/23/welcome-to-the-cambridge-mathematical-tripos/" rel="nofollow">https://gowers.wordpress.com/2011/09/23/welcome-to-the-cambr...</a>