I have a BSc degree in pure mathematics and i am graduate student in Operations research. I will have a course on "portfolio management". I am looking for some book/lecture notes/online course recommendations on the subject, if possible with exercises & solutions. (I came from a math background so i prefer rigorous materials) (here is the content of the first 5 lectures); i have no idea about finance, economy or portfolio management. Thank you.
Although you describe your class as Portfolio Management, the content of the first 5 lectures you linked to would generally be part of a first introductory course in Portfolio Theory in a US university (in my opinion). Portfolio Management would be a second, more advanced course, with additional theory but also additional industry and practical considerations. The books mentioned by madylin are very good for Portfolio Management but they might be too advanced for your class. In the CFA program Portfolio Theory is in level 1 and Portfolio Management is in Level 3.
A common textbook for Portfolio Theory would be Elton, Gruber, et al: Modern Portfolio Theory and Investment Analysis.