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

**Office hours:** M 2:00-3:00, T 2:00-3:30

**Lectures:** MWF 10:20-11:10, BLOC 457

**Course description:**
Axioms of the real number system; point set theory of the real number line; compactness,
completeness and connectedness; continuity and uniform continuity; sequences, series;
theory of Riemann integration.

**Textbook:**
William R. Wade.

*An Introduction to Analysis*, fourth edition. Published by Prentice Hall.

**Assignments** (due at the beginning of class)

*Assignment #1* (due September 10): **1.2:** 0, 3, 4(a,c), 7(a,b), 10

*Assignment #2* (due September 17): **1.3:** 0(a,c), 1(a,e) (just state the answer), 4, 6, 7, 8

*Assignment #3* (due September 24): **1.4:** 2(b,d), 4(a,c); **1.5:** 0(b,c,d), 2(a,b,c) (just state the answer), 5, 6

*Assignment #4* (not to be handed in): **1.6:** 0, 1, 3, 6

*Assignment #5* (due October 8): **2.1:** 0, 1(c,d), 2(a), 4, 7, 8; **2.2:** 0(a,b)

*Assignment #6* (due October 15): **2.2:** 1(a,b), 2(b), 3(a,b); **2.3:** 0, 3, 7

*Assignment #7* (due October 22): **2.4:** 0, 3(b,c), 4; **3.1:** 0(c,d), 1(a,d), 3(a), 6

*Assignment #8* (due October 29): **3.2:** 0(a,c), 1(b), 6; **3.3:** 0(a,c), 1(a,b), 2(a), 4

*Assignment #9* (not to be handed in): **3.3:** 3, 4, 5, 10; **3.4:** 0, 1, 4, 6

*Assignment #10* (due November 14): **4.1:** 3, 6; **4.2**: 0, 1, 2; **4.3**: 0(a,b)

*Assignment #11* (due November 19): **4.3:** 4, 9; **4.4:** 1, 3, 5(a,c)

*Assignment #12* (due November 26): **4.5:** 0(a,b), 1, 7; **5.1:** 0(a), 2(b), 3, 4

*Assignment #13* (not to be handed in): **5.2:** 0(b); **5.3:** 0(a,b), 1(b,c), 3; **5.4:** 0(b,c), 1(b), 7

**Exams**

*In-class exam #1*: October 1, covers 1.1-1.6

*In-class exam #2*: November 5, covers 2.1-2.4 and 3.1-3.4

*Theorems and definitions you may be asked to state:* limit of a sequence,
Bolzano-Weierstrass theorem, Cauchy sequence, continuity,
extreme value theorem, intermediate value theorem, uniform continuity

Practice #1 |

Practice #1 solutions (ignore the problems involving derivatives)

Practice #2 (ignore the problems involving derivatives)

*Final exam*: December 16, 8:00-10:00 am, covers 1.1-1.6, 2.1-2.4, 3.1-3.4, 4.1-4.5, 5.1-5.4, with emphasis on Chapters 4 and 5

*Axioms, theorems, and definitions you may be asked to state:* completeness axiom, well-ordering principle,
limit of a sequence, Cauchy sequence, continuity, intermediate value theorem,
extreme value theorem, uniform continuity, derivative, mean value theorem, integrability

Practice #1 |

Practice #1 Solutions
Practice #2 |

Practice #2 Solutions
(ignore the problems involving series)