Schedule


Lecture Date Topic Reading* Notes
1 Aug 29 Natural numbers and Mathematical Induction 1
Sept 1 Labor Day (No Class)
2 Sept 3 Field Axioms and Rational Numbers 2
3 Sept 5 Real numbers 3 HW 1 due
4 Sept 8 Completeness axiom and infinity 4,5
5 Sept 10 Sequences and Convergence 7
6 Sept 12 Proofs 8 HW 2 due
7 Sept 15 Properties of sequences 9
8 Sept 17 Monotone and Cauchy sequences 10
9 Sept 19 Subsequences 11 HW 3 due
10 Sept 22 Bolzano-Weierstrass Theorem 11
11 Sept 24 limsup and liminf 12
12 Sept 26 Series 14 HW 4 due
13 Sept 29 Series 14
14 Oct 1 Convergence tests 15
Oct 3 Midterm I
15 Oct 6 Metric spaces 13
16 Oct 8 Metric spaces 13
17 Oct 10 Metric spaces 13 HW 5 due
18 Oct 13 Continuity 17
19 Oct 15 Properties of continuous functions 18
20 Oct 17 Uniform continuity 19 HW 6 due
21 Oct 20 Uniform continuity 19
22 Oct 22 Limits of functions 20
23 Oct 24 Limits of functions 20 HW 7 due
24 Oct 27 Differentiation 28
25 Oct 29 Mean Value Theorem and Rolle's Theorem 29
26 Oct 31 The Riemann Integral 32 HW 8 due
32 Nov 3 The Riemann Integral 32
Nov 5 Midterm II review
Nov 7 Midterm II
28 Nov 10 Properties of the Riemann integral 33
29 Nov 12 Fundamental theorem of calculus 34
30 Nov 14 Power series 23 HW 9 due
31 Nov 17 Uniform convergence 24
32 Nov 19 Uniform convergence 25
33 Nov 21 Differentiation and integration of power series 26 HW 10 due
34 Nov 24 Taylor series 31
35 Nov 26 Weierstrass function pdf
Nov 28 Thanksgiving (No Class)
36 Dec 1 Taylor series 31
37 Dec 3 Metric spaces 21 HW 11 due
Dec 5 Metric spaces 21
Dec 10 HW 12 due
Dec 12 Exam review session
Dec 18 Final exam

*The numbers in the reading column refer to chapters in the course textbook
Ross, Kenneth A. Elementary Analysis. Springer, 2013.