Discrete mathematics arises in various disciplines, including computer science, economics, engineering, and business. In this course, students will learn about mathematical reasoning and proof, especially with respect to the discrete phenomenon often encountered in the field of computer science. There will be significant emphasis placed on solving problems in this course. Topics to be covered include: propositional and predicate logic, proofs and proof techniques, sets, functions, sequences, relations, mathematical induction, counting and countability, elementary discrete probability, and graphs. We will cover portions of Chapters 1-2, and 4-10 in the text.
At the conclusion of this course, you will be expected to be able to:
One textbook is required for this course:
There will be additional articles and resources available through Moodle.
I take the Honor Code very seriously. It enables me to be able to give take-home portions of exams, and have homework and other activities where collaboration is allowed (as detailed below) contribute meaningfully to an individual student’s final grade. You are expected to uphold both the spirit and the letter of the Honor Code. Often, Honor Code violations are acts of desperation. It is always preferable to come to me and ask for help than violate the Honor Code.
Like most things worth doing, learning the material in this course will require work. Yet, people often learn the most by making mistakes. Do not be afraid to try and fail! If you engage actively with the material, read for understanding, practice problems in a timely manner, and ask questions (in class and/or office hours), you are likely to succeed in the course overall, and have gained skills useful for your future endeavors in computer science. For many problems in mathematics and computer science, the difficulty lies in finding the correct approach, and after that has been determined, the solution arises naturally. Yet, even when a technique has been determined, the calculations may not be trivial and may not match our intuition. I am here to help you and guide you.
This class meets for 2.5 hours per week. The University-wide expectation is that you will spend at least an additional 2.5 hours a week per credit on the class, outside of class time. For this course, that is 10 hours per week. You are expected to budget the necessary time in order to succeed in the class, including reading the textbook, completing assignments, and studying for exams.
Class attendance is expected and required. Assignments are still due regardless of attendance, and you are responsible for making up all missed in-class material. Feel free to come to office hours with specific questions, but lectures will not be repeated there, so I encourage you to acquire contact information from your classmates as soon as possible. Missing more than ten percent of a given class (arriving late, leaving early, sleeping or otherwise inattentive in class) may be considered an absence.
For each absence, you must send me an email at least 1 hour before the start of class stating that you will be absent for that particular class. You do not need to tell me why; you simply need to inform me in advance. However, if you believe the absence is excused under university policy, you must also provide me with sufficient information to determine that. Even if you mention a future absence to me in person, you must still send me an email with details about your absence.
Note that you must notify me for all absences, even those deemed excused under university policy (e.g. university-sponsored activities, absences due to religious and cultural traditions). The Excused Absence Policy requires students to notify the instructor as far in advance as possible, and to complete missed work. Though university policy does not consider illness to be an excused absence, I encourage you to use your best judgment in such situations, particularly if you may be contagious. Extenuating circumstances that prevent you from contacting me in advance will be handled on a case-by-case basis.
Excused absences for which you properly notify me will not count against you. Unexcused absences for which you properly notify me will count as a half absence. Absences (excused or unexcused) for which you do not properly notify will count as a full absence. Each absence above two will subtract 3 percentage points from your final grade. If you have five or more unexcused absences (half or full), you may be involuntarily withdrawn from the course. As always, talk to me if there are extenuating circumstances.
I expect you to attend class, arrive on-time and prepared, and be alert, engaged and respectful participants in class. You should contribute to class discussions without dominating them. Participation will be evaluated over the semester as a whole, taking into account that everyone has the occasional off day.
Be willing to answer questions. Contributions that exemplify Paideia moments (where you “apply the thinking, modes of analysis, creativity, etc., from this class to either another class or to another aspect of life,” per President Burger) are highly encouraged. Your participation grade does not reflect that you always had the correct answer, but rather that you were prepared for class, involved and engaged in the classroom, physically and mentally present and focused on the course material, and respectful of others. Note that participation is different from, though often correlated with, attendance.
Some days the class will be broken up into groups to solve problems, and selected students from some groups will be asked to present at the board. There are multiple reasons for doing so. It is good practice for your future professional or scholarly careers, where you will be expected to be able to present and discuss your work of that and your team. Your use of the language of mathematics will ideally improve as you hear your classmates present ideas and realize that imprecision can lead to confusion, even if the underlying argument is valid. Collaboration is also a necessary and important part of most modern work, despite any misleading stereotypes about CS professionals. Problems that can quickly be solved individually likely already have been solved by someone, or are appropriate for automating (by a computer) or outsourcing. Interesting and rewarding problems often required failed attempts before arriving at a correct solution, and being able to work through these ideas as a team is a valuable skill for the modern world.
You are responsible for carefully reading the textbook by the beginning of class on the dates that each section/chapter is listed on the calendar. Come to class with questions!. You may be assessed on all assigned material, whether or not it is explicitly discussed in class. Supplemental material may be posted on Moodle, as appropriate.
For each assigned section or reading listed on the calendar there will be a reading question to complete on Moodle. These questions, often auto-graded by Moodle, should be straightforward from the reading. While it is important to read the sections and complete these questions, they often test only surface knowledge, and you should not assume that because you are able to answer these questions, you have fully understood the entire section or topic in depth. Naturally, you may (and are expected to use) the book and any materials posted on Moodle to complete these questions, but you may NOT use the internet or other resources. Since I want you discussing course material with your classmates, I will not preclude you talking to your classmates about these questions, but clearly they will have the most value for you if you answer them individually. If you do discuss them with others, it is expected to be a full discussion of the question, not just one person providing the answer to another. These questions are due when the reading is due (beginning of class on the listed date) and no late submissions will be accepted.
Typically, six exercises will be assigned from each section listed on the calendar. See the guidelines about how to write up exercises in this course. Illegible homework or answers without sufficient work may be given very little credit, if any. I will typically assign even-numbered exercises in the text or problems from other sources since answers to the odd exercises are found in the back of the book and you are encouraged to look at those to help you understand the material and the assigned exercises. The exercises assigned are only a sampling of the material, and you are encouraged to try others. Solutions to homework problems will be posted on Moodle after the submission deadline. You are responsible for reading the solutions in a timely fashion and asking appropriate questions if you do not fully understand the solutions.
You may work together on homework, but each student must each individually write up their own solutions, and must acknowledge anyone (other than the instructor) with whom they have collaborated. For example, students may choose to work in a group on the board in the Chapman- Whitmore Lounge, but each student must individually write up his or her own solution based on that groupwork, and then list all names of people in the group. In accordance with the Honor Code, each student is expected to be able to explain any material he or she submits, and must include the completed, signed Honor Pledge on each assignment. You are allowed to consult with anyone at Southwestern about homework exercises. It is a violation of the Honor Code to consult solutions from previous offerings of this course, solutions manuals, the internet, or people not currently at Southwestern for the assigned exercises. As such, if you want to discuss a problem with a current SU student who has previously taken a Discrete Math class, you may, but they cannot refer to solutions (their submissions or posted solutions) to guide the conversation. If in doubt, please ask me in advance. Again, homework is your chance to practice, and if you rely too much on working with others, you will likely not learn the material.
Due dates (generally Fridays at noon for each chapter) are listed on the tentative calendar. Note the exception in the first assignment: exercises from Sections 1.1 and 1.2 are due Wednesday August 31 at noon, so that you will be able to get feedback early in the semester about how you are conforming to the homework guidelines. You are responsible for budgeting your time appropriately to complete the assignments, and are encouraged to start early. Early submissions are accepted. Assignments may be submitted in class, under my office door, or on Moodle, by the posted deadline. Each student is allowed two late homeworks, due the following Tuesday at noon, without penalty. Use these wisely, as no other late homeworks will be accepted, excepting serious extenuating circumstances.
Each section will be graded out of 10 points:
Quizzes may be given in class (unannounced) or on Moodle (announced). No makeups will be given. If you miss a quiz due to a University-excused absence that you have notified me about in advance (as described above), you will be exempt from that quiz. The quiz grade will be computed by dropping the lowest two quiz scores and averaging. Unless otherwise specified, quizzes are to be completed individually (no consultation with others or any materials) and are pledged. Students are expected to email me about any technical difficulties that may occur with Moodle as soon as they arise.
There will be two tests during the semester, as well as a final exam. Make-up tests and exams may be oral and will be generally given only for appropriately documented reasons of illness, family emergency, religious obligation, or participation in a University sponsored event. Make-ups given for other reasons are at the discretion of the instructor and may include a cap on the maximum grade earned. The two tests during the semester will have an in-class component and a take- home component. The take-home component will comprise at most 40% of the test grade, and may be open-book (but closed internet and other resources) while the in-class exams will likely be closed-book. Test 1 is tentatively scheduled for Thursday October 6 (in-class) and Thursday September 29- Thursday October 6 (take-home). Test 2 is tentatively scheduled for Thursday November 10 (in-class) and Thursday November 10-Thursday November 17 (take-home). The Registrar has scheduled the final for Monday December 5 from 1:30pm-4:30pm. Tests and exams will be pledged, in accordance with the Honor Code.
The grade cutoffs are listed here. They may be modified slightly at the instructor’s discretion, but only in your favor. In truly exceptional cases an A+ may be awarded. Absences may reduce the final grade, independent of these percentages. For those taking the course on a P/D/F basis, earning at least a C- corresponds to a P.
You are expected to keep an electronic copy of any electronic submission until you receive a grade. Failure to reply to email queries in a timely manner (as specified in the email) regarding assignments incorrectly or incompletely submitted (e.g. wrong file attached) will result in no credit given for the associated assignments, or late penalties being assigned. Any concerns regarding grading of an assignment must be brought to my attention within a week of when the item is returned to the class or feedback/grades are posted on Moodle.
The best strategy for success in this course is to read the material thoroughly in advance of the assigned date, complete all homework problems, practice additional problems, and ask questions throughout the semester. Extra credit opportunities are generally expected to enhance your educational experiences either in this course or in math and computer science as a whole. There is information on Moodle about activities that can earn extra credit throughout the semester (completing specified computer or writing projects, at most one per group of activities, due on September 28, October 28, and November 30, respectively). If you think you will be wanting extra credit, I encourage you to complete these activities by the stated deadlines. There may not be other opportunities.
Cell phones are not to be used during class. Please set them to Do Not Disturb, not simply to vibrate. I strongly advise placing them in a bag rather than keeping them in a pocket or on your desk to avoid temptation. Should your phone ring, you must take it into the hallway and answer the call. It is expected that when in class you will use the computers for course activities (notetaking, writing code), not for websurfing, gaming, messaging, using Facebook, printing material for other courses, etc. You must obtain my explicit written permission to record any audio or video in the classroom.
Southwestern University will make reasonable accommodations for persons with documented disabilities. Students should contact the Center for Academic Success and Records to determine their eligibility to receive accommodations (Prothro Center for Lifelong Learning; 512-863-1286). Please notify me as early as possible about any required accommodations.
I will maintain a detailed calendar on Moodle, and you should refer to it regularly throughout the semester. I will try to adhere to the schedule as closely as possible, but all dates and details are subject to change. In those cases I will notify you in class or on Moodle.
Assignments and ideas on this syllabus build on those from everyone who has taught it before, especially Barbara Anthony. The template for this website was originally designed by Alex Godwin.