Detailed Schedule -- Principles of Analysis

Fall 2005, Prof. Little

As always, topics may be added, deleted, or rearranged during the course of the semester. Any changes will be announced in class and here.

DateClass Topic Reading (from Abbott)
8/31 Course introduction, rational and irrational numbers Section 1.1
9/2 Sets and functions Section 1.2
9/5 Logic and proofs Section 1.2
9/7 Mathematical induction Section 1.2
9/9 The completeness axiom Section 1.3
9/12 Consequences of completeness Section 1.4
9/14 Cardinality and countability Section 1.4
9/16 Cantor diagonalization Section 1.5
9/19 Infinite sums Section 2.1
9/21 Limit of a sequence Section 2.2
9/23 Limit theorems Section 2.3
9/26 Using the Limit theorems Section 2.3
9/28 The Limit Squeeze theorem Section 2.3
9/30 Monotone convergence Section 2.4
10/3 Subsequences and the Bolzano-Weierstrass theorem Section 2.5
10/5 Exam I Covers: Chapter 1, Sections 2.2 - 2.3
10/7 Begin series Section 2.7
10/10 Columbus Day Break (no class)
10/12 More series Sections 2.7, 2.8
10/14 Finish series
10/17 The Cantor set Section 3.1
10/19 Open and closed sets, compactness Sections 3.2, 3.3
10/21 Heine-Borel theorem Section 3.4
10/24 "Pathological" functions Section 4.1
10/26 Functional limits Section 4.2
10/28 Exam II Covers: Sections 2.4-2.8, Chapter 3
10/31 Continuity Section 4.3
11/2 Uniform continuity Section 4.4
11/4 The Intermediate Value Theorem and consequences Section 4.5
11/7 Derivatives Sections 5.1, 5.2
11/9 Rolle's theorem and the Mean Value Theorem Section 5.3
11/11 Spare Day
11/14 Defining integration Section 7.1
11/16 The Riemann integral Section 7.2
11/18 Properties of integrals Section 7.3
11/21 More on integration Section 7.4
11/23 Thanksgiving Vacation (no class)
11/25 Thanksgiving Vacation (no class)
11/28 The Fundamental Theorem of Calculus Section 7.5
11/30 When is a function integrable? Section 7.6
12/2 Exam III Covers: Chapters 4, 5, 7.1-7.4
12/5 Course wrap-up

The final exam for this course will be given at 2:30pm on Wednesday, December 14.

Last modified: September 24, 2005