Class
meets: MW4(2:00-3:20PM), in ARC-207.
Text:
Real Analysis: Modern Techniques and Their Applications, by J. Folland
(Wiley-Interscience; 2nd edition, 1999. ISBN-10: 0471317160)
Instructor:
Dr. Zheng-Chao Han
Office Hour:
T9:30--11:30am, or by appointment, in Hill Center-522 or via Zoom.
Email:
zchan AT math dot rutgers dot edu.
Canvas
The course will use Canvas for all course material during the se
mester.
All enrolled students should have automatic access to the site after logging into Canvas.
Current information about syllabus and homework will be found there.
Our approach: There are different ways to develop the material of real analysis. Some develop it from a very general framework, arrange topics in a most economical way, and provide the statements and proofs in forms as general as possible. While abstraction and generalization are very important aspects of analysis that a student ought to learn, the ability to see through the central ideas of a proof, and apply them in concrete situations is equally important, if not more so. We will try to convey both of these aspects in our presentation.
While the arrangment of topics in textbooks tends to give the impression of seamless flow, the creation of the ideas/theories generally did not follow this route, nor would most people learn/understand a theory this way. So we will allow ourselves to move back and forth among the ideas, not necessarily completing the whole picture on first presentation. For this reason, I may alter the order of presentation of topics from the text from time to time.
Regular Assignments: Working out problems is especially crucial in a subject such as real analysis. You would not really learn much by merely coming to all the lectures and taking good notes. So I advise you to form the habit, from the very beginning, of working out problems on a regular basis and of developing examples and counter-examples to delineate key concepts and theorems without consulting the complete details in references.
Problem sets are due in convas on the announced date. Any late submission of homework has to have the prior agreement from the instructor.
You are encouraged to discuss the course material and problems with fellow students. You may also use AI tools to assist your learning and literature searching. This kind of discussion or assistance should be limited to the strategy formulation stage, not at the write-up stage. Remember, of course, that plagiarism is absolutely forbidden; when you write up assignments and put your name on them, you are certifying that you wrote them in your own words and by yourself, and you need to make explicit acknowledgement (provide name(s) of classmate(s) with whom you have had discussion with or the specific prompts used for AI assistance) in the problem(s) for which you have engaged in some discussion or sought assistance. In addition, if you consult any other source (such as a web page or AI generated responses, solutions fro m a previous semester, etc.) in the preparation of homework, you must acknowledge this by citing that source. Failure to observe these restrictions will be treated as a violation of the Rutgers ACADEMIC INTEGRITY POLIC Y.
Your grade will be determined as follows: