Instructor: Prof. Seth Fogarty Email: sfogarty@trinity.edu

Office: CSI 270M Office Hours: See webpage

Meets: MWF 11:30-12:20 Classroom: CSI 104

Textbook: Discrete Mathematics and Its Applications, 8th Edition, by Kenneth Rosen. 

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Course Description

This is a discrete mathematics course for computer science majors, designed to introduce students to the kind of mathematical thinking employed in computer science.  This course covers a variety of topics that can be broadly split into three categories.

• Discrete Structures: A variety of discrete structures: the abstract mathematical structures used to represent discrete objects and relationships between these objects. These discrete structures include graphs, sets, tuples, permutations, and sequences.

• Formal Logic: An introduction to formal logic, sometimes called the calculus of computer science. Formal logic will be used as an introduction to mathematical reasoning and to elucidate the structure of mathematical arguments.

• Combinatorics: The mathematics behind counting and enumerating objects, with an emphasis on performing combinatorial analysis to solve counting problems and analyze algorithms.

Objectives

Discrete mathematics is both fundamental and vast. This course will not be able introduce every area of mathematics necessary for success in computer science. Thus the primary objectives of this course are not to grant students familiarity with a wide variety of topics, but to promote understanding, depth, and mathematical maturity. In specific, the objectives include:

Mathematical Reasoning: Students should be able to comprehend and construct arguments about discrete mathematics. Notably, this includes the science and art of constructing proofs.

Communicating Mathematics: Students should be able to communicate algorithmic and mathematical concepts in a variety of contexts with appropriate levels of formality.

Independent Learning: Students should be able to independently read and absorb the mathematical knowledge required to solve problems in areas of discrete mathematics they are not familiar with.

Course Structure and Assessment

This course meets three times a week. Fridays and Mondays will be primarily lectures, with short in-class exercises. Wednesdays will be devoted to other forms of pedagogy, including individual exercises, group projects, recitations, proof critiques, and high-level explorations of student-chosen topics. Assessment is broken down into the following categories.

Class Participation

Class participation accounts for 7% of the course grade. This includes both attendance and in-class exercises.

Readings

Reading from the textbook will be assigned and assessed, accounting for 8% of the course grade. Every Friday a 2-4 page reading assignment will be given on material that will not be covered in class, but will be necessary for lectures and assignments. There will be a short reading assessment due on Monday. Reading and assessment should take roughly half an hour, but also provide an opportunity to review lecture material. Reading assessments must be completed individually, and may not be submitted late.

Homeworks

Homeworks are due every Friday, and are worth 40% of the final grade. Homeworks may be completed in pairs or individually.  Collaboration between homework groups is explicitly allowed, but the individual or pair submitting the assignment must write their answers themselves.  Please note any collaborations on all submissions. Homeworks that are typeset will receive up to 4% extra credit. Homeworks are submitted at the beginning of class. Late assignments are not accepted unless specifically discussed. 

Self-Directed Learning

In late February two self-directed learning (SDL) assignments will be released. These include chapters of the book that will not be covered in class, and will have due dates corresponding to when that material will be used in lecture. These are somewhere between a large reading assessment and a small homework: they will contain problems similar to the homeworks and are counted as homework grades; but like a reading assessment they must be completed individually, do not receive any extra credit for typesetting, and do not require fully formal writing.

Exams and Quizzes

Exams and quizzes are worth 45% of the final grade. There will be several in-class quizzes, an out-of-class midterm on Tuesday, March 18th from 6pm-8pm, and a final exam on Friday May 8th from 8:30am-11:30am

Grades

The following grade cutoffs apply for this course. Grading will be stringent to reflect these cutoffs.

Honor Code 

Students are expected to abide by  the Trinity University Honor code. Reading assessments and exams must be completed individually. Homeworks can be submitted individually or in pairs. Collaboration between homework groups is explicitly allowed, but the individual or pair submitting the assignment must write their answers themselves.  Please note any collaborations on all submissions. Because the course covers the fundamentals of written mathematical communication, the use of generative large-language models (AI) is forbidden for this course.  Finally, the use of laptops, tablets, or cell phones during class is prohibited. Exceptions for the use of a laptop or during class can be given for accommodations or compelling reasons.

Attendance Policy

Students are expected to attend class regularly. Students who will miss class should contact me before their absence, and complete all homework assignments ahead of time. In certain cases electronic homework submissions can be accepted, if discussed in advance.

Late Policy

Homework should be submitted on time. Because of the rapid pace of the course, late work will not be accepted unless otherwise discussed. It is almost always better to submit what you have and move on to the next assignment, rather than become increasingly behind after a single bad week.

Accessibility

In line with the Trinity University policy on equal access and equal opportunity, this course will be made accessible to all students. Any student who feels they may need accommodations based on the impact of a disability or long illness should contact me and the office of Student Accessible Services to discuss your specific needs. Any student who feels they may need accommodations due to remote learning, technology, environment, or other issues should contact me.

Electronic Recordings of Course Instruction

Please be aware that all classroom instruction, including student participation in classroom activities, is subject to recording and dissemination on the University’s secure software infrastructure. The recordings may be made available to students enrolled in the course to facilitate online learning and review.  The written consent of any students who are personally identifiable in the recording will be obtained before any recording is used outside of class. Students are expressly prohibited from capturing or copying classroom recordings by any means; violations will be subject to disciplinary action.