Math 240: Introduction to Discrete Math (R. Jones)

Spring 2006

Lecturer: Dr. Raphael ("Rafe") Jones
Email: jones@math.wisc.edu
Phone: 263-1634
Office: 309 Van Vleck Hall
Office Hours:

Monday, 5/8 (Extra Office Hour)	4:30 - 5:30

Or by appointment.

Math 240 lecture meeting Times: TTh 9:30–10:45AM (Chem 1361)

Jump to: EXAM INFORMATION Important Announcements (updated May 6) Textbook Discussion Sections and TA Office Hours Getting Help Classlist

Go to: Old Math 240 Exams Math Lab Math Tutorial Program GUTS List of Private Math Tutors

Important Announcements (updated May 6):

REVIEW SESSION: will be on Monday, May 8 from 11:00 - 12:30 in Sterling 3425 (same room as final).  I will hand out an outline of the course and a set of 10 questions in exam-like format.  You can then work on the questions (in groups if you like) and Paul and I will circulate and answer questions.  You're also free to ask any questions regarding any reviewing you've been doing (old exams, HW exercsies, etc.)  

NOTE SHEET ON THE FINAL: You can bring to the final one 8.5 x 11 sheet of notebook paper (one side only) with whatever you want written on it.  Typewritten notes are OK as long as you type the notes yourself.  Please come up with your own notes rather than copying someone else's: it'll help cement the ideas and definitions in your mind, and make you do better on the final.  

STUDY TIPS FOR THE FINAL: The final WILL be cumulative.  However, the material covered since the second midterm will slightly more heavily represented than the rest; so if, say, 1/6 of the semester has elapsed since the second midterm, perhaps 1/4 of the final will be on that material.  

A course outline covering the whole semester is now available.  

You should study for the final in a similar way to how you studied for the two midterms.  The main difference, of course, is that there is more material to review.  As previously, the exam questions will be very much like exercises done on the homework and examples done in class.  So the best way to review is by doing exercises, both from the practice exams and from the book.  The practice exams are a very good resource, and you should do as many of the relevant problems as you can.  Here are the relevant problems (note that both the old midterms and the old finals make for good practice): 

Among the book exercises, you should concentrate on reviewing excercises from past homework assignments, and on doing similar exercises that weren't assigned. Pick odd-numbered ones so you can check your answers.  Another good source of review problems are the Supplementary exercises at the end of each chapter.  Again, pick odd ones and make sure they deal with topics that we've 
covered.  

SECTIONS THAT WILL BE COVERED ON THE FINAL EXAM: 1.1-1.8, 2.1-2.7, 3.1-3.5, 4.1-4.5, 5.1-5.3, 6.1, 6.3, 6.5, 7.1, 7.3-7.6

As with the previous exams, you should not spend too much time memorizing formulas.  However, it is  important to know the definitions of the main terms and the statements of the main theorems we have seen.  So, for example, you should not memorize the big list of propositional equivalences in section 1.2, but you should know what a truth table for a proposition is, and how to compute it.  As for algorithms, you should know the principal ones we have spent time on and had homework on: the binary search, the merge sort, the Euclidean Algorithm, and the modular exponentiation algorithm.  Don't worry about memorizing pseudocode for these algorithms; you just need to be able to apply them.  Finally, in addition to definitions and statements of theorems, you do need to know the many techniques we've learned for solving certain kinds of problems.  Examples include mathematical induction, counting techniques, and how to find a transitive closure.  

EXAM NOTE AND CALCULATOR POLICY:  Apart from the note sheet (see above), the final will be closed book and closed notes.  You should bring your calculator to the exam, although you won't need to use it much.  There will be a public calculator available for those who need it.  

Exam 2 solutions now posted

EXTRA CREDIT: you can get up to 5 additional points on your final grade (1.25%) if you complete one of the writing projects listed below.  Please see me before starting on a project-- I want to know who's working on what, and I'll give you some tips on where to begin and what to look for.  You'll get up to 5 points credit based on the clarity and quality of your writing and explanations, the thoroughness of your research, and of course the correctness of what you write.   You should write at least 3 and not more than 10 pages.  Projects are due at the same time and place as the final homework assignment of the semester -- outside Paul's office (Van Vleck 820) at 10 pm on Friday, May 5.  

Hint for #12 on Section 5.3: If you're having trouble with part a), try computing the probablility for n = 3 (i.e. the probability that the first 6 occurs on the 3rd roll) and and n = 4.  Then see if you can generalize this for any n.  For part b), try to write your sum in a form that almost looks like an infinite geometric series.  Then use the result of Example 17 in section 3.2 (that's page 233).  The answer you get should be greater than the answer you got for #11 (think about why this is so).  It's perhaps surprising that the answer is not much larger than what you got for #11: after all, it's possible you could roll the die 10 million times before the first 6 comes up. 

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Textbooks
	Rosen, Discrete Mathematics and its Applications, 5th ed., McGraw Hill, 2003. ISBN 0072930330
These books are available for purchase at the University Bookstore and at the Underground Textbook Exchange, but you can compare new and used prices at several different online booksellers at CampusBooks4Less.com. Warning: If you choose to purchase the (optional) Student Solutions Manual, you may develop a syndrome known as over-reliance, which puts you at a high risk for over-confidence and, if left untreated, could result in severe exam underperformance. Use sparingly.

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Getting Help

The first step should always be to see your TA or Dr. Jones during office hours. If you can't make our office hours, send an email to set up an appointment with one of us. You should also check out the following resources:

• Mathematics Tutorial Program A free small-group tutorial program in Van Vleck. Very structured, requires a time commitment by students.
• Math Lab A free drop-in tutorial program in Van Vleck staffed by TAs and undergraduate tutors.
• GUTS A free student-run program covering a variety of subjects. Staffed mostly by student volunteers.

Classlist
An email Classlist has been created for important announcements about this course. All students enrolled in the course are automatically added to the list. Your @wisc.edu or @students.wisc.edu email address is the one that will be used for the list, as well as for all other official communication from the University, so check your email frequently. If you are not enrolled in the course, but would like to be added to the list, please email Dr. Jones.

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^‡From Section VI.14 of the UW Madison College of Letters and Science Handbook: "The time of a two-hour block for a class and/or the due date for a take-home examination may be changed only with the prior approval of the associate dean for Student Academic Affairs. Such changes are rare. Where a student has more than two (that is, three or more) Summary Blocks scheduled within a period of 24 hours, the instructor may, within guidelines adopted by the College faculty, reschedule a final exam for that individual student to avoid hardship."

jones@math.wisc.edu