Introduction to Modern Analysis: Math 523H, Spring 2016
Class Meeting : TuTh 1:00--2:15, LGRT 141
Instructor : Luc Rey-Bellet
Office : 1423 J LGRT
Phone : 545-6020
E-Mail : luc <at> math.umass.edu
Homepage:
http://www.math.umass.edu/~lr7q
Office Hours : M 1:30-3:00
Tu 2:30--3:45, or by appointment.
Syllabus:
This course is the first part of an introduction to Analysis (the sequence Math 523 and Math 524). At its core
analysis deals with mathematical objects
such as functions, limits, sequences, and 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. On the other hand in doing analysis will learn that mathematics is much more than just methods
that work. Students will be asked to construct proofs, sometimes long one, and this will open the door to a much
deeper understanding of what the language of mathematics really is.
In Math 523 we deal mostly with "classical analysis" which is a set of ideas and objects dating back to the
19th century (and earlier of course). Modern analysis (roughly speaking 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
"beginners". It is highly recommended you borrow another text and spend some time reading through it.
Official Textbook:
Other recommended textbooks:
Grading and assignments: 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.