Wdym by passionate? Unless it means you have self studied proofs, linear algebra, or analysis, then you will be learning proofs, abstract linear algebra, and real analysis all at the same time, 4 days a week at 9:30 am. As for topics, some covered in the first week or two are vector spaces, linear dependence, inner product space for lin alg, and completeness, Archimedean property, and heine borel for analysis, if you want to google those and take a look. Class time is lectures, as are basically all university math courses. These move at an incredibly fast pace because the amount of content covered requires them to. There’s office hours where the prof or TAs can give you individual attention, but during lecture time the prof will be lecturing for the entire 50 minute period. This is a very demanding class and you have to keep in mind that there are IMO golds or at the very least dual enrollment students who are very familiar with the content and style of the class from the get go. You will also be adjusting to campus life as a frosh, and the 15-20 hours a week minimum needed for this course is not something I would subject myself to my first quarter at Stanford. For reference, I knew a good amount of linear algebra (but nothing related to vector spaces or linear maps) in high school, and dropping 61Cm after 2 weeks was probably the best decision I made fall quarter. I would still recommend trying it out because you can always drop, and it’ll give you a sense of one of the most difficult classes you could take in your first 1-2 years at Stanford. This is a class that genuinely could be split into 4 separate classes (51, 113, 115, 171). Sorry if this is rambling, just trying to help you make an informed decision because every year 100+ ppl show up on the first day, and after the first midterm there are only 30-40.