Syllabus and Homeworks
Homeworks
Homework sets will be typically assigned weekly on Thursday
and due next Th in class. They will be posted on this web site (NOT on blackboard site!).
Late homework will not be accepted. However, grades for homework assignments
may be dropped in cases of documented medical problems or similar difficulties.
Week 
Dates 
Notes 
Topics 
HW 
Due date 
1 
8/29  9/2 

13: Introduction: what are real numbers? Integer numbers and induction;
rational numbers and idea of a field; basic properties of real numbers. 
Read carefully section 3 of the textbook and subsections 4.14.4 of section 4.
In particular, work out proofs of Theorems 3.1, 3.2 and 3.5.
Write down solutions for exercises 3.2, 3.4, 3.8, 4.6. 
9/8 
2 
9/5  9/9 
9/5, 9/6: No classes  Labor day 
4: The completeness axiom. Archimedean property 
HW 2; solutions 
9/15 
3 
9/129/16 

5: Infinity, boundedness and unboundedness. 7: Sequences; limit of a sequence. 
5.2, 5.6, 7.3 (a j), 7.4, 8.1 
9/22 
4 
9/19  9/23 

89: Limit laws for sequences and formal proofs. 
8.3, 8.7, 9.1, 9.4, 9.12*, 9.15, 9.16. Problem 9.12 is optional (worth extra credit);
even if you do not solve it, you are allowed to use results of this problem to solve other problems. 

5 
9/26  9/30 
Midterm 1 on Th, 9/29 



6 
10/3  10/7 
This is the last week MAT 319/320 meet together 
10: Monotone and Cauchy sequences; 11: Subsequences 
HW 5 for MAT 319 only 
10/13 
7 
10/10  10/14 

11. Subsequences continued; 12:lim inf and lim sup. 14: series 
HW 6 (for MAT 319 only): 11.4, 11.10, 12.4, 14.2, 14.6 
10/20 
8 
10/17  10/21 

14:series; 15: integral test and alternating series 
HW 7 for MAT 319 only 
postponed to 11/1 
9 
10/24  10/28 

17, 18: continuous functions 


10 
10/31  11/4 
Midterm 2: 11/3 



11 
11/7  11/11 

20: limits of functions 
HW 8: 17.8, 17.10 (a), 17.12, 18.6, 18.10, 20.4, 20.8, 20.14, 20.20 

12 
11/14  11/18 

28: derivatives 


13 
11/21  11/25 
No classes on Nov 2325: Thanksgiving break 
29 Mean value theorem 


14 
11/28  12/2 

32 The Riemann integral (up to Th. 32.5); 33 Properties of Reimann integral 
HW 9: 28.6; 28.8, 29.2, 29.12, 29.14, 32.2, 32.6, 33.4 
12/8 
15 
12/5  12/9 





12/16 
Final exam 



