Sebastian Casalaina

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.