## discrete math - exam info

the following information is tentative for exam 2 and the final, and will be updated closer to the exam date.

### exam 1 (fri feb 21, in class)

this exam will cover chapters 1-3 of hammack, excluding sections 1.8-1.10, 3.8 and 3.10. you should expect several true/false questions (no justification and no partial credit), and several problems. for some of the problems you may not need to show any work (but you will be graded on what you write, so don't add nonsense to a correct answer, but do add some coherent thoughts if you're not sure of your answer), and for some you should explain your solutions clearly and logically in complete sentences.

here are some things which i consider important, but this is not necessarily an exclusive list (not necessarily a sufficient list?) of topics for the exam:

• be able to explain your solutions in coherent english/math and write in complete sentences.
• understand basic set constructions (union, intersection, difference, power set, complement) as well as notation
• be able to determine if an object is an element or a subset of another set (perhaps of a set constructed by methods mentioned above)
• be able to determine the cardinality of a finite set (perhaps of a set constructed by methods mentioned above)
• understand basic statement constructions (and, or, negation, conditionals, inverse, converse, contrapositive) as well as notation
• understand the use of quantifiers
• determine if two statements are logically equivalent, or if one implies the other
• basic counting, binomial theorem, and the inclusion-exclusion principle

### exam 2 (fri apr 17, 10:30-11:20am)

this exam will cover chapters 4-9 (excluding 8.4) and sec 10.1 of hammack.

here some more specific things you should be comfortable with:

• be able to write proofs clearly and coherently
• be comfortable with the following basic proof techniques: direct, cases, contrapositive, contradiction, and induction
• be able to disprove statements (counterexample)
• be able to critique and correct bad proofs
• know how to do proofs about equality and containment of sets
• know how to do proofs about implications (conditionals) and logical equivalences (if-and-only-if proofs)
• given a true statement, be able to determine what proof techniques are suitable for proving it
• given a statement be able to determine whether it is true or false and prove or disprove it

online rules and procedures: you will download the exam from the "Exam 2" assignment in canvas after 10:25am on the day of the exam. you are allowed to use the official course textbook (book of proof, 3rd ed, physical or digital) during the exam, and email me if you have questions about the exam. no other resources are allowed (no calculators etc, no notes or old homeworks, no looking at the canvas discussions, no other websites etc, no contact with others---if you have further questions please ask beforehand). the exam will include an integrity pledge that you are to handwrite and sign affirming that you are abiding by the exam rules. (there will be no proctoring so we will rely upon an honor code.) you are to then handwrite solutions. if you have a printer, you are welcome to print out the exam and write directly on that. otherwise, use blank paper and make sure your problems are clearly numbered and in order. you should finish the exam by 11:20am (a couple minutes extra is fine) and upload images of your exam (integrity pledge + solutions) to the "Exam 2" assignment on canvas. this assignment will close at 11:30am, so i recommend that you try to submit your exam several minutes early in case of technical delays. (in the event of any technical issues, email me asap, and if possible attach a copy of your exam.)

online exam format: due to the online nature of the exam, following ou's recommended guidelines, i am going to try to design the exam to have more "conceptual/critical" questions than i normally would. e.g., i might ask about why a certain proof technique might be good or bad in some situation, or i might ask you to analyze the quality/clarity of given proof. i will also ask you more standard questions like we have been doing in class, but as i don't have good source of such problems, and they are not so easy for me to come up with, i don't currently have such practice problems for you right now. hopefully i will come up with 1 or 2 on wednesday's discussion. i will also try to make the exam shorter than it would be for an in-class exam, both because i don't assume you have a distraction-free environment in which to take the test, and i presume the process will be a little slower. that said, even though the exam is open book, i recommend you study well for the exam. if you need to read the book during the exam, you will not have time to finish. you should aim to prepare so that you don't need the book during the exam, but if you forget something then you can use it to quickly look something up.

to help you review, here are some practice problems and my comment/hints from the last time i taught this course in 2018:

i suggest you try these before discussion wed (apr 15), and then you can ask any question you may have.

### final exam: tue may 5 (start between 8am and 2pm)

the final exam will be cumulative, covering everything on exams 1 and 2, as well as some aspects of functions and cardinality (ch 12, ch 14). specifically, you should be comfortable with the following:

• all topics listed above for exams 1 and 2
• be able to construct functions from one set to another, state the domain, codomain and range (image)
• prove that a function is injective/surjective/bijective or that it is not
• count the number of functions between 2 finite sets possibly with certain properties (e.g., those that are injective)
• show that 2 infinite sets have the same cardinality
• know examples of infinite sets with different cardinalities (like Z and R), and be able to show if a set is countable or uncountable

to prepare, i suggest you begin by reviewing your midterm exams, and the recent homeworks and discussions. i also recommend you try many practice problems. you can try looking at examples/exercises from the book and the list of final review problems i made from the last time i taught the course:

online rules and procedures: the final exam will be administered as a canvas quiz. it is a 2-hour exam which you are to start at the time of your choosing between 8am and 2pm on the scheduled exam day. that said there will be a 20-minute buffer to allow for technical issues, which means you have 140 minutes from the time you start (though no later than 4:20pm) until you have to submit your answers. as with exam 2, there will be an honor code (integrity pledge) in lieu of any proctoring. however, unlike exam 2, there will be text boxes for your to type in your answers to each problem. for some problems (think: problems where you need to show work or write a proof), you will be allowed to either type everything in the text box or handwrite your answer on paper. if you handwrite your answer, you can either upload an image in the answer box for that question, or you can attach all of your handwritten work as a single file in the final attachments question. please only submit pdf or image files, instead of something like a zip or tar file. (leave the final attachments question blank if you have no other attachments.) there is a "mock final" quiz on canvas that you can try to see what this will look like.

as for what is allowed, the rules are the same as for exam 2. you are allowed to use the official course textbook (book of proof, 3rd ed, physical or digital) during the exam, and email me if you have questions about the exam. no other resources are allowed (no calculators etc, no notes or old homeworks, no looking at the canvas discussions, no other websites etc, no contact with others---if you have further questions please ask beforehand).

what to expect: due to the online nature of the exam, as with exam 2, i am going to try to design the exam include more "conceptual/critical" questions than i normally would. e.g., things like critique proofs, or maybe explain why you would use one proof technique instead of another. as for the length, expect it to be about twice as long as either midterm exam. you should prepare as you would for an in-class, closed-book exam. in particular, do plenty of review problems to the point where if you see a random exercise from the book, you know more-or-less immediately how you should proceed, and that you only need to refer to the book to double check some detail. (i don't expect you to quote theorem numbers on the exam.)

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