1 introduction topology is simply geometry rendered exible. but if we wish, for example, to classify surfaces or knots, we want to think of the objects as rubbery. can be addressed to prof. more is said about all of the courses in the diagram and the math placement recommendation in what follows. the book is available online as a pdf file and is suitable for advanced undergraduate or graduate students who have a solid background in calculus and linear algebra. 22a am 22b each student receives a math placement recommendation that indicates either math ma or math 1a or math 1b or the column with math 18- 55 and am22a. in geometry and analysis, we have the notion of a metric space, with distances speci ed between points. a student should make an appointment to talk with him. the book also harvard math pdf contains many exercises and. courses in mathematicsthis document gives a brief description of the various courses in calculus and some of the intermediate level courses in mathematics. cliff taubes harvard. it provides advice and pointers for planning your course selections. questions can also be addressed to wes cain 2. brief course descriptions the following briefly describes the courses for first year students. advanced calculus by shlomo sternberg is a comprehensive and rigorous textbook that covers topics such as differential forms, integration, manifolds, lie groups, and homotopy theory.