Math 213 F1
Midterm Exam 1 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
- 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
- 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
(firstname.lastname@example.org), 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
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 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.
- 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
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
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.
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).
Back to the Math 213 Homepage
Last modified: Wed 15 Sep 2010 09:02:13 PM CDT