Unique number: 57145

Lecturer: Dr. Henry Segerman

• Email: henrys@REMOVETHISmath.utexas.edu (preferred method of contact)
• Office Phone: (512) 471-8143
• Office: RLM 10.140
• Office hours: M 4 - 5, W 3 - 5

Website: http://math.utexas.edu/users/henrys/m365c.html

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.

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:

• Midterm 1: Wednesday Feb 18, in class
• Midterm 2: Friday March 27, in class
• Midterm 3: Monday April 27, in class
• Final: Monday May 18, 9 - 12 noon, WAG 201

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:

• Students are encouraged to talk over the homework with each other and then do the homework on their own. Copying down someone else's proof defeats the point of figuring things out for yourself. Even better if you have a go at the problems on your own before talking to someone else.
• Take advantage of office hours! Seek out help before problems get too large to tackle. You will find that I have a lot of patience with people who are genuinely interested in learning, and decreasingly less for those who regularly skip class/homework/etc. Don't hesistate to ask me or others in the class if you have questions or are having trouble. I can also schedule appointments outside of office hours as needed.