This course covers key mathematical concepts used in computer science,
including: logic, proofs, counting, discrete probability,
graph theory, and boolean algebra. These topics all fall within the general
category of *discrete* mathematics as oppose to *continuous* mathematics
(see
here
for more
on this distinction.)
Throughout the course, I will use algorithmic analysis to provide motivating
examples,
so you will also learn algorithm basics.

The required textbook for this course is *Discrete Mathematics and its Applications, 7th Edition* by
Kenneth H. Rosen. Most of the topics and examples covered in this course will be adapted from this text.

Grades in the course will be based on weekly problem sets and two exams (a midterm and a final).
The problem set problems will be graded on the following scale: *check plus* (correct
answer
with at most minor issues), *check* (shows understanding but has
at least one major issue),
and *zero* (does not demonstrate a reasonable understanding of
the problem).
Each check plus earns you 2 points, each check 1 point, and each zero, of
course, 0 points. At the end of the semester, I add up all the points you
earned,
and this is your raw problem set score. I will then translate that raw
score into a letter grade.

Each problem set will be returned to you along with sample solutions, grading notes, and a guide to mapping your point score to a letter grade scale. Though this mapping will vary from problem set to problem set, depending on length and difficulty, in most cases, to earn an A on a problem set you should be aiming to get a check plus on most problems.

In determining your final grade, I will average your problem set grade with your midterm and final grades according to the below weights.

Problem Sets | 50% |

Midterm | 25% |

Final | 25% |

This course has two teaching assistants who will hold regular office hours in Room 330 in Saint Mary's Hall. Their contact information and office hour times are below.

- Shaked Atia (sa1078@georgetown.edu)
*Office hours:*Monday from 12:00 to 1:30; Thursday from 3:30 to 5:00.- Cindy Hom (ch991@georgetown.edu)
*Office hours:*Tuesday from 9:15 to 10:45; Wednesday from 10:45 to 12:15.

In addition to the teaching assistant office hours listed above, I will hold regular office hours from 2:00 to 3:30 pm on Tuesdays, in my office at 334 Saint Mary's Hall.

If you have a question for me about the material or course logistics, my preference is that you ask me immediately before or after class, or during my office hours. If you instead e-mail me, I cannot guarantee a timely response (I am a bad e-mail correspondant). Therefore, if you have a last minute question (e.g., about a problem set), you will likely be better served e-mailing one of the teaching assistants.

The following rules describe my expectations and grading policies for problem sets:

- You must work
**alone**on problem sets. You may only discuss problems with me or the teaching assistants. The only materials you can reference when working on these problems are your course notes and the assigned textbook. In particular, you**may not**reference online sources, solutions from previous classes, or talk to other students when working on problem set problems. - I will post each problem set on the below schedule by the beginning of class on the day it is assigned. For the most part, each problem set covers the material taught in class the week it is assigned as is due on the first class of the next week. There are some exceptions to this timing due to holidays and travel. Please check the assignment and due dates carefully for each problem set.
- Problem sets should be handed in at the beginning of class on the day they are due. That is, bring a physical copy of the problem set to class to give to me before the lecture begins.
- Problem sets not handed in by the beginning of lecture will be
considered late, and 10% of the points deducted.
Problem sets not handed until the day
*after*the deadline will have an additional 10% deducted (slide late problem sets under my door if I am not in my office). Beyond this point, problem sets will not be accepted. - You should expect to get your problem sets back within nine days. That is, problem sets handed in on Tuesday will come back Thursday of the next week, if not earlier. I will let you know if more time is needed for a grading a given problem set.

There will be two exams in the course: a midterm and a final.
The final exam is **not** cumulative; that is,
it covers material from the second half of the course starting with discrete
probability and ending with boolean algebra.

I take academic integrity seriously.
To repeat the problem set instructions from above:
You must work **alone** on problem sets.
You may only discuss problems with me.
The only materials you can reference when working on these problems are your course notes and the assigned textbook.
In particular, you **may not** reference online sources or talk to other students.

You may not bring any outside material into exams.

You may not reference any problem sets, exams, or solutions from prior teachings of this course.

When in doubt, ask me what is allowed.

Below is the current schedule for the course. I will add more detail regarding the topics covered (and corresponding textbook sections) as the semester continues. I will adjust this schedule if needed if our pace proves too fast or slow.

**Week 1** (9/1)

Introduction to the course and its topics; begin work on logic and proofs.

**Problem Set 1 Assigned (Due on 9/13):** [Download]

__Textbook Chapter(s):__ 1

**Week 2** (9/6 and 9/8)

Logic and proofs continued.

__Textbook Chapter(s):__ 1

**Week 3** (9/13 and 9/15)

Sets, functions, and sums.

**Problem Set 2 Assigned (Due on 9/20):** [Download]

__Textbook Chapter(s):__ 2

**Week 4** (9/20 and 9/22)

Algorithms: their specification, correctness, and complexity.

**Problem Set 3 Assigned (Due on 9/29; notice this is a Thursday due
date):**
[Download]

__Textbook Chapter(s):__ 3

**Week 5** (9/27 and 9/29)

*No Class on Tuesday, 9/27*

Begin induction on Thursday, 9/29.

**Problem Set 4 Assigned (Due on 10/11):** [Download]

__Textbook Chapter(s):__ 5

**Week 6** (10/4 and 10/6)

Finish induction; introduction to recursion.

__Textbook Chapter(s):__ 5

**Week 7** (10/11 and 10/13)

Basic Counting

**Problem Set 5 Assigned (Due on 10/20; notice this is a Thursday due
date):**
[Download]

__Textbook Chapter(s):__ 6

**Week 8** (10/18 to 10/20)

The first lecture this week will continue our discussion of counting.
The second lecture will be an optional review session for the midterm.
Notice, the problem set is due on *Thursday* this week and will cover material
from Tuesday's lecture.

__Textbook Chapter(s):__ 6

**Week 9** (10/25 and 10/27)

*No Class on Tuesday, 10/25*

Your **midterm** is on Thursday, 10/27.

**Week 10** (11/1 and 11/3)

Discrete probability.

**Problem Set 6 Assigned (Due on 11/15):**
[Download]

__Textbook Chapter(s):__ 7

**Week 11** (11/8 and 11/10)

Discrete probability continued; recurrence relation basics.

(*Reminder:* Monday, 11/7 is the last day to withdrawl.)

__Textbook Chapter(s):__ 7 and 8

**Week 12** (11/15 and 11/17)

Graph theory.

**Problem Set 7 Assigned (Due on 11/22):**
[Download]

__Textbook Chapter(s):__ 10 and 11

**Week 13** (11/22 and 11/24)

Graph theory.

(**Problem Set 8 Assigned (Due on 12/6):**
[Download]

__Textbook Chapter(s):__ 10 and 11

**Week 14** (11/29 and 12/1)

Graph theory concluded and introduction to boolean algebra.

__Textbook Chapter(s):__ 10, 11, and 12

**Week 15** (12/6)

Overflow material, wrap-up and exam review.

**Final Exam:** Wednesday, 12/14 from 4:00 to 6:00 pm, in STM 110 (our
normal classroom).