This section of Discrete Structures II will be using an active learning format, also known as a flipped format.
What does
Active Learningmean?Instead of listening to your instructor lecture on a topic and then trying to apply what you've heard, you will be expected to read assigned parts of our text and contribute comments related to your reading. Then in most of the face-to-face meetings you will work in groups on more challenging problems related to the reading.
The two main goals of this course are shared by many other mathematics courses. They are to promote the development of problem solving skills, and to help you develop effective communication skills (see below for more on this objective) for mathematics and related fields. Logic is part of the course and is a fundamental tool for mathematics communication, whether it is for proving a theorem, demonstrating the validity of an algorithm, or explaining the logic behind the solution to a problem.
Another goal that is more specific to this course is to connect computer science and mathematics - Most students taking this course are computer science majors or minors. The topics are all fundamental ones in computer science. Developing an awareness of these connections should help in your future courses in computer science.
Blackboard will be the main launching platform for the course. From our Blackboard page, you will be able to join Zoom for our virtual meetings. You will also be able to access reading assignments on Perusall from Blackboard.
Perusall is free and you should be able to log into it directly from Blackboard, but you can also get a free account to see what it's all about at http://Perusall.com. A few other courses use it, so you may already have an account.
Gradescope will be used for at least one problem set. No need to get an account on this platform. You will be able to use it through Blackboard.
Applied Discrete Structures - We will be using a copy of the pdf in Perusall. In addition, you can use the html version. A hard copy is available on Lulu.com, but I don't recommend it.
- You can get the whole book on LuLu: Full Version.
- Or you can get the second half, which is what we will be using most of the semester: Part 2 - Algebraic Structures. This part is missing the chapters on graphs and trees though.
We will also use some of the materials in another book that I coauthored. You do not need to buy the book since you will be able to download all the information you need for free.
We will be using Mathematica in this course. Students can download a copy of Mathematica for their personal computers at no cost. Click here for details
We may also use Sage for some of the course. Sage (sagemath.org) is a free, open source, software system for mathematics. Sage can be used either on your own computer, a local server, or on CoCalc (https://cocalc.com).
Grades will be based on the following factors:
- Two Hour Exams: 15% for each
- Final exam 30%
- Reading Assignments : 25% of your grade
- Quizzes and Problem Sets: 15% of your grade
The first hour exam will be on Chapters 9 and 10 of the text. The second exam will be on Chapter 11. The final exam will be comprehensive. In addition to prior material, it will be on Chapter 15. However, Chapter 15 builds on Chapter 11.
Cheat Sheets
The exams will be closed book with no technology, but two 8.5 by 11 pages (both sides) of notes will be allowed in the two hour exams and 4 pages for the final.
You are expected to take exams on the scheduled dates. The Final exam will be scheduled between April 29 and May 6. You are expected to leave these dates open until we get a definite date/time for the final exam, which will be posted on SIS. Do not schedule travel before May 6.
There will be short 5-10 minute quizzes at the end of some classes. I'll let you know in advance when there will be a quiz. The quizzes will potentially be on anything before that day's class material, not new material from that day. The lowest quiz grade will be dropped. If you miss a quiz, you will get a zero, which can be the dropped grade.
Due to the Active Learning format of the course, you'll be expected to read the text associated with all classes but the first few before the class. This is a graded activity, which counts for 25% of your grade. Grades for the reading assignments will be based on your engagement on Perusall. Engagement includes reading and watching the material (there are videos associated with most readings), asking questions, answering classmates' questions, upvoting other posts, participating in quizzes that are on Perusall, and even making observations about the reading. Most students find it easy to get full credit for most assignments, which is a score of 2. However, your score can be as high as 3, which translates to a grade of 150% for the assignment. Perusall quizzes are not the same as in-class quizzes. They don't contribute to your quiz grade.
Once the deadline has passed on a reading assignment, you will still have access to the material, but you cannot get any further credit. Be aware of the due dates - for most of the semester, that means you need keep ahead of material we cover in your reading.
The two general topics we cover in this course are graphs and algebric structures. A more detailed list of topics that we will cover is posted on the Blackboard page for this course. If you're not familiar at all with these topics, don't worry. We start from the basics in both. What you do need to have a good grasp of is the material in Discrete Structures I. This includes basic set theory, counting, logic, relations, functions and recursion. The following SageMath cells can give you an inkling of what the general topics are about.
A couple examples of SageMath cells:
First, a directed graph with 7 vertices. We will start the semester studying graphs. Click on the "Evaluate" button to get a result. You can edit the input too. For example, if you add ",7:[6]" to the list just before "})" you will see an extra edge from 7 to 6. If you replace DiGraph with Graph, you get an undirected graph.
... and the addition table for integers mod 11. We will study algebraic structures such as this one in a few weeks. If you replace 11 with some other integer you get a different table. I don't suggest anything too large - less than 50? You can also change "addition" to "multiplication"
All students are advised that there is a University policy regarding academic integrity.It is the students' responsibility to familiarize themselves with these policies. Students are responsible for the honest completion and representation of their work. Link to the Academic Integrity Policy
We are a campus that cares about the mental health and well-being of all individuals in our campus community, particularly during this uncertain time. If you or someone you know are experiencing mental health challenges at UMass Lowell, please contact Counseling Services, who are offering remote counseling via telehealth for all enrolled, eligible UMass Lowell students who are currently residing in Massachusetts or New Hampshire. I am also available to talk with you about stresses related to your work in my class.
If you have a documented disability that will require classroom accommodations, please notify me as soon as possible, so that we might make appropriate arrangements. Please speak to me during office hours or send me an email, as I respect, and want to protect, your privacy. Visit the Student Disability Services webpage for further information.
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One of the objectives of this course is to help you develop your mathematical communications skills. You'll be expected to contribute to the discussion of the assigned readings. In our face-to-face classes you'll be working in groups to solve more challenging problems. The following are a list of the things you should keep in mind for this course. I'll be looking for you to attempt to follow these guidelines.
Source: Richard Wong, UCLA, Active Learning Exchange on MAA Connect