Math 300: Introduction to Mathematical Reasoning


Instructor: Joseph Palmer
Email: j.palmer at rutgers.edu
Syllabus: link
Schedule: 6:40-8:00pm Mondays and Wednesdays in TIL-251
Textbook: A Transition to Advanced Mathematics 8th ed. by Smith, Eggen, and St. Andre (ISBN 1-285-46326-9)
Office Hours: Wednesdays, 1-3pm in my office (Hill 340)

Sakai: You can check your grades in this course with sakai.

Grade Breakdown:

Your final grade in the course will be computed as follows:
    Homework:  9%
Workshop participation:5%
Midterm 1:23%
Midterm 2:23%
Final Exam:40%

Homework Assignments:

All of the homework for the course will be posted here.

Homework 1 - due Monday, Feb 4:
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
Selected solutions for Homework 1

Homework 2 - due Monday, Feb 11:
Section 1.4: 5c, 7ad, 11c
Section 1.5: 3cdf, 7ab, 11
Suggested Problems 2
Section 1.4: 5, 6, 7, 8, 9
Section 1.5: 3, 4, 7
Selected solutions for Homework 2

Homework 3 - due Monday, Feb 18:
Section 1.6: 1bd, 2a, 3, 4a
Section 1.7: 3a, 5bc
Suggested Problems 3
Section 1.6: 1, 2, 3, 4, 5, 6
Section 1.7: 1,2,3,5,8,10
Selected solutions for Homework 3

Homework 4 - due Monday, Feb 25:
Section 2.1: 4abcd (no proofs needed), 7, 13, 18b
Section 2.2: 11a, 12
Suggested Problems 4
Section 2.1: 3, 4, 5, 6, 9, 15, 16, 17, 18
Section 2.2: 1 - 11, 14, 16, 18, 19
Selected solutions for Homework 4

Homework 5 - due Monday March 4:
Section 2.3: 1ceo (no proofs), 9a, 12, 18
(For 18 from section 2.3 I also require that the family you give satisfies Ai ≠ Aj when i≠ j)
Section 2.4: 4el, 5aq
Section 2.5: 3
Suggested Problems 5
Section 2.3: 1, 2, 4b, 9, 10, 11, 13, 17
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

Suggested problems from 1.8 and 2.5:
Section 1.8: 2, 5c, 7, 9, 10, 13
Section 2.5: 12
Some example problems from section 1.8

Midterm 1 will be on Monday, March 11:
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


Homework 6 - due Monday, April 1:
Section 1.8: 7b, 10, 13
Section 2.5: 12
Section 3.1: 1, 9, 10cd, 13
Section 3.2: 3abc, 6ceh, 8, 16abe
Suggested Problems 6
Section 1.8: 2, 5c, 7, 9,
Section 3.1: 2, 3, 4, 5, 6, 7, 11, 16
Section 3.2: 1, 2, 3, 4, 6, 9, 10, 14
Selected solutions for Homework 6

Homework 7 - due Monday, April 8:
Section 3.3: 4g, 5,6,9a,11
Section 3.4: 1ghij, 5, 8b, 9, 10 (induction is a good idea for 10)
Suggested Problems 7
Section 3.3: 2, 3, 4, 7, 8, 14
Section 3.4: 1, 2, 3, 4, 6, 7, 8
Selected solutions for Homework 7

Homework 8 - due Monday, April 15:
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 8 (and some problems from 4.3/4.4)

Suggested Problems for sections 4.3 and 4.4 (in preparation for the exam)
Section 4.3: 1, 2, 3, 4, 5, 6, 10
Section 4.4: 1, 2, 3, 4

Midterm 2 will be on Wednesday, April 17:
It will cover Sections 3.1 - 3.4, 4.1 - 4.4. It will be approximately 8 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 9 - due Monday, May 6 (the last day of class):
Section 5.1: 7, 12, 21b
Section 5.2: 1, 3b, 4a, 8
Section 5.3: 5ab, 7 (as an example for #7, consider A = evens and B = odds, so A union B is the integers)
Suggested Problems 9
Section 5.1: 1, 5, 13, 18, 21abcd
Section 5.2: 1, 3, 4, 5, 7
Section 5.3: 10, 14

Tentative Schedule:

Date       Sections       Topics
W: 1/23 1.1 Intro, Propositions
M: 1/28 1.2, 1.3 Conditions, quantifiers
W: 1/30 1.4 Basic proofs I
M: 2/4 1.5 Basic proofs II, HWK #1 due
W: 2/6 1.6 Proofs with quantifiers
M: 2/11 1.7 Even more proofs, HWK #2 due
W: 2/13 2.1 Set theory
M: 2/18 2.2 Set operations, HWK #3 due
W: 2/20 2.3 Indexed families of sets
M: 2/25 2.4 Induction, HWK #4 due
W: 2/27 2.5 More induction
M: 3/4 2.5/1.8 Induction and proofs from number theory, HWK #5 due
W: 3/6 2.5/1.8 Induction and number theory (and review)
M: 3/11 --- Midterm 1
W: 3/13 3.1 Relations
M: 3/25 3.2 Equivalence relations
W: 3/27 3.3 Partitions
M: 4/1 3.4 Modular arithmetic, HWK #6 due
W: 4/3 4.1 Functions as relations
M: 4/8 4.1/4.2 Functions as relations, Constructions of functions, HWK #7 due
W: 4/10 4.3 Onto, one-to-one
M: 4/15 4.4 (and 4.5?) Inverse functions (and set images), HWK #8 due
W: 4/17 --- Midterm 2
M: 4/22 5.1 Equivalent sets (finite)
W: 4/24 5.1 (and 2.6?) Counting
M: 4/29 5.2 Infinite sets
W: 5/1 5.3 Countable sets
M: 5/6 --- Catch up and review , HWK #9 due
M: 5/13 --- FINAL EXAM (8-11pm in TIL-251)

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