The purpose of this course is to understand and use (abstract) discrete structures that are backbones of computer science. In particular, this class is meant to introduce logic, proofs, sets, relations, functions, counting, probability, and relations, with an emphasis on applications in computer science.
Kenneth H. Rosen. Discrete Mathematics and Its Applications (7th Edition). McGraw-Hill, 2011.
Online textbook resources available here.
The instructor will periodically post updates to the course website. It is each student’s responsibility to regularly monitor these updates.
The instructor and TA will periodically email enrolled students with announcements. Students must check their Pitt email at least once per day to ensure these announcements are received.
When contacting the course staff via email, messages must be addressed to (or CC) both the instructor and the TA. Email subject should be prefaced with “”.
All assignment submissions must be the sole work of each individual student. Students may not read or copy another student’s solutions or share their own solutions with other students. Students may not review solutions from students who have taken the course in previous years. Submissions that are substantively similar will be considered cheating by all students involved, and as such, students must be mindful not to post their code publicly. The use of books and online resources is allowed, but must be credited in submissions, and material may not be copied verbatim. Any use of electronics or other resources during a quiz or examination will be considered cheating.
Cheating in this course will result in a report to the appropriate school and/or university authority. The instructor will impose a grade of F for the course, and additional sanctions may be imposed by school or university authorities.
Please read, understand, and abide by the Academic Integrity Code for the School of Arts and Sciences.
Students are encouraged to attend all lectures, which frequently include material that is not directly taken from the text. If a student misses a lecture, he/she is still responsible for the material covered and is advised to acquire notes from a classmate.
This course may include open discussion or other interactions among students. To allow all participants to express their viewpoints, all discussion must remain civilized and respectful, and participants must avoid comments and behaviors that disparage others. A student who feels their viewpoints are not being respected is encouraged to contact the instructor, who will work to correct the situation without revealing the student’s specific concerns to the rest of the class. A student in this situation who does not feel comfortable contacting the instructor directly is encouraged to contact the TA, who will uphold the same degree of confidence in relaying the issue to the instructor.
To ensure the free and open discussion of ideas, students may not record lectures, discussion or other course activities without the advance written permission of the instructor. Any recording properly approved in advance can be used solely for the student’s own personal use.
All course material is subject to copyright, including notes, slides, assignments, and solutions. Students are allowed to use the provided material only for personal use, and may not share the material with others, including posting the material on the Web or other file sharing venues.
We believe that students should be able to distinguish between helping one another understand the core concepts of the course material and cheating. We encourage students to discuss the content of the course in ways that will improve understanding without violating academic integrity, such as clarifying the objective of an assignment or discussing general solution tactics.
All assignments specify a precise due date and time. Late assignments will not be accepted. Students must ensure they understand each assignment’s submission procedure in advance of its deadline to ensure that submission difficulties do not cause an assignment to be rejected.
All graded materials that a student receives back should be saved in until after the term has ended and he/she has received and accepts his/her final grade. In this way, any grade discrepancies can be easily resolved.
An evaluation grade can be appealed up to two weeks after it has been returned. After this point, no appeals will be considered. The goal of a grade appeal is to ensure a fair and consistent score. Thus, a score will not be adjusted on an issue of partial credit if the awarded points are consistent with the grading policy adopted for the class as a whole.
When appealing a grade, first contact the grader: email (CC'ing the instructor) for assignments, or return the hard copy for quizzes. If the grader does not find any mistakes made in the original grade, and is unable to clarify adequately the reasons for any assessed penalties, directly contact the instructor describing why you feel the assignment was graded unfairly. The entire assignment will be re-graded by the instructor, so the score may increase, remain the same, or even decrease.
Students must be present for all exams and quizzes. Make-up exams will be given in the event of a documented emergency. The instructor must be informed of the emergency in advance of the missed exam. Missing an exam or quiz under any other circumstances will result in a score of 0.
If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your instructor and Disability Resources and Services, 140 William Pitt Union, 412-648-7890, firstname.lastname@example.org, as early as possible in the term. Disability Resources and Services will verify your disability and recommend reasonable accommodations for this course.
In order to accommodate the observance of religious holidays, students should inform the instructor (by email, within the first two weeks of the term) of any such days which conflict with scheduled class activities.
Students are responsible for reading assigned materials prior to the lecture in which they will be discussed. Readings are from Rosen, 7/e.
This schedule is subject to change.
|Lec.||D Date||C/E Date||Topics||Readings||Slides|
|9/04||No class: Labor Day|
|4||9/11||9/07||Predicates and quantifiers||1.4||[PDF]|
|5||9/13||9/12||Logic programming, nested quantifiers||1.5||[PDF]|
|6||9/18||9/14||Rules of inference, proofs||1.6–1.7||[PDF]|
|9||9/27||9/26||Set identities, functions||2.3||[PDF]|
|10||10/02||9/28||Sequences and summations||2.4||[PDF]|
|10/10||No class: Fall break|
|13||10/11||10/12||Proof by induction||5.1||[PDF]|
|14||10/16||10/17||Midterm exam review||[Practice]|
|18||10/30||10/31||Recursive definitions, structural induction||5.3||[PDF]|
|21||11/08||11/09||Permutations and combinations||6.3–6.4||[PDF]|
|22||11/13||11/14||Generalized permutations and combinations||6.5||[PDF]|
|24||11/20||11/21||Probability theory and conditional probability||7.2||[PDF]|
|11/22||11/23||No class: Thanksgiving break|
|26||11/29||11/30||Expected value and variance||7.4||[PDF]|
|28||12/06||12/07||N-ary relations, final exam review||9.4||[PDF] [Practice]|
|12/13||Final Examination D (10:00)|
|12/15||Final Examination C (10:00), E (12:00)|
Homework will be assigned about once per week. Each homework assignment must be handed in at the start of lecture on its assigned due date. For each assignment, fill out its cover (linked below) and staple your submission with the cover at the front.
Your two lowest homework grades will be dropped.
This schedule is subject to change.
|HW1||Propositional logic||[PDF]||8/30||9/06, 9/07|
|HW2||Logical equivalences||[PDF]||9/06||9/13, 9/14|
|HW3||Predicates and quantifiers||[PDF]||9/13||9/20, 9/21|
|HW5||Sets and functions||[PDF]||9/27||10/04, 10/05|
|HW6||Sequences and sums, integers||[PDF]||10/04||10/11, 10/12|
|HW7||Primes, induction||[PDF]||10/11||10/25, 10/26|
|HW8||Strong induction||[PDF]||10/25||11/01, 11/02|
|HW9||Structural induction, counting||[PDF]||11/01||11/08, 11/09|
|HW10||Pigeonhole, P&C||[PDF]||11/08||11/15, 11/16|
|HW11||Generalized P&C, probability||[PDF]||11/15||11/29, 11/30|
|HW12||Bayes' theorem, expected value||[PDF]||11/29||12/06, 12/07|