Professor:
Dr.
Janet Vassilev
Office:
Humanities
467
Office Hours: TWTh 1112
Telephone: (505) 2772214
Email: jvassil@math.unm.edu
webpage: http://www.math.unm.edu/~jvassil
Date

Section

Topic

Homework

8/25

3 and 4

Proof
Techniques


8/27

5 and 6

Sets and Relations

3.1,
3.6(a,b,d,g,i), 3.7(a,b,c), 3.9, 4.4, 4.8, 4.11, 4.17, 4.19, 5.7, 5.14, 5.18,
5.25(a,b), 6.10(a,d), 6.12(a,b,c), 6.14, 6.21, 6.25, 6.27(b,d,e)

9/1

7

Functions

Homework 1 Solutions

9/3

8 and 10

Cardinality
and Natural numbers

7.4(b,c),
7.6(a,b), 7.7(b,g), 7.8, 7.13, 7.14, 7.17, 7.26, 7.27, 7.32, 8.3(a,c,d),
8.13, 8.18, 8.20, 8.22

9/8

10 and 11

Induction and
Ordered Fields

Homework 2 Solutions

9/10

12

Completeness

10.3,
10.4, 10.6, 10.7, 10.14, 10.20, 10.21b, 11.4, 11.6, 11.8, 11.9

9/15

13

Topology of
Reals

Homework
3 Solutions Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7

9/17

14

Compact Sets

12.3(b,h,l),
12.4(b,h,l), 12.6, 12.8, 12.12(a,b), 13,3(a,b), 13.4(a,b), 13.5(c,d),
13.7(a,b,f), 13.12, 13.20,(a,c), 13.21(b,d)

9/22

15

Metric Spaces

Homework 4 Solutions

9/24

16

Convergence


9/29


Midterm 1


10/1

17

Limit Theorems

14.3(a,c),
14.4, 14.5a, 14.8, 14.9, 14.11, 14.12

10/6

18

Monotone and
Cauchy Sequences

Homework 5 Solutions

10/8

19

Subsequences

16.6(b,c),
16.8b, 16.9a, 16.13, 16.15, 17.5(d,f), 17.6(a,b), 17.7, 17.8, 17.18, 18.3b,
18.4, 18.14

10/13

20

Limits of
Functions

Homework 6 Solutions

10/15

21 and 22

Continuous
Functions


10/20

23

Uniform
Continuity


10/22

25

The Derivative

19.3(a,d),
19.4(a,b), 19.8, 19.9, 19.17, 19.19, 20.13, 20.14, 20.20, 21.8, 21.13, 21.16,
22.3(a,e,g,h), 22.4, 22.7, 22.9

10/27

26

The Mean Value
Theorem

Homework 7 Solutions

10/29

27

L’Hopital’s
Rule

23.3(a,e),
23.5, 23.6, 23.10, 23.15, 25.6, 25.8, 25.11, 25.12, 26.6, 26.9, 26.11, 26.13,
26.23

11/3

28


Homework 8 Solutions

11/5

29

The Riemann
Integral


11/10


Midterm 2


11/12

30

Properties of
the Riemann Integral


11/17

31

Fundamental
Theorem of Calculus


11/19

32

Convergence of
Series

26.6,
26.8, 26.18, 26.23, 27.6, 28.9, 28.12, 29.8, 29.9, 29.11a, 29.13, 29.15,
20.5, 30.10, 30.11, 30.21

11/24

33

Convergence
Tests

Homework 9 Solutions

11/26

34

Power Series


12/1

35

Pointwise and
Uniform Convergence


12/3

36

Applications
of Uniform Convergence

32.3,
32.5 (e,k), 33.6, 33.9, 33.11, 33.13, . 34.9, 34.10, 35.3, 35.7, 35.10,
35.14, 35.15

12/8

37

Uniform
Convergence of Power Series

Homework 10 Solutions

12/10


Review


12/17


Final Exam

