Department of Mathematics

Transitions, MTH 299-03

Tentative Schedule and Homework Assignments

Chapter numbers refer to:

Chartrand, Polimeni, and Zhang. Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition (2012).

L Date Chapter and Topic HW Comment
1 8/27 General proof techniques. Discussion on what this class is about.

Due 9/3

HW 1		 Read Chapter 0: Communicating Mathematics before the recitation.
If you don't have the book yet, read this.
R 8/28 Recitation
2 8/29 2.1 - Statements,
2.2 - Negation of a Statement,
2.3 - Disjunction and Conjunction

Due 9/5

HW 2		 Please read chapters 0,1 and 2. We will start talking about Chapter 2 at the next lecture. We will return to Chapter 1 later in the course.
9/1 Labor Day - no class
3 9/3 2.4 - The Implication
2.5 - More on Implications

Due 9/8

HW 3
R 9/4 Recitation
4 9/5 2.6 - Biconditional
2.7 - Tautologies and Contradiction
2.8 - Logical Equivalence
2.9 - Fundamental Properties of Logical Equivalence

Due 9/10

HW 4
5 9/8 2.10 - Quantified Statements

Due 9/12

2.68, 2.70c,e,f, 2.78, plus the following.
6 9/10 2.10 - continued
3.2 - Direct proofs

Due 9/15

3.8, 3.10, plus the following. 		Lecture Notes
R 9/11 Recitation
7 9/12 3.3 - Proof by Contrapositive
3.4 - Proof by Cases

Due 9/17

3.16, 3.21, 3.50, 3.60 		Lecture Notes
8 9/15 4.1 - Proofs Involving Divisibility

Due 9/19

4.2, 4.4, 4.8
9 9/17 4.2 - Proofs Involving Congruence

Due 9/22

4.14, 4.18, 4.22
R 9/18 Recitation
10 9/19 4.3 - Proofs Involving Real Numbers

Due 9/24

4.78, 4.89, 4.90
9/22 Last day to withdraw with tuition refund
11 9/22 1.1 - Describing a Set
1.2 - Subsets
1.3 - Set Operations

Due 9/26

1.4, 1.8, 1.68, 1.12, 1.14, 1.22a,b,c,d, 1.30, 1.76
12 9/24 1.4 - Indexed Collections
1.5 - Partitions
1.6 - Cartesian Products
4.4 - Proofs Involving Sets

Due 9/29

1.36 , 1.38, 1.46, 1.50, 1.59, 1.64, 1.66(bonus), 4.43, 4.48.
R 9/25 Recitation
13 9/26 4.5 -Properties of Set Operations
4.6 - Proofs Involving Cartesian Products

Due 10/1

4.56, 4.62, 4.64(bonus), 4.68, 4.70 		For 4.68 we proved one of the inclusions in class; for HW prove the remaining one. For 4.70 you can use finite or infinite sets. Make sure you specify your universal set.
Read Sections 4.5 and 4.6 in the textbook.
R 9/29 Review The MLC offers a review session on Tuesday, 6:30pm-8:30pm in C100 Wells Hall. Review sheet.
R 10/1 Review The MLC offers a review session on Wednesday, 7:30pm-9:30pm in A134 Wells Hall. Review solutions.
M 10/2 Midterm Exam
14 10/3 5.1 - Counterexamples
5.2 - Proof by Contradiction

Due 10/8

5.2, 5.6, 5.8, 5.10, 5.28, 5.32		 Lecture Notes
15 10/6 5.2 - Continued
5.4 - Existence Proofs

Due 10/10

5.33a, 5.44, plus the following additional problems; 5.47 - bonus
16 10/8 5.4 - Continued
5.5 - Disproving Existence Proofs

Due 10/13

5.50, 5.57, 5.62, 5.52 - bonus 		Lecture Notes
R 10/9 Recitation
17 10/10 6.1 - Mathematical Induction

Due 10/15

6.6b, 6.14, 6.16, 6.48
18 10/13 6.2 - A More General Principle of Mathematical Induction

Due 10/17

6.18, 6.24, 6.26, 6.29 		Reading assignment: Section 6.3
19 10/15 6.4 - The Strong Principle of Mathematical Induction

Due 10/20

6.42, 6.44, 6.62 		Reading assignment: Chapter 7
10/15 Last day to withdraw with no grade reported
R 10/16 Recitation
20 10/17 8.1 - Relations
8.2 - Properties of relations
8.3 - Equivalence Relations

Due 10/22

8.1: 8.4, 8.6, 8.10
8.2: 8.12, 8.14, 8.16, 8.22
8.3: 8.24 		Lecture Notes
21 10/20 8.4 - Properties of Equivalence Classes
8.5 - Congruence Modulo n

Due 10/24

8.3: 8.28, 8.30
8.4: 8.38, 8.40
8.5: 8.45, 8.50
22 10/22 8.6 - The Integers Modulo n

Due 10/27

8.44(prove your answers), 8.46, 8.56, 8.58
R 10/23 Recitation
23 10/24 9.1 - The Definition of Function
9.2 - The Set of All Functions from A to B
9.3 - One-to-One and Onto Functions

Due 10/29

9.1: 9.4, 9.8, 9.10, 9.12a,b,d
9.3: 9.20, 9.63, 9.67c,d, 9.78-bonus
24 10/27 9.4 - Bijective Functions

Due 10/31

9.31, 9.32, 9.34-bonus 		Lecture Notes
25 10/29 9.5 - Composition of Functions

Due 11/3

9.44, 9.46
R 10/30 Recitation
26 10/31 9.6 - Inverse Functions

Due 11/5

9.42b,c,d, 9.54, 9.57, 9.81
27 11/3 9.7 - Permutations
10.1 Numerically Equivalent Sets

Due 11/7

9.58, 9.60, 10.5
28 11/5 10.2 - Denumerable Sets
10.3 - Uncountable Sets

Due 11/10

10.4, 10.6, 10.10, 10.20, 10.22
R 11/6 Recitation
11/7
R 11/10 Review The MLC offers a review session on Tuesday, 6:30pm-8:30pm in A234 Wells Hall. Review sheet.
R 11/12 Review The MLC offers a review session on Wednesday, 7:30pm-9:30pm in A126 Wells Hall. Review solutions.
M 11/13 Midterm Exam
29 11/14 12.1 - Limits of Sequences

Due 11/19

12.4, 12.6, 12.45, 12.46 		Lecture Notes
30 11/17 12.1 - continued

Due 11/21

HW 30 		Please click on the link to find the assigned problems.
31 11/19 12.1 - continued

Due 11/24

HW 31 		Please click on the link to find the assigned problems.
R 11/20 Recitation
32 11/21 12.2 - Series

Due 11/26

HW 32 		Please click on the link to find the assigned problems.
33 11/24 11.1 - Divisibility Properties of Integers
11.2 - The Division Algorithm

Due 12/1

11.1: 11.6, 11.10, 11.14
11.2: 11.18, 11.22, 11.26 		Lecture Notes
11/26 Preliminary set of review problems for the final exam Updated Dec. 8
11/27 Thanksgiving - no class
11/28 Thanksgiving - no class
34 12/1 11.3 - Greatest Common Divisors 11.30, 11.32, 11.34, 11.36 Office hours on Tuesday are moved to 10 am-noon.
These will not be collected and graded as regular homework, but the material covered will be on the final exam. Please make sure to work on them, and bring questions to class.
35 12/3 11.4 - The Euclidean Algorithm 11.38, 11.42
R 12/4 Recitation
12/5 Review Review solutions
12/8 Review session 5:15 pm - 7:15 pm Room B117 WH
E 12/10 Final Exam 3:00 pm - 5:00 pm Room N100 BCC
Bring your student ID.