605.203.82 - Discrete Mathematics

Expanded Course Description

We recommend this course be taken by itself.  If you have significant travel requirements limiting your Internet access, you may wish to reconsider taking this course.  This course requires programming experience in Java or Python. The catalog has been updated to reflect that requirement. If your programming experience is minimal or rusty then a refresher course first may be appropriate. This course will be offered in Spring 2024.  An onsite version is offered in the Fall terms.

Course Structure

The course materials are divided into modules which can be accessed by clicking Course Modules on the left menu. A module will have several sections including the overview, content, readings, lectures, discussions, quizzes, and assignments. You are encouraged to preview all sections of the module before starting. You should regularly check the Calendar and Announcements.

Course Topics

Course topics Include:

• Propositional Calculus
• Formal Proofs and Types ofProofs
• Introduction to Matrix Algebra
• Proof by Induction
• Sets
• Counting and Probability
• Functions and Function Inverses
• Relationships and Equivalence Relations
• Graphs
• Trees

Course Goals

This is an undergraduate course in topics in discrete mathematics designed to help students meet the mathematics requirements for admission into the part-time graduate program in Computer Science.  The course will attempt to provide the appropriate background and motivation for the study of advanced topics in Computer Science. 

By the end of the course, you will be able to:

• Apply standard mathematical terminology, properties, and concepts in set theory, functions, simple combinatorics, relations, and graphs and trees.
• Apply appropriate methods of proof, including proofs by induction.
• Relate topics in discrete mathematics to applications in computer science
• Analyze and apply patterns of discrete mathematical structures to demonstrate mathematical thinking.
• Develop logical reasoning skills for both direct and indirect arguments.

Course Learning Outcomes (CLOs)

• Apply standard mathematical terminology, properties, and concepts in set theory, functions, simple combinatorics, relations, and graphs and trees.
• Apply appropriate methods of proof, including proofs by induction.
• Relate topics in discrete mathematics to applications in computer science
• Analyze and apply patterns of discrete mathematical structures to demonstrate mathematical thinking.
• Develop logical reasoning skills for both direct and indirect arguments.

Textbooks

There are two required textbooks for the course. The first is:

Rosen, K.H. (2012). Discrete mathematics and its applications (7th ed). New York, NY: McGraw Hill.  ISBN-10: 0073383090; ISBN-13: 978-0073383095
For Fall 2023, we will switch to the 8th edition.

Textbook information for this course is available online through the appropriate bookstore website: For online courses, search at http://ep.jhu.edu/bookstore.

Required Software

This course assumes you have access to a personal computer or laptop to use for programming during the course. The operating system can be Windows (recommended), Linux, or MacOS.  You may use Java , but Python is recommended. You may not use MATLAB or a scripting language.  You should download and install an IDE for Java or Python (Jupyter is not permitted). Then spend some time becoming comfortable with it.

NOTE: Problems with the computer system that you have chosen to use for developing your programming assignments do NOT constitute a legitimate excuse for late assignments. You are strongly encouraged to have backup arrangements in the event of a drive failure, power problems, or other issues that limit your access.

Mathematical Symbols

At various points during the semester, you may need to submit work incorporating mathematical symbols. There are several options for dealing with this.

• Use equation editing software in a PDF source document (e.g., LaTeX, or MS Equation)
• Write in Html using any standard Html editor (e.g., Frontpage, or Mozilla Kompozer). On an HTML page you can use Unicode Entity Codes for Math to get the symbols. Unicode Entity Codes for Math can also be used to enter symbols directly into text boxes on the Blackboard site. For example, they can be used in the test tool if answers require symbols.     http://sites.psu.edu/symbolcodes/accents/math/mathchart/
• You can write by hand (or type and just write in the symbols by hand), scan the paper, and submit as a PDF attachment. Do NOT submit an image file.  Photographs of documents will not be accepted.  If you submit a handwritten document, we will make a sincere effort to read it accurately but are not responsible for deductions due to handwriting issues.
• Scanner apps are acceptable, provided you submit a PDF.  Possibilities include

Student Coursework Requirements

It is expected that each module will take approximately 10-15 hours per week to complete. Here is an approximate breakdown: reading the assigned sections of Rosen and doing the assigned practice problems (approximately 2-3 hours per week), reading the assigned sections of the zyBook and doing the interactive exercises (approximately 1-2 hours per week), listening to the audio annotated slide presentations (approximately 2-3 hours per week), and taking the quizzes (approximately 1 hour, including review), participating in the discussions (approximately 2 hours per week, when needed) and doing assigned homework (approximately 3-4 hours per week) and working on collaborative problems or projects (approximately 2-4 hours per week).  You must be able to commit time during the week for this course.  You will not be able to do everything you need to do solely on the weekends. 

This course will consist of seven basic student requirements:

Homework Assignments (25% of Final Grade Calculation)

Collaborative Problems (12% of Final Grade Calculation) 

Projects (30% of Final Grade Calculation) 

Discussion (10% of Final Grade Calculation) 

There are several opportunities for discussion and reflection over the course of the semester.

• Muddiest Point Discussions – Modules 4, 8 and 11 contain asynchronous discussions on the module learning objectives. (e.g., “I struggled to understand X”, “I see how Y is applicable in my work”, etc.) to help you further understand unclear aspects of the material. For these you are required to post to each person in your current collaboration group.
• Missionaries and Cannibals Discussion – Module 1
• Socks Problem – Module 6
• Instant Insanity Reflection– Module 12
• Card Trick Discussion and Reflection– Module 13

Some Notes about Discussions - If you are unfamiliar with discussion forums you may be unsure about exactly what you are supposed to post, so here are some guidelines.

• It is important to remember that discussions are intended to be interactive. So, if you do all your posts at the end, no one can interact with you.  Similarly, if you do all your posts up front, others can respond, but you need to come back in and respond to them as well.  In volleyball, it is not enough for someone to serve and someone to hit it back, you must keep the ball in the air and not let it drop.
• A quality post should address the question posed, but it does not have to be the end-all and be-all of responses. Leave something for others to say. Your response, especially follow-on responses, can include, but are not limited to, one or more of the following:

• It is fine to say that you agree (or disagree) with someone, but it is important to say why and to give supporting arguments. This shows you understand the subject and that you are thinking about it. One of the primary purposes of discussion is to help you take ownership of the material and to get you to think about it more deeply.
• Students are encouraged to be creative or even humorous in thread titles. Be sure to include your name in the thread.  For example, "Sometimes it is good to be last - Jane" or "Call me LIFO – Harry."
• If you have difficulty composing a written post, consider experimenting with a voice to text application, which will allow you to compose out loud.
• Finally, of course, you want to phrase all your posts in a positive and constructive manner, the way you would want responses to your posts to be.

• Presence (1 points) – Makes a reasonable, original post
• Substance (2 points) – Contributes substantial content to discussion
• Community (2 point) – Posts to at least two threads other than own.
• Students will be penalized for not including a thread title, not including their name in the thread title, and not addressing the recipient of a post by name.
• Posts outside the scope of the module will be ignored in the grading.

• Presence (10 points) – Makes a good, original post, relevant to the covered part of the course by Saturday.
• Follow up (10 points) – makes helpful, quality replies to all members of their current collaboration group by Monday.
• Students will be penalized for not meeting posting deadlines, not responding to everyone in their group, not including a thread title, not including their name in the thread title, and not addressing the recipient of a post by name.

Online Text Interaction (10% of Final Grade Calculation)

You will need to complete the interactive exercises in the online textbook. Parts of the zyBook marked optional will not be scored, but you are encouraged to complete them. While it is preferred that you complete activities within the time frame of the module, for time management reasons, you may work ahead and still get the credit. You can track your zyBook performance on the zyBook website. You must click on the zyBook Activity link in the Module to make sure your credit is posted back to the gradebook.

Show and Tell (5% of Final Grade Calculation)

In each module, three students will each record and present a short video on an interesting mathematical item for Show and Tell.  Signup and a rubric are in Module 0. Students presenting will be graded on the depth of their presentation and its applicability to the course, and in particular its applicability to the module in which it is presented.  They will also be graded on their response to comments and questions by others. Videos should be posted no later than Sunday midnight to allow others time to view and comment.  If you are not presenting, participate for extra credit by asking questions and making comments, which are due by Tuesday midnight. The extra credit will be added to your presentation score. Students presenting in the same week must coordinate to prevent overlap.

Quizzes (10% of Final Grade Calculation)

Each module of the course content has one or more quizzes items in the module. You are expected to complete these each week during the associated module to gauge their mastery of the material and identify areas needing additional study and review. These questions are scored by the computer. Quizzes are weighted proportionally. Quizzes will remain available until the beginning of Module 14 for study and review purposes.  You will get one attempt on each quiz and generally a time limit of 30 minutes. A couple of quizzes will allow additional time. The lowest quiz will be dropped. Where there are terminology differences between the lectures, Rosen text and zyBook, the quizzes will go by the lecture.

Grading Policy

Grades will be based on 1000 points over the semester. All students need to get a B- or higher in Discrete Mathematics to satisfy the prerequisite requirement. Students earning a grade below B- will not be allowed to move forward with the program.  As you see from the table, there are some extra credit points available in most of the grade components.  We will use a +/- grading system with grades of A+, A, A-, B+, B, B-, C, and F possible, as follows:

Due Dates

A note about due dates: All times are specified in terms of EST/EDT, local to the instructor. Final Discussion posts, zyBook, homework, quizzes, collaborative problems, and projects for the module are always due on Tuesday 11:59 PM. See the calendar and course outline.  LATE work will not be accepted, except by prior arrangement. Submissions after the deadline will be accepted by Blackboard but will be marked late. We generally will not quibble over a couple of minutes lateness. Multiple submissions will also be accepted, so if you think of something you forgot to do, a new answer for a question, or if we ask you to redo something, just go ahead and resubmit to Canvas in the same place as the first submission. There is a three-hour grace period on the deadline for homework and projects only.

Final grades will be determined by the following weighting:

Course Policies

Plagiarism

Plagiarism is defined as taking the words, ideas or thoughts of another and representing them as one's own. If you use the ideas of another, provide a complete citation in the source work; if you use the words of another, present the words in the correct quotation notation (indentation or enclosed in quotation marks, as appropriate) and include a complete citation to the source. See the course text for examples.

Students should read policies pertaining to academic misconduct and netiquette at http://ep.jhu.edu/genpolguid. Please read below to see how the Academic Misconduct Policy applies to this class. You will be asked to take an Honor Pledge.  You are expected to do your own work and turn in your own work. Help from other sources must be acknowledged. It is okay to discuss problems with others for perspective or to make sure you understand it correctly, but the code you write must be your own. Downloading code from other sources for the programming assignments 1, 2, and 3 is not allowed. Contact me if you have any questions, no matter how slight, about this policy, or if you have questions about a particular assignment.  Students violating this code will receive a zero on the plagiarized work, e.g., plagiarizing a homework problem will result in a zero on the entire homework assignment or a plagiarized quiz problem will result in a zero on the quiz. Plagiarism will be reported to the Associate Dean.  Subsequent incidents will result the student failing the course.

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.