I am looking for online math courses for the foundation of Phd courses. Any suggestions will be appreciated??

hi.. please be more specific. A PhD course in what? algebraic topology? number theory? .. even "pure maths" is quite a big field.Even without hearing exactly what you want, I doubt you'll find anything really useful. Your best bet is to find online lecture notes for well established courses at decent universities or books on their recommended reading list.

Phd Finance

In terms of online lecture notes, you might want to check out MIT's OpenCourseWare site, especially the courses offered by the Sloan School of Management. But I agree with peterw, that even the lecture notes you may find there are not a good substitute for quality books and papers.

What works for me is to go to the nearest university research library, download a representative sample of papers that interest me, get completely confused by them, and then make a list of the concepts/ideas that I need to know in order to be able to read the papers. What's useful is to markup up the paper with the concepts and terms that I don't know about (cadlag or Snell envelope for example) and then google for some idea of where the concepts come from. I've actually found lecture notes not nearly as useful as books and review papers. What I've found to be useful is to go to Amazon and buy one thick book on the topic, and one thin book on the topic. The thick book goes into very rich detail, whereas the thin book does things very concisely.The other useful thing that I've found is to look for papers that talk about the history of the field (Rebonato does a very good job of this for interest rate models and Derman and Taleb's books are useful for this). This is useful for a number of reasons. First it's easier to spend the effort learning the stuff when you know that everyone else had a hard to to figure this out in the first place. Second, there is a huge amount of stuff that gets taught for historical reasons, which isn't that useful now. Examples are spending time with short rate models instead of LMM, spending a huge amount of time learning about complete markets when all real markets are incomplete. If you go to the latest research, it will be obvious what is useful and what isn't, and the foundational stuff for a Ph.D. should be geared toward literacy so that you can understand and expand on the latest researce. If you do the foundational stuff without look at the the latest research, you end up spending a lot of time on things that are of historical interest only.