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Math 19/CoSc 19/EngS 66

Discrete Mathematics in Computer Science

Instructor: Carl Pomerance (carl.pomerance at dartmouth.edu)

Abstract | Classes | Tutorials | Staff | Textbook | Grading | News and current assignment | Past assignments | Exams | Honor Code


The final exam will be held in Kemeny 105
from 3 PM to 6 PM on Monday, December 8.

Revised office hours for the week of December 1:
Tuesday through Friday, 9 AM to 11 AM, and by appointment.
Also, 9 to 11 on Monday, December 8.


This course integrates discrete mathematics with algorithms and data structures, using computer science applications to help motivate the mathematics.

Here is a tentative syllabus:

1. Logic and proof techniques
3 lectures, Rosen Ch. 1.

2. Induction
2 lectures, Rosen Ch. 4.

3. Set theory
3 lectures, Rosen Secs. 2.1, 2.2, 8.1, 8.5, 2.3.

4. Counting
3 lectures, Rosen Ch. 5.

5. Asymptotics
2 lectures, Rosen Secs. 3.1, 3.2, 2.4, 3.3.

6. Discrete probability
6 lectures, Rosen Ch. 6, Secs. 7.5, 7.6; plus some supplementary material.

7. Hashing
2 lectures, perhaps from supplementary sources.

8. Grahphs and trees
6 lectures, Rosen Chs. 9, 10.


Room: 004 Kemeny
Lectures: Monday-Wednesday-Friday 12:30 pm--1:35 pm (12 hour)
X-hour: Tuesday 1:00 pm--1:50pm


There may be occasional tutorials during our x-period, Tuesdays, 1 PM - 1:50 PM, in our classroom


Carl Pomerance -- 339 Kemeny / Tel. 6-2635
Office hours: Tuesday, Wednesday, Thursday 9:00 AM--9:55 AM and by arrangement at other times.
Homework grader:
Vissuta Jiwariyavej


Kenneth H. Rosen
Discrete Mathematics and Its Applications, McGraw Hill.

This book is available from Wheelock Books and elsewhere.


Your grade will be based on numerical scores for homework, two midterm exams, and a final exam. As much as possible, grades will be based on demonstrated knowledge. However relative performance may be used as a criterion for increasing grades, and grade borderlines will be chosen to place a relatively small number of students on borderlines. At the end of the term, if one of the midterms or your homework average is the lowest of the 4 grades, it will be dropped, with the remaining midterm(s)/homework grades each counting 25% of the grade, and the final counting 50%. If the final exam grade is the lowest, each of the 4 grades will count 25%.


Homework is due at the start of the class period on the due date. Late homework is not accepted unless there is a prior arrangement.
Homework will be generally due once per week on Mondays.
Assignments will be posted on this website, with extra problems and/or comments added as the week progresses.

Past assignments

Homework due Friday, November 21:
Section 9.2, nos. 22, 24, 26, 28, 34, 48, 60
Section 9.3, nos. 10, 24, 35, 38, 40, 42, 44
Section 9.4, no. 20
Section 9.7, nos. 8, 20

Homework due Monday, November 10:
Sec. 6.4, nos. 6, 8, 10, 16, 24, 30.
Sec. 7.5, nos. 6, 16.
Sec. 7.6, nos. 10, 14.
The assignment is complete.

Homework due Monday, November 3:
Sec. 6.1, nos. 14, 16, 20, 36.
Sec. 6.2, nos. 10, 24, 26, 28.
Sec. 6.3, nos. 2, 10.
The assignment is complete.

Homework due Monday, October 27:
Section 2.4, nos. 4, 14, 16, 20
Section 3.2, nos. 6, 8, 20, 24
Section 3.1, no. 44
Section 3.3, no. 12.

Homework due Monday, October 20:
Section 5.1, numbers 30, 32, 34
Section 5.2, numbers 14, 18, 36
Section 5.3, numbers 10, 18, 24
Section 5.4, numbers 8, 12, 22
Section 5.5, numbers 10, 16.

Homework due Monday, October 13:
Section 2.1, nos. 8, 18, 22, 26.
Section 2.2, nos. 4, 10, 30, 48.
Section 2.3, nos. 6, 10, 14, 18, 30.
Section 8.1, nos. 4, 6.
Section 8.5, nos. 2, 30, 36.
The assignment is complete.

Homework due Monday, October 6:
Section 1.5, nos. 16, 24.
Section 1.6, nos. 14, 24, 28.
Section 1.7, nos. 4, 8.
Section 4.1, nos. 10, 12.
Section 4.2, no. 32. Also give a correct proof that every postage of at least 7 cents can be made with 3-cent and 4-cent stamps.
Section 4.3, nos. 4, 6, 8.

Homework assignment due Monday, September 29.
Section 1.1, nos. 14, 18, 28
Section 1.2, nos. 4, 12, 21, 26
Section 1.3, nos. 16, 18, 36, 44.
Section 1.4, nos. 2 (also determine the truth value of each), 32.


There will be two midterm exams, held in the evenings of Tuesday, October 14 (topics 1, 2, 3) and Tuesday, November 11 (topics 4, 5, 6) from 7:00 pm to 9:00 pm. I will attempt to construct the exams to be doable in 60 minutes; the extra hour is to help with possible scheduling conflicts, but I will allow you to spend the full two hours if you wish.

The (cumulative) final exam will be held on Monday, December 8 from 3:00 pm to 6:00 pm in our Kemeny classroom.

Honor Code

Students are encouraged to work together to do homework problems. What is important is a student's eventual understanding of homework problems, and not how that is achieved. The honor principle applies to homework in the following way. What a student turns in as a homework solution is to be his or her own understanding of how to do the problem. Students must state what sources they have consulted, with whom they have collaborated, and from whom they have received help. Students are discouraged from using solutions to problems that may be posted on the web, and as just stated, must reference them if they use them. The solutions you submit must be written by you alone. Any copying (electronic or otherwise) of another person's solutions, in whole or in part, is a violation of the Honor Code.

The honor principle applies to exams as follows: Students may not give or receive assistance of any kind on an exam from any person except for the professor or someone explicitly designated by the professor to answer questions about the exam. Students may not use library or internet sources on take-home exam problems, but they may use their textbook and personal notes.

If you have any questions as to whether some action would be acceptable under the Academic Honor Code, please speak to me, and I will be glad to help clarify things. It is always easier to ask beforehand than to have trouble later!


I encourage any students with disabilities, including "invisible" disabilities such as chronic diseases and learning disabilities, to discuss appropriate accommodations with me, which might help you with this class, either after class or during office hours. Dartmouth College has an active program to help students with disabilities, and I am happy to do whatever I can to help out, as appropriate.

The Student Disabilities Coordinator, Nancy Pompian, can be reached at 6-2014 if you have any questions. Any student with a documented disability requiring academic adjustments or accommodations is requested to speak with me by the end of the second week of the term. All discussions will remain confidential, although the Academic Skills Center may be consulted to verify the documentation of the disability and advise on an appropriate response to the need. It is important, however, that you talk to me soon, so that I can make whatever arrangements might be needed in a timely fashion.