Homework and Syllabus
Introduction to Discrete Mathematics
MATH 2001 Spring 2020
Homework is due in class and must be stapled
with your name and homework number on it to
receive credit. After Homework 3, your homework must
by typeset in LaTeX. You will be graded on the
clarity of your exposition.
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 |
| Monday
January 13 |
Introduction |
Hammack Chapter 1 Sections
1.1-2 |
|
| Wednesday
January 15 |
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) |
|
| Friday January 17 | Introduction to sets: Overview. |
Hammack Chapter 1 Sections 1.3-4 | HW 1 Hammack Chapter 1 Section 1.1 Exercises: 2, 8, 18, 30, 38, 40. |
| Monday January 20 |
MLK
DAY |
NO CLASS |
NO CLASS |
| Wednesday January 22 |
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) |
|
| Friday January 24 |
Sets
continued: Venn diagrams, subsets, union,
intersection, difference, complement. |
Hammack Chapter 1 Sections
1.5-7 |
HW 2 5 points extra credit for typing in LaTeX Hammack Chapter 1 Section 1.2 Exercises: 2, 4, 8, 12, 18. |
| Monday
January 27 |
Sets continuted: Products
of sets, power sets, indexed sets, sets of numbers. |
Hammack Chapter 1 Sections
1.8-10 |
|
| Wednesday
January 29 |
Sets continued: Maps of
sets. |
||
| Friday
January 31 |
Introduction to Euclid:
Incidence planes |
Read Hartshorne's Geometry:
Euclid and Beyond, Chapter 2 Section 6,
pp.65--71. Also take a look at Euclid's Elements, as made available through the Clay Math Institute. Here is a short introduction to incidence planes following my lecture. |
HW 3 5 points extra credit for typing in LaTeX Hammack Chapter 1 Section 1.3 Exercises: 2, 6, 12. Chapter 1 Section 1.4 Exercises: 2, 10, 14, 19. Chapter 1 Section 1.5 Exercises: 2, 4, 6. Chapter 1 Section 1.6 Exercise: 2. Chapter 1 Section 1.7 Exercises: 4, 5, 6. Chapter 1 Section 1.8 Exercises: 2, 11, 12. Not for credit (do not turn these in): Harthsorne Exercise 6.3, p.71. |
| Monday February 3 |
Introduction
to logic: Overview. |
Hammack Chapter 2 Sections
2.1-2 |
|
| Wednesday February 5 |
Logic
continued: Overview of proofs. |
Hammack Chapter 2 Sections 2.3-4 | |
| Friday February 7 |
Review General review, review of incidence planes, and answering questions about LaTeX |
Please read again
this short introduction to incidence
planes following my lecture. |
HW 4 Hammack Chapter 2 Section 2.1 Exercises: 2, 4, 6. Chapter 2 Section 2.2 Exercises: 2, 6. Chapter 2 Section 2.3 Exercises: 8, 10. Chapter 2 Section 2.4 Exercise: 4. |
| Monday February 10 |
Review Homework review |
||
| Wednesday February 12 |
Review General review continued |
||
| Friday February 14 |
MIDTERM I | MIDTERM I |
MIDTERM I |
| Monday February 17 |
Review
Midterm I |
Hammack Chapter 2 Sections
2.5-7 Read Chapter 4 of The Not So Short Introduction to LaTeX 2e |
|
| Wednesday February 19 |
Logic
continued: Statements, and or not, conditional
statements, biconditional statements, truth tables,
logical equivalence. |
Hammack Chapter 2 Sections 2.8-10 | |
| Friday February 21 |
Logic
continued: Quantifiers, translating English into
symbolic statements, negating statements, logical
inference. |
HW 5 Hammack Chapter 2 Section 2.5 Exercises: 4, 6, 8. Chapter 2 Section 2.6 Exercises: 4, 6. Chapter 2 Section 2.7 Exercises: 2, 4, 8. |
|
| Monday
February 24 |
Euclid continued: Betweenness planes | Read Hartshorne's Geometry: Euclid and Beyond, Chapter 2 Section 7, pp.73--79. | |
| Wednesday
February 26 |
Techniques of proof: Definitions
(4.2), direct proof, mathematical writing (5.3). |
Hammack Chapter
4 |
|
| Friday
February 28 |
Techniques of proof
continued: contrapositive proof. |
Hammack Chapter 5 | HW 6 Hammack Chapter 2 Section 2.9 Exercises: 2, 3, 4, 5. Chapter 2 Section 2.10 Exercises: 2, 4, 10. Chapter 4 Exercises: 1, 3, 5, 7, 9. |
| Monday March 2 |
Techniques
of proof continued: Proof by contradiction. |
Hammack Chapter
6 |
|
| Wednesday March 4 |
Techniques
of proof continued: Proving non-conditional
statements. |
Hammack Chapter 7 | |
| Friday March 6 |
Techniques of proof continued: Proofs involving sets, disproof. | Hammack Chapter
8 and Chapter
9 |
HW 7 Hammack Chapter 5 Exercises: 1--5, 16--20. Extra credit: Chapter 6 Exercises: 2--8. |
| Monday
March 9 |
Techniques of proof
continued: Proof by induction. |
Hammack Chapter
10 |
|
| Wednesday
March 11 |
Techniques of proof continued: Proof by induction continued. | ||
| Friday March 13 | Review |
HW 8 Hammack Chapter 7 Exercises: 19--21. Chapter 8 Exercises: 2, 6, 10--18 even. Not for credit (do not turn these in): Chapter 9 Exercises: 2, 4, 6, 8, 10, 12, 14. Chapter 10 Exercises: 1--5. |
|
| Monday March 16 |
Review |
||
| Wednesday March 18 |
Review |
||
| Friday March 20 |
Review
-- MIDTERM II cancelled |
MIDTERM II
cancelled |
|
| March 23--27 | SPRING BREAK |
SPRING BREAK |
SPRING BREAK |
| Monday
March 30 |
Review Midterm II | |
|
| Wednesday
April 1 |
Relations: Reflective, symmetric, transitive. | Hammack Chapter 11 Sections 11.1-2 | |
| Friday
April 3 |
Functions and maps: Introduction | Hammack Chapter 12 Sections 12.1-3 | HW 9 Hammack Chapter 11 Section 11.1 Exercises: 2, 6, 10. Not for credit (do not turn these in): Chapter 11 Section 11.2 Exercises: 2, 5, 11, 12. |
| Monday April 6 |
Functions and maps continued: Composition, inverse, image, pre-image, injective, surjecive, and bijective. | Hammack Chapter 12 Sections 12.4-5 | |
| Wednesday April 8 |
Functions continued. | Hammack Chapter 12 Sections 12.6 | |
| Friday April 10 | Equivalence relations: Introduction | Hammack Chapter 11 Sections 11.3-4 | HW 10 Hammack Chapter 12 Section 12.1 Exercises: 4, 6. Chapter 12 Section 12.2 Exercises: 5, 10. Chapter 12 Section 12.3 Exercises: 1, 2. Not for credit (do not turn these in): Chapter 12 Section 12.4 Exercises: 2, 6, 10. Chapter 12 Section 12.5 Exercises: 2, 8. |
| Monday
April 13 |
Equivalence relations
continued: Partitions, quotients, universal
properties. |
Hammack Chapter 11 Sections 11.5-6 | |
| Wednesday
April 15 |
Partially ordered
sets: Introduction |
Here is a short note on POSets. |
|
| Friday
April 17 |
Review |
HW 11 Hammack Chapter 11 Section 11.3 Exercises: 2, 4. |
|
| Monday April 20 |
Partially
ordered sets continued: Zorn's Lemma. |
||
| Wednesday April 22 |
Cardinality:
Introduction. |
Hammack Chapter 14 Sections 14.1-2 |
|
| Friday April 24 |
Cardinality
continued: Countability, comparing cardinality,
Cantor--Berstein--Schroeder Theorem. |
Hammack Chapter 14 Sections 14.3-4 |
HW 12 Hammack Chapter 11 Section 11.4 Exercises: 4, 6. Not for credit (do not turn these in): Chapter 14 Section 14.1 Exercises: 4, 10. Chapter 14 Section 14.2 Exercises: 3, 9. Chapter 14 Section 14.3 Exercises: 4, 8, 10. Chapter 14 Section 14.4 Exercises: 1, 2. |
| Monday
April 27 |
Review |
||
| Wednesday
April 29 |
Review |
||
| Friday May 1 | READING DAY |
NO CLASS |
NO CLASS |
| Saturday
May 2 |
FINAL
EXAM 4:30 - 7:00 PM ECCR
108 (Lecture room) |
FINAL EXAM |
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.
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.
Here is a sample homework file to use: (the .tex
file, the .bib
file, and the .pdf
file). 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.