100313 Real Analysis

Real Analysis is one of the core advanced courses in Mathematics curriculum. It introduces to measures, integration, elements from functional analysis, and the theory of function spaces. Knowledge of these topics, especially Lebesque integration, is instrumental in many areas, in particular for stochastic processes, partial differetial equations, applied and harmonic analysis, and is a prerequisite for the graduate course in Functional Analysis. The course is suitable for undergraduate students who have taken Analysis I, Analysis II, and Linear Algebra I; it should also be taken by incoming students of the Graduate Program in the Mathematical Sciences. Due to the central role of integration in the applied sciences, this course provides an excellent foundation for mathematically advanced students from physics and engineering

Instructor of Record:	Peter Oswald
Email:	p.oswald@jacobs-university.de,
Phone:	200-3179
Office hours:	Tuesdays 2-3:30pm (or by appointment) in Research I, 113

TA:	TBA
Email:	TBA

Lectures :

Tue 11:15am-12:30pm and Th 9:45-11:00am in East Hall 8

• [LL] E.H. Lieb, M. Loss, Analysis, 2nd edition, AMS, Providence RI, 2001 (covers most of the course in chapters 1-2 and 4-6, is with focus on applications to the theory of weak solutions for variational PDEs, on reserve).
• [F] G.B. Folland, Real Analysis , Wiley-Interscience, New York, 1999 (more advanced, more details on abstarct measure theory, has also chapters on topological spaces, functional analysis, probability theory).
• [R] W. Rudin, Real and Complex Analysis , MacGraw-Hill, Boston, 3rd edition, 1987 (chapters 1-9 cover the main parts of the course).

Weekly homework will be announced in class and posted online. Check the website on a regular basis! Written solutions need to be turned in on the due date and in class (usually on Thursday of the following week. No late homework will be accepted. Note: Homework is your individual work, copying from others is against our Code of Academic Integrity, and will in the end backfire.

A Midterm Exam (probably during the week after the Fall reading days) and a Final Exam will be given. Exact dates and details about the exams will be given in class at a later time.

Only valid and timely excuses (as regulated by Jacobs University policies, and confirmed by the registrar) will be accepted if you miss homework deadlines, or exams. The golden rule is to approach me before things go wrong, "negotiations" after things happened are not productive.

• The final grade will be computed from the weighted average of percentages of maximal scores with the weights

  Homework:	30%
  Midterm Exam (in Week 8 or 9):	30%
  Final Exam (examination period):	40%

  
  according to the following table:

  Cutoff score:	95%	90%	85%	80%	75%	70%	65%	60%	55%	50%	45%	40%
  IUB Points:	1.0	1.33	1.67	2.0	2.33	2.67	3.0	3.33	3.67	4.0	4.33	4.67