### Foundations of Mathematical Analysis, 7.5 hp

**Syllabus: **The course deals with real numbers, theorems on continuous functions on compact sets, derivation and integration in R

^{n}, series of functions, uniform convergence, implicit functions. The course aims at giving a deeper understanding of the foundations of real analysis.

**Textbook: **Rudin, Principles of Mathematical Analysis, McGraw-Hill, third edition.**Complemetary material:** Ekedahl, Läsanvisningar till Analysens grunder, en, sv.

**Time and Place:** August 31–December 11, 2015. Distance.

**Instructor:** Yishao Zhou

**Exam: **It consists of two parts (i) a written part: three sets of homeworks, and (ii) an oral part. Roughly speaking, to pass the course you are required a satisfactory homework handed in on the assigned due date, and thereafter a successful oral which will take place after the last lecture. Delay for hand-ins is allowed but it will reduce your course grade. The details of grading can be found in grading policy.

**Practical notes:** The course will be running for about 15 weeks. An oral exam takes place in the week starting December 14. Each topic (12 in total) below corresponds to a quarter of the full time study week and three weeks for doing homework (PS1, PS2, PS3) which should be turned in on due time. They are divided in three blocks which will be apparent when you get your problems sets.

There is a News Forum which we can use for course information and suggestions from you and a Discussion Forum where you can ask questions, answer questions and discuss problems and ideas you have.