Homework and Syllabus
Introduction to Discrete Mathematics
MATH 2001 Fall 2024
Homework must be submitted via Canvas, and is due at the start of class, with your name and homework number on it to receive credit. You will be graded on the clarity of your exposition. Messy, disorganized, or poorly written assignments will not receive credit.
Please read
the suggested texts before class, and then after class
make sure to attempt the homework for the sections we
covered that day.
You may find the Math Academic Resource Center ("MARC") to be useful as a meeting point for discussing homework, and a place to get some further help understanding the material.
| Date | Topics |
Reading |
Homework |
| L1 Monday August 26 |
Introduction: Course logistics. Introduction to sets: Introduction to sets, and cartesian products |
Hammack Chapter 1 Sections 1.1-2 | HW 1a Hammack Section 1.1 Exercises: 8, 18, 40. Section 1.2 Exercises: 2, 4, 12. |
| L2 Wednesday August 28 |
Introduction to LaTeX | Read over Chapters 1--2 of The Not So Short
Introduction to LaTeX 2e Bring a laptop with LaTeX installed (see the bottom of the page). We will use the following .tex and .bib files (which generated this .pdf). You will also want to download the following .pdf, which is included as a graphic. You can also find these files in this directory. |
|
| L3 Friday August 30 |
Introduction to sets: Subsets and power sets. | Hammack Chapter 1 Sections 1.3-4 | HW 1 DUE Homework must be submitted via Canvas Solution to 1.2.4 Solution to 1.2.12 HW 2a Hammack Section 1.3 Exercises: 2, 6, 12. Section 1.4 Exercises: 2, 10, 14. |
| Monday September 2 |
LABOR
DAY |
NO CLASS |
LABOR DAY |
| L4 Wednesday September 4 |
Introduction to LaTeX continued | Read over Chapter 3 of The Not So Short Introduction
to LaTeX 2e Bring a laptop to class with LaTeX installed (see the bottom of the page). We will use the following .tex and .bib files (which generated this .pdf). You can also find these files in this directory. And here is the simple template we used. |
|
| L5 Friday September 6 |
Sets continued: Union, intersection, difference, complement, Venn diagrams. (For complements, we are using the notation A^C, whereas the book is using the notation \overline A.) | Hammack Chapter 1 Sections 1.5-7 | HW 2 DUE 5 points extra credit for typing in LaTeX. You must submit both the .pdf and .tex file to recieve extra credit. Solution to 1.3.12 Solution to 1.4.10 HW 3a Hammack Section 1.5 Exercises: 2, 4, 6. Section 1.6 Exercise: 2. Section 1.7 Exercises: 5, 6. |
| L6
Monday September 9 |
Sets continuted: Indexed sets, sets of numbers, Russell's paradox. | Hammack Chapter 1 Sections 1.8-10 | HW 3b Hammack Section 1.8 Exercises: 2, 8, 11, 12, 13, 14. |
| L7 Wednesday September 11 |
Introduction to logic: Overview, statements, and, or, not. | Hammack Chapter 2 Sections 2.1-2 | HW 3c Hammack Section 2.1 Exercises: 2, 4, 6. Section 2.2 Exercises: 2, 6, 9. |
| L8 Friday September 13 |
Logic continued: Conditional statements, biconditional statements. | Hammack Chapter 2 Sections 2.3-4 | HW 3 DUE 5 points extra credit for typing in LaTeX. You must submit both the .pdf and .tex file to recieve extra credit. Solution to 1.6.2 Solution to 1.8.14 HW 4a Hammack Section 2.3 Exercises: 1, 8, 10. Section 2.4 Exercise: 2, 3, 4. |
| L9 Monday September 16 |
Logic continued: Truth tables, logical equivalence. | Hammack Chapter 2 Sections 2.5-6 | HW 4b Hammack Section 2.5 Exercises: 4, 6, 8. Section 2.6 Exercises: 4, 6, 9. |
| L10 Wednesday September 18 |
Logic continued: Quantifiers, translating English into symbolic statements, negating statements, logical inference. | Hammack Chapter 2 Sections 2.7-11 | HW 4c Hammack Section 2.7 Exercises: 2, 8. Section 2.9 Exercises: 2, 5. Section 2.10 Exercises: 4, 10. |
| L11 Friday September 20 |
Review: Homework review |
HW 4 DUE 2 points extra credit for typing in LaTeX. You must submit both the .pdf and .tex file to recieve extra credit. Solution to 2.6.9 Solution to 2.10.4 |
|
| L12 Monday September 23 |
Review: General review |
|
|
| L13 Wednesday September 25 |
Review: Review practice exam |
Practice exam
and solutions. |
|
| Friday September 27 |
MIDTERM I | MIDTERM I |
|
| L14 Monday September 30 | Counting:
Lists, the multiplication principle. |
Hammack Chapter 3 Sections
3.1-2 |
HW 5a Hammack Section 3.2 Exercises: 1-6. |
| L15 Wednesday October 2 | Review Midterm I |
||
| L16 Friday October 4 | Counting
continued: The addition and subtraction
principles, factorials and permutations. |
Hammack Chapter 3 Sections 3.3-4 | HW 5 DUE 2 points extra credit for typing in LaTeX. You must submit both the .pdf and .tex file to recieve extra credit. Solution to 3.2.2 Solution to 3.2.6 HW 6a Hammack Section 3.3 Exercises: 1-3. Section 3.4 Exercises: 7, 10, 12. |
| L17 Monday October 7 | Counting continued: Counting subsets, Pascal's triangle and the binomial theorem. | Hammack Chapter 3 Sections 3.5-6 | HW 6b Hammack Section 3.5 Exercises:1-3. Section 3.6. Exercises: 3, 5, 7. |
| L18 Wednesday October 9 | Counting continued: The
inclusion-exclusion principle, counting multisets |
Hammack Chapter 3 Sections 3.7-8 | HW 6c Hammack Section 3.7 Exercises: 1-3. Section 3.8 Exercises: 7, 9, 11. |
| L19 Friday October 11 | Counting continued: The division
and pigeonhole principles, combinatorial proof. |
Hammack Chapter 3 Sections 3.9-10 | HW 6 DUE 2 points extra credit for typing in LaTeX. You must submit both the .pdf and .tex file to recieve extra credit. Solution to 3.6.7 Solution to 3.8.11 HW 7a Hammack Section 3.9 Exercises: 2-4. Section 3.10 Exercises: 1-3. |
| L20 Monday October 14 |
Techniques of proof: Direct proof. | Hammack Chapter 4 | HW7b Hammack Chapter 4 Exercises: 1, 3, 5, 7, 9, 10. |
| L21 Wednesday October 16 |
Techniques of proof continued: Contrapositive proof. | Hammack Chapter 5 | HW7c Hammack Chapter 5 Exercises: 1, 3, 5, 16, 18, 20. |
| L22 Friday October 18 |
Techniques of proof continued: Proof by contradiction. | Hammack Chapter 6 | HW 7 DUE Solution to 3.10.2 Solution to 3.10.3 HW8a Hammack Chapter 6 Exercises: 2-7. |
| L23 Monday October 21 | Techniques of proof continued: Proving non-conditional statements. | Hammack Chapter 7 | HW8b Hammack Chapter 7 Exercises: 16-21. |
| L24 Wednesday October 23 | Techniques of proof continued: Proofs involving sets, disproof. | Hammack Chapter 8 and Chapter 9 | HW8c Chapter 8 Exercises: 2, 6, 10. Chapter 9 Exercises: 2, 4, 6. |
| L25 Friday October 25 |
Review: Homework review |
HW 8 DUE Solution to 7.20 Solution to 8.10 |
|
| L26 Monday October 28 |
Techniques of proof continued: Proof by induction. | Hammack Chapter 10 | HW9a Hammack Chapter 10 Exercises: 1-6. |
| L27 Wednesday October 30 | Review: General review |
||
| Friday November 1 | Review: Review practice exam |
Practice exam
and solutions. |
|
| L28
Monday November 4 |
MIDTERM II | MIDTERM II |
|
| L29
Wednesday November 6 |
Relations:
Reflexive, symmetric, transitive |
Hammack Chapter 11 Sections
11.1-2 |
HW9b Hammack Section 11.1 Exercises: 2, 6, 10. Section 11.2 Exercises: 2, 5, 12. |
| L30 Friday November 8 |
Techniques of proof continued: Proof by induction continued. | |
HW 9 DUE Solution to 10.1 Solution to 11.2.2 HW10a Hammack Chapter 10 Exercises: 19-24. |
| L31 Monday November 11 |
Relations continued: Equivalence relations, equivalence classes and partitions. | Hammack Chapter 11 Sections 11.3-4 | HW10b Hammack Section 11.3 Exercises: 2, 4, 11. Section 11.4 Exercises: 3, 4, 6. |
| L32 Wednesday November 13 |
Review Midterm II | HW10c Hammack Chapter 10 Exercises: 7-12. |
|
| L33 Friday November 15 |
Relations continued: Equivalence relations, equivalence classes and partitions, continued. | Hammack Chapter 11 Sections 11.3-4 | HW 10 DUE Solution to 11.3.4 Solution to 11.4.4 HW 11a Cancelled |
| L34 Monday November 18 | Relations continued: Integers modulo n, relations between sets. | Hammack Chapter 11 Sections 11.5-6 | HW11b Hammack Section 11.5 Exercises: 1, 2, 4, 5, 6, 7. |
| L35
Wednesday November 20 |
Functions and maps: Introduction. (We use the term "map" whereas the book uses the term "function". We use the term "source" whereas the book uses the term "domain". We use the term "target" whereas the book uses the term "codomain".) | Hammack Chapter 12 Sections 12.1-3 | HW11c Hammack Section 12.1 Exercises: 4, 6. Section 12.2 Exercises: 5, 10. Section 12.3 Exercises: 1, 2. |
| L36 Friday November 22 |
Functions and maps continued: Composition, image, pre-image, injective, surjective, bijective, inverse. | Hammack Chapter 12 Sections 12.4-6 | HW 11 DUE Solution to 11.5.6 Solution to 12.2.10 HW 12a Hammack Section 12.4 Exercises: 2, 6, 10. Section 12.5 Exercises: 2, 8, 9. |
| November 25--29 | THANKSGIVING BREAK |
NO CLASS |
THANKSGIVING BREAK |
| L37 Monday December 2 |
Functions and maps continued: Composition, image, pre-image, injective, surjective, bijective, inverse, continued. | Hammack Chapter 12 Sections 12.4-6 | HW12b Hammack Section 12.6 Exercises: 1, 3, 5, 6, 9, 10. |
| L38 Wednesday December 4 | Functions and maps continued: Further topics. | ||
| L39 Friday December 6 |
Review: Homework review |
HW 12 DUE |
|
| L40 Monday December 9 |
Review: General review |
||
| L41 Wednesday December 11 | Review: Review practice exam |
Practice exam and
solutions to be posted. |
|
| Friday December 13 | READING DAY |
NO CLASS |
NO CLASS |
| Sunday
December 15 |
FINAL EXAM Section 002 7:30 PM -- 10:00 PM Section 003 1:30 PM -- 4:00 PM (Lecture Room) |
FINAL EXAM |
I strongly encourage
everyone to use LaTeX for typing
homework. If you have a mac,
one possible easy way to get started is with texshop; download the MacTex.pkg
package. If you are using linux,
there are a number of other possible ways to go, using
emacs, ghostview, etc. If you are using windows,
you're on your own, but I'm sure there's something
online. This site can help you find LaTeX symbols by
drawing: http://detexify.kirelabs.org/classify.html.
You may also want to try https://cocalc.com
(formerly https://cloud.sagemath.com/)
or https://www.overleaf.com
(formerly https://www.sharelatex.com/)
for a cloud version.