Instructor: Alena Erchenko

Course on canvas.dartmouth.edu.⇗

Syllabus

Date Topic References
01/03 Introduction. Basic Set Theory.

(R) Chapter I
(L) Introduction,
Section 0.3
01/05 Bijections, invertible maps. Cardinality. Cantor's theorem.

(L) Introduction, Section 0.3
01/08 Ordered fields

(R) Chapter II, Section 1-2
(L) Section 1.1
01/10 Least upper bound. Existence of square roots

(R) Chapter II, Section 3-4
(L) Section 1.2

01/11

(block 10X, 12:15pm - 1:05 pm ET)

 Metric spaces

(R) Chapter III, Sections 1-2
(L) Section 7.1
01/12 Ball neighborhoods. Open sets

(R) Chapter III, Section 2

(L) Section 7.2
01/15 No class -> Moved to X-hour on 01/11
01/17 Open and closed sets. 

(R) Chapter III, Sections 2

(L) Section 7.2
01/19 Convergence. 

(R) Chapter III, Section 3

(L) Section 7.3
01/22 Complete spaces. 

(R) Chapter III, Section 4

(L) Section 7.4
01/24 Compact sets

(R) Chapter III, Section 5

(L) Section 7.4.2
01/26 Equivalent definitions of compactness. 

(R) Chapter III, Section 5

(L) Section 7.4.2
01/29 Heine-Borel. Connected sets

(R) Chapter III, Section 6

(L) Sections 7.4.2 and 7.2.2
01/31 Continuous function. Functions on connected spaces.

(R) Chapter IV, Sections 1, 5
02/02 Intermediate Value Theorem. Limits (R) Chapter IV, Section 2, 5
02/05 Rational functions (R) Chapter IV, Section 3
02/07 Functions on a compact (R) Chapter IV, Section 4
02/09 Sequences of functions (R) Chapter IV, Section 6
02/12 Derivatives (R) Chapter V, Section 1-2
02/14 Mean Value Theorem (R) Chapter V, Section 3
02/15
(block 10X, 12:15pm - 1:05 pm ET)		 Taylor's Theorem (R) Chapter V, Section 4
02/16 Riemann Integral (R) Chapter VI, Section 1
02/19 Properties of integral (R) Chapter VI, Sections 2-3
02/21 Integrable functions
02/23 Fundamental Theorem (R) Chapter VI, Sections 4-5
02/26 Interchange of limit operations (R) Chapter VII, Section 1
02/28 Power series (R) Chapter VII, Sections 2-3
03/01 The fixed point theorem  (R) Chapter VIII, Section 1
03/04 Review
03/08
(11:30am-2:30pm ET)		 Final exam