Introduction to Modern Analysis: Math 523H, Spring 2017

Class Meeting : TuTh 11:30--12:45, LGRT 177

Instructor : Luc Rey-Bellet

Office :  1423 J LGRT
Phone :  545-6020
E-Mail :   luc <at>
Office Hours :   Th 9:30-10:30   Fr 10:00--11:30,   or by appointment.

Course Web page: Please bookmark The page will be updated regularly. Check it often.

Syllabus: This course is the first part of the Introduction to Analysis sequence (Math 523 and Math 524). At its core analysis deals with mathematical objects such as functions, limits, sequences, series and integrals. The ideas and objects in analysis play an important role in differential equations, probability, numerical analysis, geometry, and in most areas of applied mathematics. But in studying analysis one learns that mathematics is much more than just a set of methods that work. Students will be asked to construct proofs, sometimes long ones, and this will open the door to a much deeper understanding of the nature of mathematics. In Math 523 we deal mostly with "classical analysis" which is a set of ideas and objects formalized in the 19th century. Modern analysis (roughly speaking early 20th century) objects will appear in Math 524. Topics covered in this class are

Textbooks and references: We will follow the textbook only loosely. There are many textbooks to chose from on the topic. The official textbook is suitable for self-learning for "beginners". It is highly recommended you borrow another text and spend some time reading through it.

Official Textbook:

Other recommended textbooks:

Grading and Exams: Your grade will be based on homework's (%30), a mid-term exam (%30), a final exam (%30) and class attendance (%10).

Homework: Homework will be assigned regularly (essentially every week) and graded.