# Schedule for MAT 319 - Foundations of Analysis - Fall 2023

Reminder MAT 319 and MAT 320 follow the joint schedule through October 3
Week 1
Aug 28-Sept 1
Tuesday (1st-6th lecture by Prof. Ntalampekos)
Sets and functions
Induction
1.1
1.2
Homework 1 (Due Week 2)
p. 10: 6, 15, 16, 22
p. 15: 1, 9, 16
p. 22: 3, 4, 12
Thursday Infinite sets 1.3
Week 2
Sept 4-8
Tuesday Algebraic and order properties of the reals
Absolute value on the reals
2.1
2.2
Homework 2 (Due Week 3)
p. 30: 7, 8, 26
p. 35: 2, 4, 17
p. 39: 4, 6, 11
Thursday Completeness of the reals 2.3
Week 3
Sept 11-15
Tuesday Applications of the supremum 2.4 Homework 3 (Due Week 4)
p. 44: 4, 7, 12, 13, 15
p. 52: 3, 5, 7, 9
Thursday Intervals 2.5
Week 4
Sept 18-22
Tuesday (7th-10th lecture by Prof. Schul)
Sequences and limits
3.1 Homework 4 (Due Week 5)
p. 61: 5ab, 6, 8, 9, 10, 12
p. 69: 2, 5, 7
Thursday Limit theorems 3.2
Week 5
Sept 25-29
Tuesday Monotone sequences 3.3 Homework 5 (Due Week 7)
p. 77: 1, 7, 9
Thursday Monotone sequences 3.3
Week 6
Oct 2-6
Tuesday Midterm I
During lecture time
Cumulative Practice questions
Everything from here is for MAT 319 only. The website for MAT 320 is in this link.
Thursday Subsequences and the Bolzano-Weierstrass Theorem 3.4
Week 7
Oct 9-13
Tuesday Fall Break
No classes in session
Thursday The Cauchy Criterion 3.5 Homework 6 (Due Week 8)
p. 84: 1, 4(b), 11, 12
p. 91: 1, 2(a), 4, 5
Week 8
Oct 16-20
Tuesday Properly Divergent Sequences
Infinite Series
3.6
3.7
Homework 7 (Due Week 9)
p. 93: 1, 2, 3
p. 100: 4, 6, 11, 12
Thursday Infinite Series
Limits of Functions
3.7
4.1
Week 9
Oct 23-27
Tuesday Limits of Functions 4.1 Homework 8 (Due Week 10)
p. 110: 4, 6, 10(b), 15
p. 116: 4, 5, 9
Thursday Limit Theorems 4.2
4.3
Week 10
Oct 30-Nov 3
Tuesday Continuous Functions 5.1
5.2
Homework 9 (Due Week 12)
p. 123: 4
p. 129: 7, 10, 11, 13
p. 140: 1, 4, 6, 17
Thursday Continuous Functions on Intervals 5.3
Week 11
Nov 6-10
Tuesday Midterm II
During lecture time
Cumulative
(with focus on material after Midterm I)
Practice questions
Thursday Continuous Functions on Intervals 5.3
Week 12
Nov 13-17
Tuesday Uniform Continuity 5.4 Homework 10 (Due Week 14)
p. 148: 2, 6, 7, 10
p. 170: 1(a)(c), 4, 8a
p. 179: 3(c), 6, 13
Thursday The derivative 6.1
Week 13
Nov 20-24
Tuesday The mean value theorem 6.2
Thursday Thanksgiving Break
No classes in session
Week 14
Nov 27-Dec 1
Tuesday L'Hospital's rules 6.3 Homework 11 (Due Week 15)
p. 187: 5, 8, 11
p. 196: 4, 11
p. 206: 6(a), 8, 12
Thursday Taylor's theorem 6.4
Week 15
Dec 4-8
Tuesday Riemann Integral 7.1 Practice Homework (not to turn in)
p. 215: 8, 9, 12
Thursday Integrable functions 7.2
Dec 14 Thursday Final Exam
Thursday, December 14, 11:15am-1:45pm
Classroom: Simons Center SCGP 103
Cumulative (with focus on material after Midterm II) Practice questions

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