Homework and Syllabus
Introduction to Discrete Mathematics
MATH 2001 Spring 2022
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. You must submit just one pdf file with all of the homework problems in the correct order.
For Homework 3 through 6, your homework must be typeset
in LaTeX. You must submit both the .pdf and .tex
file to recieve credit. For Homework 7 and after, you
will get 1 point extra credit for writing your solutions in
LaTeX, and you will lose 1 point of credit for not writing
your solutions in LaTeX.
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 it useful to use a computer algebra system to
check some of your computations. The program Mathematica,
for instance, is available free to students via
the University of Colorado.
You may find the Mathematics
Academic Resource Center ("MARC" MATH 175) to be
useful as a meeting point for discussing homework.
An asterix * indicates that a homework assignment has not been finalized.
| Date | Topics |
Reading |
Homework |
| L1 Monday
January 10 |
Introduction: Course
logistics. Introduction to sets, and cartesian
products (will be covered in Friday's lecture). |
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
January 12 |
Introduction to LaTeX |
Read 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. |
|
| L3 Friday January 14 | 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 January 17 |
MLK
DAY |
NO CLASS |
MLK DAY |
| L4 Wednesday January 19 |
Introduction
to LaTeX continued |
Read 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). |
|
| L5 Friday January 21 |
Sets
continued: Union, intersection, difference,
complement, Venn diagrams. |
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
January 24 |
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
January 26 |
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 January 28 |
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 January 31 |
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 February 2 |
(SNOW
DAY) 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 February 4 |
Review |
|
HW 4 DUE Homework must be typed in LaTeX. You must submit both the .pdf and .tex file to recieve credit. Solution to 2.6.9 Solution to 2.10.4 |
| L12 Monday February 7 |
Review General review |
||
| L13 Wednesday February 9 |
Review Practice exam |
Practice exam and
solutions. |
|
| Friday February 11 |
MIDTERM I | MIDTERM I |
|
| L14 Monday February 14 |
Techniques of proof: Definitions (4.2), direct proof, mathematical writing (5.3). | Hammack Chapter
4 |
HW 5a Hammack Chapter 4 Exercises: 1, 3, 5, 7, 9, 10. |
| L15 Wednesday February 16 |
Review Midterm I | Read Chapter 4 of The Not So Short Introduction to LaTeX 2e | |
| L16 Friday February 18 |
Techniques of proof continued: contrapositive proof. | Hammack Chapter 5 | HW 5 DUE Solution to 4.7 Solution to 4.9 HW 6a Hammack Chapter 5 Exercises: 1, 3, 5, 16, 18, 20. |
| L17
Monday February 21 |
Techniques of proof continued: Proof by contradiction. | Hammack Chapter 6 | HW 6b Hammack Chapter 6 Exercises: 2--7. |
| L18
Wednesday February 23 |
Techniques of proof continued: Proving non-conditional statements. | Hammack Chapter 7 | HW 6c Hammack Chapter 7 Exercises: 16--21. |
| L19 Friday February 25 |
Techniques of proof continued: Proofs involving sets, disproof. | Hammack Chapter 8 and Chapter 9 | HW 6 DUE Solution to 6.3 Solution to 7.20 HW 7a Chapter 8 Exercises: 2, 6, 10. Chapter 9 Exercises: 2, 4, 6. |
| L20 Monday February 28 |
Techniques of proof continued: Proof by induction. | Hammack Chapter 10 | HW 7b Hammack Chapter 10 Exercises: 1--6. |
| L21 Wednesday March 2 |
Techniques of proof continued: Proof by induction continued. | ||
| L22 Friday March 4 |
Relations: Reflexive, symmetric, transitive. | Hammack Chapter 11 Sections 11.1-2 | HW 7 DUE Solution to 8.10 Solution to 10.1 HW 8a Hammack Section 11.1 Exercises: 2, 6, 10. Section 11.2 Exercises: 2, 5, 12. |
| L23
Monday March 7 |
Relations continued: Equivalence relations, equivalence classes and partitions. | Hammack Chapter 11 Sections 11.3-4 | HW 8b Hammack Section 11.3 Exercises: 2, 4, 11. Section 11.4 Exercises: 3, 4, 6. |
| L24
Wednesday March 9 |
Relations continued: Integers modulo n, relations between sets. | Hammack Chapter 11 Sections 11.5-6 | HW 8c Hammack Section 11.5 Exercises: 1, 2, 4, 5, 6, 7. |
| L25 Friday March 11 | Review |
In class we went
through Chapter 6 Exercise 20 |
HW 8 DUE Solution to 11.4.4 Solution to 11.5.6 |
| L26 Monday March 14 |
Review Homework review |
||
| L27 Wednesday March 16 |
Review General review continued |
Practice exam
and solutions. |
|
| Friday March 18 |
MIDTERM
II |
MIDTERM II |
|
| March 21--25 | SPRING BREAK |
NO CLASS |
SPRING BREAK |
| L28
Monday March 28 |
Functions and maps: Introduction | Hammack Chapter 12 Sections 12.1-3 | HW 9a Hammack Section 12.1 Exercises: 4, 6. Section 12.2 Exercises: 5, 10. Section 12.3 Exercises: 1, 2. |
| L29
Wednesday March 30 |
Review Midterm II | ||
| L30 Friday April 1 |
Functions and maps continued: Composition, image, pre-image, injective, surjecive, bijective, inverse. | Hammack Chapter 12 Sections 12.4-5 | HW 9 DUE Solution to 12.2.10 Solution to 12.3.2 HW 10a Hammack Section 12.4 Exercises: 2, 6, 10. Section 12.5 Exercises: 2, 8, 9. |
| L31 Monday April 4 |
Functions and maps continued: Composition, inverse, image, pre-image, injective, surjecive, and bijective. | Hammack Chapter 12 Sections 12.6 | HW 10b Hammack Section 12.6 Exercises: 1, 3, 5, 6, 9, 10. |
| L32 Wednesday April 6 |
Partially ordered sets: Introduction | Here is a short note on POSets. | |
| L33 Friday April 8 |
Partially ordered sets continued: Zorn's Lemma. | HW 10 DUE Solution to 12.6.5 Solution to 12.6.6 |
|
| L34
Monday April 11 |
Cardinality: Introduction, sets with equal cardinality, countable and uncountable sets. | Hammack Chapter 14 Sections 14.1-2 |
HW 11a Hammack Section 14.1 Exercises: 4, 10, 12. Section 14.2 Exercises: 3, 9, 11. |
| L35
Wednesday April 13 |
Cardinality continued: Countability, comparing cardinality, Cantor--Berstein--Schroeder Theorem. | Hammack Chapter 14 Sections 14.3-4 |
HW 11b Hammack Section 14.3 Exercises: 4, 8, 10. Section 14.4 Exercises: 1, 2, 5. |
| L36 Friday April 15 |
Set functions and elementary probability: Finitely additive set functions, finitely additive measures, definition of probability for finite sample spaces. | Apostol 13.1-6 | HW 11 DUE Solution to 14.1.10 Solution to 14.3.8 HW 12a Apostol Exercises 13.4: 5, 6. Exercises 13.7: 1, 2, 13, 14. |
| L37 Monday April 18 |
Set functions and elementary probability continued: Examples, combinatorial analysis. | Apostol 13.8-10 | HW 12b Apostol Exercises 13.9: 1, 2, 4. Exercises 13.11: 2, 3, 4. |
| L38 Wednesday April 20 |
Set functions and elementary probability continued: Conditional probability, independence. | Apostol 13.12-13 | HW 12c Apostol Exercises 13.14: 1--6. |
| L39 Friday April 22 |
Set
functions and elementary probability continued: Compound
experiments, Bernoulli trials, probability for
countable sample spaces. |
Apostol 13.16, 17, 21. | HW 12 DUE Solution to Apostol 13.7.14 Solution to Apostol 13.9.1 |
| L40
Monday April 25 |
Review |
||
| L41
Wednesday April 27 |
Review |
Practice exam and solutions. |
|
| Friday April 29 | READING DAY |
NO CLASS |
READING DAY |
| Tuesday May 3 | FINAL EXAM 1:30
PM -- 4:00 PM ECCR
1B55 (Lecture room) |
FINAL EXAM |
You may want to use LaTeX
for typing homework. If you have a mac,
one possible easy way to get started is with texshop;
you will want to download the MacTex
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 sharelatex) for a cloud version.