MATH 446-200
Principles of Analysis I
Fall 2015
Instructor: David Kerr
Office: Blocker 525L
Office hours: T 10:00-11:30 or by appointment
Lectures: MWF 1:50-2:40, BLOC 161
Course description: Construction of the real and complex numbers, topology of metric spaces, compactness and connectedness, Cauchy sequences, completeness and the Baire category theorem, continuous mappings, introduction to point-set topology.
Textbook: N. L. Carothers. Real Analysis. Published by Cambridge University Press.
Assignments (due at the beginning of class)
Assignment #1 (due September 9):  ch 1:  8, 13, 17, 24, 25, 33 , 34, 36
Assignment #2 (due September 16):  ch 1:  37, 47;  ch 2:  4, 8, 13, 15, 19, 20
Assignment #3 (due September 23):  ch 2:  23, 24;  ch 3:  1, 4, 5, 14, 18, 23
Assignment #4 (not to be handed in):  ch 3:  24, 29, 30, 31, 32, 34, 36, 37, 39, 40;  ch 4:  4, 7
Assignment #5 (due October 7):  ch 4:  3, 11, 12, 13, 26, 29, 33, 62
Assignment #6 (due October 14):  ch 5:  5, 8, 28, 42, 46, 53, 56, 61
Assignment #7 (due October 21):  ch 6:  2, 9, 12, 17, 22, 26; ch 7:  5, 9
Assignment #8 (due October 28):  ch 7:  18, 22, 24, 44; ch 8:  1, 3, 12, 17
Assignment #9 (due November 11):  ch 8:  66, 75, 77, 84; ch 9:  5, 12, 15, 40
Assignment #10 (due November 18):  ch 9:  4, 37, 45, 49; ch 10:  7, 8, 10, 18
Assignment #11 (due December 2):  ch 10:  19, 25, 32, 33, 38; ch 11:  7, 9, 12, 15, 20, 22
Assignment #12 (not to be handed in):  ch 11:  47, 48, 51, 52, 54, 57, 63; ch 12:  3, 6, 22, 23, 25, 26
Exams
In-class exam #1: September 30, covers Chapters 1, 2, and 3 and the first section in Chapter 4 on open sets
In-class exam #2: November 4, covers Chapters 4, 5, 6, 7, and 8
Definitions you may be asked to state: continuity at a point, connectedness, total boundedness, completeness, compactness, uniform continuity
Final exam: December 15, 3:30-5:30 pm, covers Chapters 1 to 12
Definitions you may be asked to state: countability, continuity, connectedness, total boundedness, completeness, compactness, uniform continuity, pointwise convergence, uniform convergence, equicontinuity