Midterm Exam 1 Information

Basic Information

• Exam date, time, and location: The exam will be given during the regular class time, Friday, 9/17/2010, 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.
• Expanded Open House hour schedule: In addition to my regular Open House (Wednesdays/Thursdays, 5 pm, 159 Altgeld), I will hold a special Open House Tuesday, 9/14, at the same time and location. 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

The exam will cover Sections 2.1 - 2.4 and 4.1 - 4.2 of the Rosen text. As a general rule, anything that was covered in class or in the homework assignments (both the graded and non-graded problems) is fair game for the exam. If you are not sure, ask! Here is a more detailed syllabus:
• Sets (2.1): Sets, elements of sets, subsets, power sets, empty set. Cartesian products. Standard sets: N, Z, R, Q. Set notations.
• Set operations (2.2): Intersection, union, difference, complement. Venn diagrams. Set identities (in particular, De Morgan's Laws). Formal proofs of set identities (as in class examples and hw).
• Functions (2.3): Formal definition of a function. Representation by arrow diagram. Domain, codomain, range, graph. Properties of functions: Onto, one-to-one, one-to-one-correspondence; and the equivalent terminology surjective, injective, and bijective. Floor function. Compositions.
• Sequences, summations, and products (2.4): Sequences, formal definition. Geometric and arithmetic progressions. Summation and product notation. Formula for sum of finite geometric series, and sum of first n positive integers. (Of the formulas in Table 2, p. 157, those are the ones that you should memorize.)
• Cardinality and countability (2.4): Formal definition of countability, Countability of rationals and uncountability of reals (just know these results - no proofs).
• Induction and strong induction (4.1/4.2). Principle of induction. Base step, inductive step, induction hypothesis. Strong induction. Induction proofs: sum/product formulas, inequalities, identities for Fibonacci numbers, and other recurrences. See the class handouts Induction Proofs, I, and Induction Proofs, II for tips and practice problems. Solutions to most of these practice problems ar also available.

Other information

Exam format: The exam will have 6 - 9 problems, usually with multiple parts; some may be in true/false, or multiple choice format. Some of the problems will be computational in nature (e.g., evaluate a sum or product), while others will ask for precise statements of definitions/formulas/theorems (e.g., De Morgan's Law). There will be two or three problems that require a full-fledged proof (such as the set theory proofs from the first week of class, or the induction proofs covered over the past few class hours).

Homework versus exams. While most of the exam problems will be at a level comparable to the homework problems, and reworking the homework problems is an excellent preparation for the exam, an exam is not just a scaled-down version of a homework assignment. Homework and exam serve different purposes, and there are some important differences between the two: First, questions asking to state a theorem, definition, formula, etc., would not make sense in homework assignments (where you could just look up the answer in the book), but are perfectly appropriate for an exam. Second, problems that require elaborate computations or which are highly non-routine would be inappropriate for an hour exam because of the limited amount of time available, but may be suitable as homework assignments.

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: Redo the homework problems (both the graded and non-graded hw). Review class notes and corresponding sections in the text, and study/rework examples there. Make up a "cheat sheet" of the key concepts and formulas and try to commit those to memory. Start studying early. Try to find someone, or a group, to study with. Lastly, take advantage of the Open House (see above).

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