MAT 241: Discrete Mathematics
Fall 2020
Exam 1 information
- Day 12: discuss sections 1–2
- Day 13: discuss sections 3–5
- Day 14: discuss section 6
1. Allowed materials
-
You are strongly encouraged to print out
tables1.pdf
(found on Moodle) and bring to the exam for use. (You may also look at it on your computer screen instead.) - Calculators are allowed on exams. All you need is basic arithmetic functions like add/multiply.
- You are strongly discouraged to use the textbook, homework, or class notes during the exam. (See next section.)
- You are not allowed to use other resources (Internet search, friends, etc.) during the exam.
- You may only use other electronic devices (computer, smart phone) to the extent of following exam logistics (below).
2. Open or closed book? Yes.
What does it mean that you are strongly discouraged to use the textbook, homework, or class notes?- You should treat the exam as a closed book, close notes exam.
- However, because I cannot easily monitor the use of books/notes during the exam this semester, to not place dishonest students at an unfair (dis)advantage*, accessing these resources is officially not considered cheating (so even the most honest student may access these materials in good conscience).
- * (Dis)advantage: nevertheless, needing to flip through the textbook will, on balance, put you at a disadvantage:
- If you spend more than a few minutes searching through your textbook, you will likely not have enough time to finish the exam.
- Moreover, if you don't memorize as if for a closed book exam, you may not even recognize what concepts you may need to look up.
- Not spending time to fully understand something (e.g., Euclidean Algorithm), thinking you can simply look it up and then figure it out on the spot, is a recipe for disaster.
- The best way to succeed is to treat this exam as a closed book exam, and study accordingly.
3. Academic integrity
Recall this excerpt from the syllabus:- You may not consult any materials from any previous offerings of this course or from any other similar course offered elsewhere unless explicitly permitted.
- You may not look up solutions in any form, including from solution manuals or online repositories.
- You are required to completely understand any solution that you submit and, in case of any doubt, you must be prepared to orally explain your solution to me. If you have submitted a solution that you cannot verbally explain to me, then you have violated this policy.
4. How to study
Lots of research has shown that reading over material isn't a very good way to prepare for exams. The best thing to do is to practice. Reading how to swing a baseball bat or how to cross-country ski might give you some good ideas on how to get better the next time you try it, but it's not even close to just getting out there and swinging a bat or skiing.
How can you practice? Go back to look at the assignments. Instead of reviewing the same problems you already did, try to do similar problems. For each type of question, do some $\star$-ed ones in the textbook and check your solutions in the back of the book.
Can you write down thoughts for all of the topics listed below? Can you invent questions to try for the topics listed below? Practice these under test conditions and see how you do. Even though the solutions may not be available, just trying to do them can be incredibly useful. You can work with other students to see if you think you've got the right answers. Even if you don't know for sure if you've got the right answer, just practicing with these exercises can be helpful.
Go back and pick out all of the content from class that you understand least well. Then, without simultaneously looking at your notes, write down all that you know about that content. Think about what I might ask you to do on an exam that would be scary. Try to do that yourself. If you can't, work with other people in the class or stop by Math Lab and office hours to get help on doing that.
Recall that it is against the academic integrity policy to seek out resources from past versions of this course or similar courses offered elsewhere. The textbook has more than enough practice problems.
There are a lot of definitions and theorems that you must memorize: do not cram the night before, start reviewing early.
Get a good night's sleep the night before; make sure to set your alarm and don't sleep through it. You won't get any extra time if you come late.
5. Exam content
The exam covers everything we have done, up to and including Chapter 3. (Chapter 4 will be on the next exam.) Here are some topics we emphasized:- stable marriage problem: deferred acceptance algorithm, details of the algorithm, proof that the algorithm works, understand the optimality proof.
- sets: lots of definitions and notation, fundamental set properties, proofs.
- logic: propositions, truth tables, implications and derived implications, logical equivalence, predicates and quantifiers, negating quantified statements, tautologies, proofs.
- boolean algebra: definition, sets and logic as examples, the duality principle, proofs.
- axiomatic mathematics: entities that do or do not require proofs.
- elementary number theory: lots of definitions, the Well Ordering Principle, understand the proof of the Quotient-Remainder Theorem, proofs.
- applications of elementary number theory: Euclidean Algorithm, linear congruence, Chinese Remainder Theorem, Fermat's Little Theorem; in this section, the emphasis is on using—not proving—these famous and useful theorems.
- proofs: strategies (I may or may not tell you which one to use), induction; pay attention to example proofs in the text, some are quite famous: Quotient-Remainder Theorem, infinitude of primes, irrationality of $\sqrt2$, Fundamental Theorem of Arithmetic, prime divisibility property.
As usual, please note that this document is not a contract. I may have inadvertently left something off that ends up on an exam question. Moreover, I will not be able to test all of this material given the time limitations of the exam. I will have to pick and choose some subset of it.
6. Logistics
The exam will take place during our usual class time. I will proctor you via Zoom.Before class time:
- Read this document carefully. Ignorance is not an excuse.
- Prepare enough paper to write on.
- On the first sheet, write at the top an academic integrity statement of your own devising. You should say that you didn't consult any unauthorized resources (Internet search, friends, other sources of help, etc.).
- Sign your name after the statement.
At class time:
- Find a PDF of the exam questions on Moodle near the bottom; pull it up on your computer.
- Work things out on notebook/blank paper. You do not need to print out the questions.
- After you are done or the time is up, scan your work and upload to Moodle near the bottom.
- Download your submission from Moodle to double check that you uploaded correctly.
- You may leave early after you finish scanning and uploading your exam.
Timing:
- You have the full 50 minutes of class time for the exam.
- To give you more flexibility, since this class is scheduled within the 70-minute B4 block, you may start up to 10 minutes early
or
end up to 10 minutes late. - Recall that
or
is notxor
(see Table 2.5 on p.40), so you may do both and have up to 70 minutes to work. - To accommodate for scanning, you may submit up to 10 minutes after the 70 minutes end.
- Moodle will still accept submissions after the cutoff time, but it will be marked "late."
- If this happens, you should email me ASAP and explain why you were late, and assert that you did not spend any more than 70 minutes working on the exam.
- Summary:
time description 09:00 CDT Zoom opens, PDF of exam questions available on Moodle, you may start working 09:10 class/exam officially starts 10:00 class/exam officially ends 10:10 flex time ends, you must stop working 10:20 deadline for submitting to Moodle
Proctoring:
- Please turn on your camera but mute your microphone.
- During the exam, don't unmute to talk to me: you will end up talking to everyone else as well.
- If you need to contact me, you can send me a message privately via the "chat" function in the Zoom meeting.
- Aim the camera at you, not your desk; don't hold up your work for others to see.
- Disconnect from the meeting after you've finished scanning and submitting to Moodle.
Tips:
- Label your questions clearly, especially if you are doing things out of order (try not to).
- Show your work; box your final answer if appropriate.
- Do not write in columns.
- Even though you are under time pressure, try to write legibly; if I can't read your handwriting, I can't give you credit.
- Make sure your scan is legible. If I can't open your PDF or read your content, I can't give you credit.