**Instructor: **David Kerr
**Office:** Blocker 525L

**Office hours:** T 10:00-11:30 or by appointment

**Lectures:** MWF 12:40-1:30, BLOC 164

**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 7): **ch 1:** 8, 13, 14, 17, 23, 24, 25, 33

*Assignment #2* (due September 14): **ch 1:** 37, 45; **ch 2:** 4, 6, 8, 13, 15, 19

*Assignment #3* (due September 21): **ch 2:** 22, 23; **ch 3:** 1, 2, 5, 14, 18, 23

*Assignment #4* (not to be handed in): **ch 3:** 24, 29, 30, 32, 34, 36, 37, 40; **ch 4:** 3, 4, 5, 7, 11

*Assignment #5* (due October 5): **ch 4:** 3, 5, 11, 19, 26, 29, 33, 62

*Assignment #6* (due October 12): **ch 5:** 5, 8, 22, 25, 34, 46, 53, 56

*Assignment #7* (due October 19): **ch 6:** 2, 3, 5, 9, 26; **ch 7:** 2, 5, 9

*Assignment #8* (due October 26): **ch 7:** 12, 18, 22, 44; **ch 8:** 1, 3, 12, 17

*Assignment #9* (due November 9): **ch 8:** 66, 75, 77; **ch 9:** 4, 5, 12, 15

*Assignment #10* (due November 16): **ch 9:** 19, 28, 37, 45, 46; **ch 10:** 7, 8, 10, 14

*Assignment #11* (due November 30): **ch 10:** 19, 23, 25, 32, 33; **ch 11:** 7, 9, 12, 15, 20, 22

*Assignment #12* (not to be handed in): **ch 11:** 47, 48, 51, 52, 57; **ch 12:** 3, 6, 22, 23, 25, 26

**Exams**

*In-class exam #1*: September 28, covers Chapters 1, 2, and 3 and the first five pages of Chapter 4

*Definitions you may be asked to state:* metric space, normed vector space, bounded subset of a metric space,
convergent sequence, Cauchy sequence

*In-class exam #2*: November 2, 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 12, 10:30 a.m. - 12:30 p.m.

*Definitions you may be asked to state:* countability, continuity,
connectedness, total boundedness, completeness, compactness, uniform continuity,
pointwise convergence, uniform convergence, equicontinuity