Math 365C Real Analysis I, Spring 2009
Unique number: 57145
Lecturer: Dr. Henry Segerman
Lectures: RLM 7.120, MWF 11 am - 12 noon.
Text: Principles of Mathematical Analysis by Rudin, Third Edition.
We will mostly follow Rudin, covering the first 7 chapters, and homework will be assigned from it. You may also find it helpful to get hold of a copy of Introduction to Analysis by Maxwell Rosenlicht, which is inexpensive and has good material for intuition but does not go into as much depth as Rudin.
Prerequisites: Either consent of Mathematics Advisor, or two of M341, 328K, 325K (Philosophy 313K may be substituted for M325K), with a grade of at least C. Students who receive a grade of C in M325K or M328K are advised to take M361K before attempting M365C.
Course description: This course is an introduction to Analysis. Analysis, together with Algebra and Topology, form the central core of modern mathematics. Beginning with the notion of limit from calculus and continuing with ideas about convergence and the concept of function that arose with the description of heat flow using Fourier series, analysis is primarily concerned with infinite processes, the study of spaces and their geometry where these processes act and the application of differential and integral to problems that arise in geometry, pde, physics and probability.
A rigorous treatment of the real number system, Euclidean spaces, metric spaces, continuity of functions in metric spaces, differentiation and Riemann integration of real-valued functions of one real variable, and uniform convergence of sequences and series of functions.
Homework: (10% of your grade) Homework will be assigned weekly and listed on this page. Homework will be collected in class on Friday. Late homework will not be accepted. Your lowest 3 homework scores will be dropped.
|Homework 1||Due Friday Jan 30th.|
|Homework 2||Due Friday Feb 6th.|
|Homework 3||Due Friday Feb 13th.|
|Homework 4||Due Friday Feb 27th.|
|Homework 5||Due Friday Mar 6th.|
|Homework 6||Due Friday Mar 13th.|
|Homework 7||Due Friday Mar 27th.|
|Homework 8||Due Friday Apr 3rd.|
|Homework 9||Due Friday Apr 10th.|
|Homework 10||Due Friday Apr 17th.|
|Homework 11||Due Friday May 1st.|
|Homework 12||Due Friday May 8th.|
Exams: (90% of your grade) There will be three in class midterms, each worth 20% of your grade. There will also be a comprehensive final, lasting 3 hours and worth 30% of your grade. If you do better as a percentage on the final than in any of the midterms then your percentage on the final will be used in place of the lowest midterm. There will be no make-up exams.
No books, notes or calculators will be allowed in any of the exams. Exam dates are:
Students with Disabilities: The University of Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471- 6259, 471-6441 TTY.
Some general information: