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.
Canvas will be the main launching platform for the course. This is the first semester using Canvas so bear with me!
Gradescope will be used for problem sets. No need to get an account on this platform. You will be able to access it through Canvas.
Applied Discrete Structures - The most convenient form factor is the html version. I'd suggest that you download the pdf version if you have to work off-line. A hard copy is available on Lulu.com, but I don't require 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 be using Mathematica in this course. Mathematica, Wolfram Cloud, and Wolfram|Alpha Pro are available at no charge to UMass students. They are useful for solving technical problems, obtaining step-by-step solutions, and more. To get access, go to https://www.uml.edu/IT/Services/Software/Mathematica.aspx and enter your UMass email. Learn how to use Mathematica at www.wolfram.com/wolfram-u/.
We will also occasionally use SageMath. SageMath can be used either on your own computer, a local server, or on CoCalc (https://cocalc.com). SageMath cells are contained on this page and in the online version our text.
Grades will be based on the following factors. The percentages are an example of "reasonable" weights. Read below for more on reasonable weights.
- Two Hour Exams: 20% for each
- Final exam 30%
- Quizzes and Problem Sets: 30% of your grade
The weights above are arbitrary examples. If the percentage for the quizzes were changed to 20% and the two hour exams to 25% each, that would be reasonable, right? If you did poorly in the quizzes and had a low grade on that factor, you would prefer the exam percentages to be higher. On the other hand, if you did well in the quizzes, the new set of weights would probably decrease your average. In our first class of the semester we will establish a set of constraints on the weights. This will determine a three dimensional polyhedran of reasonable weights. When we do this, I'll have some constraints that I'll insist on. For example, the final exam will always be worth at least 30%. I'll be open to suggestions for the rest. When the time comes to compute your average, what I'll do for each student is to optimize the average grade from among all the reasonable weights.
This idea comes from Benjamin Grimmer: The Grading Polyhedron
The first hour exam on February 19 will be on Chapters 9 and 10 of the text. The second exam on April 2 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, and Chapter 9 to some extent.
Cheat Sheets
The exams will be closed book with no technology, but one hand-written 8.5 by 11 page (both sides) of notes will be allowed in the two hour exams and three pages for the final.
You are expected to take exams on the scheduled dates. The Final exam will be scheduled between May 2 and May 9. 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 10. The date of the final will be set around a month into the semester. You can get it on SIS. If the date of the final exam conflicts with another final exam, you need to let me know as soon as possible, not a few days before the final.
There will be short 5-10 minute quizzes at the end of most classes. The quizzes will potentially be on anything before that day's class material, not new material from that day. The lowest four quiz grades will be dropped. If you miss a quiz, you will get a zero, which can be one of the dropped grades. The first quiz will be on January 29 and the last one will be on April 23. There will not be a quiz on the day of an exam (naturally!) and on the class before each exam.
The way I grade quizzes: The minimum quiz grade if you participate is 5 out of 10 - you get that for entering your name. The remaining 5 points is based on the correctness of your response.
The two general topics we cover in this course are graph theory and algebric structures. A more detailed list of topics that we will cover is posted on the Canvas 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 is a good grasp of the material in Discrete Structures I. This includes basic set theory, counting, logic, matrix algebra, 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"
I don't totally oppose the use of AI in studying for this course. However, be aware of its limitations. I've experimented with both ChatGPT and Microsoft CoPilot, asking it questions related to this course and have had mixed results. One example is that I've asked both to construct `cubic' graphs (graphs whose vertices all have degree three) and they usually give me graphs with vertices having different degrees. If you do use AI in problem sets, attribute it, including the prompt you used to get an answer. This leads to the next general topic... .
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 are registered with Disability Services and will require academic accommodations, please notify me via the Accommodate semester request process as soon as possible so that we might make appropriate arrangements. It is important that we connect to discuss the logistics of your academic accommodations; please speak to me during office hours or privately after class as I respect and want to protect your privacy. If you need further information or need to register for academic accommodations, please visit the Disability Services Website.
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