Math 300: Introduction to Mathematical Reasoning
Instructor: Joseph Palmer
Email: j.palmer at rutgers.edu
Syllabus: link
Schedule: 6:10-7:30pm Tuesdays and Thursdays in SC-216
Textbook: A Transition to Advanced Mathematics 8th ed. by Smith, Eggen, and St. Andre (ISBN 1-285-46326-9)
Office Hours: Wednesdays 10am-noon in my office
Sakai: You can check your grades in this course with
sakai.
Homework Assignments:
All of the homework for the course will be posted here.
Homework 1 - due Thurs. Sept 15:
Section 1.1: 1(all parts), 4abcd (no proofs for #4), 13ab
Section 1.2: 3, 7abc, 13abcd, 16abcd
Section 1.3: 3, 12
Suggested Problems 1
Section 1.1: 3, 7
Section 1.2: 6, 8, 12, 14, 16
Section 1.3:1, 4, 8, 10, 13
Homework 2 - due Thurs. Sept 22:
Section 1.4: 5c,7ad, 11c
Section 1.5: 3cdf, 7ab, 8,
Section 1.6: 1bd, 2a, 3, 4a
Suggested Problems 2
Section 1.4: 5, 6, 7, 8, 9
Section 1.5: 3, 4, 7, 11
Section 1.6: 1, 2, 3, 4, 5, 6
Selected solutions for Homework 2
Homework 3 - due Thurs. Sept 29:
Section 1.7: 3a, 5bc
Section 2.1: 4abcd (no proofs needed), 7, 13, 18b
Suggested Problems 3
Section 1.7: 1,2,3,5,8,10
Section 2.1: 3, 4, 5, 6, 9, 15, 16, 17, 18
Selected solutions for Homework 3
Homework 4 - due Thurs. Oct 6:
Section 2.2: 11a, 12
Section 2.3: 1ceo (no proofs), 9a, 12, 18
(For 18 from section 2.3 I also require that the family you
give satisfies A
i ≠ A
j when i≠ j)
Suggested Problems 4
Section 2.2: 1 - 11, 14, 16, 18,
19
Section 2.3: 1, 2, 4b, 9, 10,
11,
13, 17
Selected solutions for Homework 4
Homework 5 - due Thurs. Oct 13:
Section 2.4: 4el, 5aq, 7a
Section 2.5: 3
Suggested Problems 5
Section 2.4: 4, 5, 6, 7, 9, 10, 11
Section 2.5: 1, 5, 6, 7, 8, 9, 10
Selected solutions for Homework 5
Midterm 1 will be on Tuesday, October 18th:
It will cover Sections 1.1-1.8 and 2.1-2.6. It will be approximately 7 questions,
one of the questions will be a list of statements you have to decide is either True
or False.
Topics for Midterm 1
Solutions for Midterm 1
Homework 6 - due Thurs. Oct 27:
Section 1.8: 7b, 10, 13
Section 2.5: 12
Section 3.1: 1, 9, 10cd, 13
Suggested Problems 6
Section 1.8: 2, 5c, 7, 9,
Section 3.1: 2, 3, 4, 5, 6, 7, 11, 16
Selected solutions for Homework 6
Homework 7 - due Thurs. Nov 3:
Section 3.2: 3abc, 6ceh, 8, 16abe
Suggested Problems 7
Section 3.2: 1, 2, 3, 4,
6, 9, 10,
14
Selected solutions for Homework 7
Homework 8 - due Thurs. Nov 10:
Section 3.3: 4h, 5,6,9a,11
Section 3.4: 1ghij, 5, 8b, 9, 10
Suggested Problems 8
Section 3.3: 2, 3, 4, 7, 8, 14
Section 3.4: 1, 2, 3, 4, 6, 7, 8
Selected solutions for Homework 8
Homework 9 - due Thurs. Nov 17:
Section 4.1: 6a, 9, 11c, 13abc, 14abc, 15a
Section 4.2: 4a, 5a
Suggested Problems 8
Section 4.1: 1, 2, 6, 8, 10, 11, 15
Section 4.2: 1, 2, 5, 9, 12
Selected solutions for Homework 9
Suggested Problems for sections 4.3 and 4.4
(no homework to turn in for these due to the exam)
Section 4.3: 1, 2, 3, 4, 5, 6, 10
Section 4.4:
Midterm 2 will be on Tuesday, November 22:
It will cover Sections 3.1 - 3.4, 4.1 - 4.4. It will be approximately 7 questions.
The topics from the first midterm will not be the focus of this exam, but
the techniques of the previous exam are still relevant (that is, you should know how
to show set equality, use induction, prove statements by contrapositive, etc)
Topics for Midterm 2
Solutions for Midterm 2
Homework 10 - due Thurs. Dec 8:
Section 5.1: 7, 12
Section 5.2: 3b, 4b,
Suggested Problems 10
Section 5.1: 1, 5, 13, 18, 21abcd
Section 5.2: 1, 3, 4, 5, 7
Section 5.3: 5ab, 7 (as an example for #7, consider A = evens and B = odds, so A union B is the integers), 10, 14
Selected solutions for Homework 10
The Final Exam will be on Tuesday, December 20 (8-11pm):
The final will cover every section we've talked about in class:
1.1-1.7, 2.1-2.5, 1.8, 3.1-3.4, 4.1-4.4, 5.1-5.3, and parts of 2.6
Practice problems for the final
(
!!!: there is a typo on problem 5 of the practice problems, you have to also assume
that the set S has cardinality 10 - this is corrected on the solutions)
Solutions, partial solutions, and hints for the practice problems
Topics for the final exam
Solutions for the final exam
(the final exam solutions are a little bit rough sometimes. Email me
if you have any questions about the problems on the exam.)
Course Calendar
This will be updated throughout the semester to stay as accuate as possible.
September
| Monday | Tuesday | Wednesday | Thursday | Friday |
5
| 6
First meeting
Intro and 1.1
| 7
| 8
1.2 and 1.3
| 9
|
12
| 13
1.4
| 14
| 15
1.5
HWK 1 due | 16
|
19
| 20
1.6
| 21
| 22
1.7 and 2.1
HWK 2 due | 23
|
26
| 27
2.1 and 2.2
| 28
| 29
2.2 and 2.3
HWK 3 due | 30
|
October
| Monday | Tuesday | Wednesday | Thursday | Friday |
3
| 4
2.3 and 2.4
| 5
| 6
2.4 and 2.5
HWK 4 due | 7
|
10
| 11
2.5 and 1.8
| 12
| 13
2.5 and 1.8
Review Ch1&2
HWK 5 due | 14
|
17
| 18
Midterm 1
(Ch1+Ch2) | 19
| 20
3.1
| 21
|
24
| 25
3.1/3.2
| 26
| 27
3.2
HWK 6 due | 28
|
November
| Monday | Tuesday | Wednesday | Thursday | Friday |
31
| 1
3.3/3.4
| 2
| 3
3.4
HWK 7 due | 4
|
7
| 8
4.1
| 9
| 10
4.2
HWK 8 due | 11
|
14
| 15
4.3
| 16
| 17
4.4
HWK 9 due | 18
|
21
| 22
Midterm 2
(Ch3+Ch4) | 23
| 24
no class
| 25
|
28
| 29
5.1
| 30
| 1
5.1
| 2
|
December
| Monday | Tuesday | Wednesday | Thursday | Friday |
5
| 6
5.2
| 7
| 8
5.3
HWK 10 due | 9
|
12
| 13
Review
| 14
| 15
no class
| 16
|
19
| 20
FINAL
EXAM
(8-11pm) | 21
| 22
| 23
|
Course Outline
We will attempt to cover the following sections from the textbook in approximately the following order:
Logic, Proofs, and Sets
1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7
2.1, 2.2, 2.3, 2.4, 2.5, 1.8
Relations and Functions
3.1, 3.2, 3.3, 3.4
4.1, 4.2, 4.3, 4.4, 4.5
Counting
5.1, 2.6, 5.2, 5.3
If we have time we may also discuss some subset of the following:
Further Topics
5.4, 5.5, 6.1, 6.2, 3.5, 4.6, 4.7, 7.1, 7.2