Math 213 F1

Midterm Exam 2 Information

Basic Information

• Exam date, time, and location: The exam will be given during the regular class time, Friday, 10/15/2010, 2:00 - 2:50, in the usual room, 147 Altgeld.
• Exam rules: No calculators, closed books/notes, and, of course, no cheating.
• Missed Exam policy. I don't give make-up exams, but if you miss the exam with a valid excuse (e.g., illness), the exam will be counted as "excused". (See the Course Information Sheet for an explanation of an "excused" exam score.) The absence must be documented by an "absence letter" from the Dean's Office at 300 Student Services Building, 610 East John St., phone 333-0050.
• Grading. The exam will account for approximately 1/6 of the total points to be earned in this class. See the Course Information Sheet for the complete grading policy. After the exam has been graded and the scores entered into the grading system, you can view your scores via this link.
• Open House hours: Tuesdays, Wednesdays, and Thursdays, 5 pm, in 159 Altgeld (or an adjacent room in case 159 is taken). I will stay as long as someone is there. Take advantage of this opportunity! I'm happy to answer questions by email (ajh@illinois.edu), but keep in mind that email is best suited for quick, nontechnical questions (e.g., do we have to know XYZ?); for technical questions that require a lengthy explanation it's better to ask in person.

Syllabus

• Basics of Counting (5.1) Product and sum rules. Simple inclusion-exclusion. Examples 1-8, 10, 11, 12, 15-18. Skip: Tree diagrams (p. 343).
• The Pigeonhole Principle (5.2) Basic version (k+1 objects, k pigeonholes) and generalized version (N objects, k pigeonholes). Examples 1-8. Skip: Final part, "Elegant applications".
• Combinations and Permutations (5.3): Examples 1-15.
• Binomial Coefficients (5.4): Binomial theorem (you need not know the proof). Examples 1-4. Skip: Final part, "Some other identities ...".
• Generalized Combinations and Permutations (5.5): Permutations with repetition. Combinations with repetition. Donut type problems. Counting integer solutions. Skip: Final part, "Distributing objects into boxes".
• Basic Probability (6.1): Equally likely outcome model. Examples 1-8. Skip: Example 10 (Monty Hall problem). (This is a famous and interesting problem. Read it if you are interested, but it's not going to be on the exam.)
• Probability Theory (6.2): General model with finitely many outcomes, and a general (not necessarily uniform) probability assignment. Success/failure (Bernoulli) trials, and the binomial distribution. Conditional probability. Independence. Examples 1-9, 13, 14. Skip: Random variables (p. 408-409), Monte-Carlo Algorithms and Probabilistic Method (p. 411-414).
• Bayes' Theorem (6.3): Bayes' Theorem, basic version (Theorem 1) Examples 1-3. (Skip Theorem 2 and the last example, Example 4.)

Other information

• Leave all answers in "raw", unevaluated form, e.g., involving factorials and binomial coefficients.
• Indicate briefly how you arrived at each component in your formula (e.g., by a "bubbled-in" phrase like "pick 2 days out of 366").
• All problems have a simple answer consisting of at most two or three terms of simple shape, if approached in the right way. This simple answer is the one you are expected to derive. A messy sum will not count. (Example: the probability that there are at least 2 sixes in 100 coin tosses can easily be given in very simple form, using the complement rule, and this is the expected solution; by contrast, a sum of 99 binomial probabilities from k=2 to k=100 would not qualify as a simple answer, and would not earn credit.)
• All problems are doable with minimal amount of calculations, using standard techniques, of the type illustrated in the class examples and homework problems. If you get entangled in a lengthy calculation, you are on the wrong track, and it's better to move on to another problem. Continuing would be counterproductive. You won't get credit for answers arrived at by brute force counting.
• Note on poker problems: You need not know any special poker terms ("full house", etc.); all you need to know is the basic composition of a deck of cards (52 cards total, split into 4 suits of 13 cards each).
• Note on word counting problems: Assume (as in the hw problems) that there are 26 letters. Unless otherwise indicated, we are only counting upper case words (again just like in the class examples and hw problems).
• Note on calendar day/month problems: Basic assumptions, such as the number of days per year (or per month) to work with, will be given in the problem. (In the text the usual assumptions are 366 days per year and 30 days per month; in any case, in the exam, this will be specified.)

Past Math 213 exams. Click on this link for some old Math 213 exams. This should give you some idea of the length and difficulty level of the exam. In terms of material covered, however, they are not representative since the old exams were based on a different syllabus, so it would not make much sense to use these exams to prepare for our exams.

Tips on preparing for the exam:

• Start studying early. Try to find someone, or a group, to study with.
• Start your prepration with your class notes, make sure you understand the basic concepts and techniques, rework the class examples. The class examples were carefully selected to illustrate the different types of combinatorial and probability problems at a level appropriate for this class.
• For additional practice, study the corresponding section in the text, and rework the examples there using the above syllabus as a guide. Note that the examples in the text vary widely in difficulty. Many are very easy warmup problems, but a few are quite difficult, well above exam level. The examples listed in the above syllabus are all of the "doable" kind.
• Redo the homework problems (both the graded and non-graded hw), especially those you got wrong, or you weren't sure about.
• Lastly, take advantage of the Open House (see above).

Last modified: Mon 11 Oct 2010 04:11:01 PM CDT A.J. Hildebrand