Class Hours:
T-R 9:30 - 10:45 in Ungar 402.
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. The first term, given in the Fall (MTH533/633), introduces the set of real numbers,
the concepts of continuity, differentiability and integrability, and the convergence
of sequences and series of functions. It deals mostly with the
one dimensional case up to the rigorous definition and properties of the Riemann integral and the Fundamental Theorem of Calculus. The second term (MTH534/634), in the Spring, presents the transcendental functions,
power series and the introduction to multidimensional Calculus - metric spaces, continuity, differentiation, Inverse Function Theorem, Implicit Function Theorem, Optimization and Lagrange multipliers, and other topics (Fourier series and elements of differential equations) if time permits.
Note:
MTH433 is a simplified version of the first semester (only MTH533) and MTH733-734 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; this is a proof oriented course.
- homework is very important, even though its relative weight is small.
Midterms and Final:
Cover all sections listed under homework, including homework not collected but discussed in class.
The final has 10 problems and is double in length compared to the Midterms. Partial credit will be given. All exams are graded on a curve.
Approximate grade scale: A, A-: 90-100; B, B+: 80-89; B-: 70-79; C, C+: 60-69;
C-: 50-59; D, F: 0-49.
***The Honor Code is strictly enforced. Cellphones should be off and not used during the exam.
The approximated homework schedule is given below.
Actual assignments, with due dates will be sent out by Blackboard
Announcemts and emails, after being posted in Assignments.
Homework before Midterm 1
Section 5.4: 2, 4, 5, 6, 9, 11, 12.
Section 6.1: 4, 6, 8, 10, 12, 14.
Section 6.2: 5, 8, 11, 12.
Section 6.3: 4, 5, 6, 7.
Section 3.4: 3, 5, 6, 8, 10, 12.
Section 6.4: 2, 4, 5, 6, 7, 8, 9, 10, 13, 14.
Section 6.5: 3, 4, 5, 6, 8, 11, 12, 13.
Midterm 1 - TBA
Sections covered: All. 5.4, 6.1, 6.2, 6.3, 3.4, 6.4, 6.5.
Homework from Midterm 1 to Midterm 2
Section 7.1: 5, 8, 10, 11, 12.
Section 7.2: 8, 11, 12, 14, 15.
Section 7.3: 3, 8, 9, 10, 11, 12, 14.
Section 7.4: 7, 8, 9, 12, 13.
Section 7.5: 8, 10, 11, 12, 14.
Section 8.1: 3, 5, 6, 11,15.
Section 8.2: 1, 4, 8, 10, 11.
Section 8.3: 1, 2, 3, 10, 11.
Midterm 2 - TBA
Sections covered: All material covered after Midterm 1:
7.1, 7.2, 7.3, 7.4, 7.5, 8.1, 8.2, 8.3.
Exam format: same as Midterm 1.
Homework Midterm 2 to Final
Section 8.4: 10, 15.
Section 8.5: 7, 8, 9, 10.
Section 9.1: 8, 10.
Section 9.2: 5,10.
Section 9.3: 4, 5, 9.
Section 9.4: 3, 8, 9, 10, 12, 13.
Section 9.5: 8, 9, 13.
Section 9.6: 3, 4, 7, 8.
Section 9.7: 6, 7, 8, 9, 10.
Final - as scheduled by the Registrar.
Location: same classroom
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.