| Instructor | Douglas Weathers |
|---|---|
wweathers at coastal dot edu |
|
| Office hours | TBD MTWTh |
Welcome to MATH 174!
This is a class about learning to communicate mathematically. The goal is that at the end of the course a student who once was nervous about approaching new and difficult mathematics will be emboldened.
We will learn this boldness in the context of discrete mathematics, which is frustratingly defined as “the study of discrete structures.” A discrete structure is something whose elements enjoy a clear separation from each other. Consider the following question: What is the number following 1? In the set of natural numbers, the answer is simply 2. In the set of real numbers, there is no answer: you will find another real number between 1 and 1.1, between 1 and 1.01, and so on. In fact, it will not be possible for you to even list all the numbers between 1 and 1.01. Discrete structures are more like the former example, the natural numbers.
Examples of discrete structures include sets, families of statements with logical connectives, sequences, Boolean matrices, graphs, and partial orders. Oh, and you’re also going to learn how to count real good.
This course is a challenging one. Work hard, have faith in your own abilities, and reach out to me and your classmates when you need help!
You will be provided with a free web textbook and a series of videos (linked from the book). You are intended to use these yourself, and use the office hours to ask questions about what you have learned.
The videos and the book are meant to compliment one another. The book is much more thorough, and the videos are meant to provide short demonstrations and examples. Some students may prefer to watch the videos before diving into the book’s motivation and explanations; other students may prefer to read the text and then watch an example in action. Try both orders to see which works best for you, but use both resources.
We will use Microsoft Teams to communicate with one another. The link to join has been e-mailed to you. If you are not happy with your name in the Coastal Carolina system, you are welcome to join with another e-mail address.
Communication: You are encouraged to contact me via e-mail or Teams (direct message or class chat). I will respond to all correspondence within 24 hours if not sooner (correspondence sent Friday may receive a response Monday).
I love talking to students! That’s why I am here. Don’t hesitate to reach out as soon as you have trouble with the material, or for any other reason.
Code of conduct: In a typical summer course we would see each other every day and our course community would grow naturally. Because the ongoing COVID-19 pandemic makes in-person meetings dangerous, we will have to mindfully create our community online. To that end, you may find yourself speaking to your classmates online more often than you would expect to.
This is an inclusive classroom where students of all races, ethnicities, genders, religions, sexual orientations, and abilities are encouraged to learn mathematics. You are to respect your fellow classmates at all times.
Access to our community workspace is a privilege. Students who harass their classmates may lose that privilege, and if an offense is particularly egregious there will not be a warning.
Academic integrity: Coastal Carolina University is an academic community that expects the highest standards of honesty, integrity and personal responsibility. Members of this community are accountable for their actions and are committed to creating an atmosphere of mutual respect and trust. For more, see https://www.coastal.edu/aic.
Accomodations: Coastal Carolina University is committed to equitable access and inclusion of individuals with disabilities in accordance with the Americans with Disabilities Act and Section 504 of the Rehabilitation Act. Individuals seeking reasonable accommodations should contact Accessibility & Disability Services (843-349-2503 or https://www.coastal.edu/disabilityservices/).
Prerequisite: MATH 130/130I with a C or better.
Course topics: Set theory, logic, proofs, recursion, sequences, asymptotics, induction, combinatorics, probability, relations, digraphs, and Boolean algebra.
Course objectives: Successful students in this course will learn particular mathematical facts and then apply them. This will be achieved through five themes: mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and applications and modeling.
Student outcomes: Students successfully completing MATH 174 will have the ability to:
MATH 174 employs fluency-based grading, which is designed to make both of our lives better. Each assessed problem in the homework and the weekly exams may be reassessed, so that your failures are productive.
The problems you do will be graded on the E/M/P/I scale.
Another feature of fluency-based grading is rewarding growth. You are not expected to know everything on the first day of class – just by the last day! So, you will be able to revise much of your work in this class.
The summer semester MATH 174 course will be graded in the following categories.
Homework. Each week you will be assigned a selection of problems from the textbook. These problems will be due the day before that week’s exam so that I may post solutions. For that reason, no late homework will be accepted. Start early and get help often. I will choose a representative few of these problems to assess (i.e., grade).
When each assignment’s solutions are posted, you will have a good idea of whether you did well. At this point, you may choose up to two problems on that assignment to be reassessed. You will receive similar problems. You may ask for feedback as many times as necessary within one week of the solutions being posted, subject to my ability to respond and give meaningful feedback. (So for best results, e-mail early.) If you score better on the new problems after the week has ended, the better score will replace the old one.
When you submit a homework problem for reassessment, you will also need to write a few sentences describing where your original solution failed and how your new solution addresses that. New solutions without commentary will not be accepted!
Weekly exams. There will be an exam on the Monday of the second, third, fourth, and fifth weeks. These exams will be taken over a two-hour block. Exam problems will be similar to homework problems.
Each exam beginning with the second will give you a chance to revise questions from the previous exam. For example, the third exam will contain questions from the material covered since the second exam – all of which must be attempted – and questions from the material covered on the second exam. Keep track of how well you do on each exam question, and if necessary, you may choose questions from this group to revise. The final exam will contain questions that allow you to revise questions from the fourth exam.
Due to time constraints on the exam, verbal commentary is not necessary on reassessed exam problems.
Final exam. On the last day of class there will be a final exam. It will be a longer exam of the same type as the weekly exams. The final exam may not be reassessed.
Participation. I have an introductory activity planned, as well as weekly activities. These activities are not stressful; they are just another way to think about the material. Participation in these will earn a score of Good, Adequate, or Lacking at the end of the semester. Students who make a good-faith effort to participate in all of the activities will earn a Good; students who only participate in some activities or participate half-heartedly will earn an Adequate; students who do not participate enough for an Adequate score will earn a Lacking. Your participation score is up to my discretion, but you may expect it to be administered fairly.
Your final grade. One goal of fluency-based grading is that you will always know what your grade is and what needs to be done in order to pass the course. Below are the minimum cutoffs for each grade.
| Grade | Exams (weekly and final) | Homework | Participation |
|---|---|---|---|
| A | 80% E/M, 40% E | 90% E/M, 60% E | Good |
| B | 70% E/M, 30% E | 80% E/M, 50% E | Good |
| C | 60% E/M, 20% E | 70% E/M, 40% E | Adequate |
| D | 50% E/M | 60% E/M | Adequate |
Furthermore, all three requirements must be met for a grade; earning two out of three requirements will result in the “plus” version of the grade below. Since there is no F+, failure to earn achieve all three D-level criteria will result in a grade of F. Consider the following examples.
You are expected to attend class every day. Here are the things we will consider “attending class”:
What qualifies as a “substantial” conversation is up to my discretion, but I intend to be reasonable. Here are two examples of substantial conversations, one of each type.
Hi Douglas, I am confused about the third example in the office hour recording. You say that the only upper bound of A = {a,b,c} is c. However, d is above b. Why wouldn’t d be an upper bound as well? Thanks, [STUDENT WHO OVERSLEPT].
(In the following example, Alicia missed office hours because she had to take care of her younger sibling. Bob posts first on our Microsoft Teams channel. This conversation would count as attendance for Bob as well, had he also missed office hours.) BOB: Hey, I’m having trouble with the fourth problem on the homework. I’m getting 36 as my answer, but I’m not sure it’s right. ALICIA: I got 84 for my answer. What did you do? BOB: I did (7-1+3 choose 7), like the video said. ALICIA: Oh yeah… Since we’re choosing 3 objects out of 7 with replacement, n=7 and r=3. So it’s (7-1+3 choose 3), not choose 7. BOB: Oh, duh. Thanks.