Class Hours: TR 2:00-3:15 in Dooly Memorial 204.
Text:
Foundations of Analysis
by Joseph L. Taylor
Pure and Applied Undergraduate Texts;
Volume: 18; 2012; 398 pp; Hardcover
MSC: Primary 26; 03;
Print ISBN: 978-0-8218-8984-8
Product Code: AMSTEXT/18
Additional reading:
Advanced Calculus
by Patrick M. Fitzpatrick, American Mathematical Society, 2nd Revised edition (January 13, 2009)
Introduction to Real Analysis
by William Trench,
available online
Principles of Mathematical Analysis
by Walter Rudin, McGraw-Hill; 3rd edition (January 1, 1976) - QA300. R8 1976
Mathematical Analysis
by Tom M. Apostol, Reading, Mass., Addison-Wesley Pub. Co., 1974 - QA300. A573 1974
Description:
MTH533 - MTH534 Introduction to Real Analysis is a two semester
proof oriented Advanced Calculus course introducing the set of real numbers,
the concepts of continuity, differentiability and integrability, and the convergence
of sequences and series of functions. The first semester deals mostly with the
one dimensional case and the second semester with the multidimensional case
as well as applications to partial differential equations and Fourier series.
MTH433 is a simplified version of the first semester and MTH730-731 develops the subject at the Ph.D. level.
Prerequisites:
MTH 310 (or 211) and 230.
Grading policy:
Homework (20%), Exam 1 (20%), Exam 2 (20%) and Final (40%).
General rules / information:
- check this page for updates.
- make sure that you have access to the UM listserv (email list via Blackboard) for this class
- you must show your work in order to obtain credit.
The homework will be updated on a weekly basis.
Due dates, solutions and other information will be provided via Blackboard.
Homework 1
Do problems A and B from Handout 1 and
Section 1.1: 4, 5, 8, 9, 10, 11, 12, 14 from the textbook (Taylor).
Homework 2
Section 1.2: 12, 14, 16, 17, 20.
Section 1.3: 5, 10, 12, 13, 14.
Homework 3
Section 1.4: 4, 7, 8, 9, 10.
Section 1.5: 1, 2, 6, 8, 12.
Notes - Chapter 1
Lecture 1 ,
Lecture 2 ,
Optional problems Chapter 1
... To be updated ...
Final
Includes all sections listed under homework, including homework not collected.
Total 10 problems. Partial credit will be given/ graded on a curve like the two Midterms.
***The Honor Code is strictly enforced. Cellphones should be off and not used during the exam.