**Instructor: **David Kerr
**Office:** Milner 121

**Office hours:** MT 2:00-3:30, or by appointment

**Lectures:** MWF 12:40-1:30, Zach 119D

**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 9): **1.2:** 0, 3, 4(a,c), 6, 7(a), 10

*Assignment #2* (due September 13): **1.3:** 0(a,b), 1(a,d) (just state the answer), 7, 8;
**1.4:** 2(b,d), 4(a,d)

*Assignment #3* (due September 20): **1.5:** 0(b,d), 2(a,c), 6, 7; **1.6:** 0, 1, 3, 7; **2.1:** 0, 2(a)

*Assignment #4* (due October 4): **2.2:** 2(b), 3(b); **2.3:** 0(a,d), 3, 7;
**2.4:** 0, 4, 7; **3.1:** 0(c,d)

*Assignment #5* (due October 11): **3.1:** 1(a,d), 3(a), 6; **3.2:** 0(a,c), 1(b), 6; **3.3:** 0(a,c)

*Assignment #6* (due October 18): **3.3:** 1(a), 2(a), 4, 10; **3.4:** 0(d), 1(b), 4, 6; **4.1:** 0, 1, 4

*Assignment #7* (due October 25): **4.2:** 0, 1, 2; **4.3:** 0(a,b), 1(c), 2, 4, 9; **4.4:** 1, 3, 5(a,d)

*Assignment #8* (due November 1): **4.5:** 0, 1, 7; **5.1:** 0(a), 2(b), 3, 4; **5.2:** 0(b)

*Assignment #9* (due November 15): **5.3:** 0(a,b), 1(b,c), 3; **5.4:** 0(b,c), 1(b), 7; **6.1:** 0(a,b)

*Assignment #10* (due November 22): **6.1:** 1(b,c), 2(d), 3(b), 8; **6.2:** 0(d), 1(f), 2(c), 4; **6.3:** 0(d), 1(b), 2(b,d)

*Assignment #11* (not to be handed in): **6.3:** 5, 6, 8, 10; **7.1:** 1, 2, 3, 4, 5, 6 **7.2:** 1, 2, 3; **7.3:** 1, 4, 5, 6;

**Exams**

*In-class exam #1*: September 25, covers 1.1-1.6 and 2.1-2.2

*Axioms and definitions you may be asked to state:* completeness axiom, well-ordering principle, definition of the limit of a sequence

Practice |

Practice solutions
*Exam #2*: November 6, 7:00-8:30, Heldenfels 120, covers 2.3-2.4, 3.1-3.4, 4.1-4.5, 5.1-5.2

*Theorems and definitions you may be asked to state:* Bolzano-Weierstrass theorem, Cauchy sequence, continuity,
extreme value theorem, intermediate value theorem, uniform continuity, derivative, mean value theorem, integrability

Practice #1 |

Practice #1 solutions
Practice #2
*Final exam*: December 9, 10:30-12:30

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

Practice #1 |

Practice #1 Solutions
Practice #2 |

Practice #2 Solutions