Here
is a link to a paper I wrote that discusses some of the potential
pitfalls
that arise in trying to
solve counting problems. It refers to some of
the same
examples we will discuss in class.
Our final exam
will
take place on Thursday, May 7 from 8 - 11 AM in Sage 3303 and Sage 3510.
If you are in sections 1-3, please
report to Sage 3510. If you are in sections 4-8, please report to Sage
3303.
No books,
notes or
calculators are
allowed. The final exam will contain all of the formulas
included on
the previous three exams.
There will
be a review class conducted by Dr. Schmidt on
Wednesday, May 6 from 3 - 5 PM in Darrin 324.
Here are some
practice
problems.
Dr. Schmidt will
also have office hours on Monday, May 4 from 3 - 4 PM.
FORMAT OF THE FINAL EXAM:
The final exam will consist of two parts:
The first part will consist of three problems, all of which you must
solve. These problems will be worth
15 points each, for a total of 45
points.
The second part will consist of four problems. You must choose three of the
four to solve.
You will need to indicate on the front of the exam which problem you do
not want graded.
These problems will be worth 20 points each, for a total of 60 points.
Thus, the final exam is worth 105 points just like all of our other exams.
TOPICS COVERED
ON THE FINAL EXAM:
Below is a list of topics to be
potentially covered on the exam, with
textbook citations. Since we didn't necessarily
discuss every section in its entirety, the class
notes
are the best guide to the exact material covered.
Propositional Logic (1.1)
Propositional Equivalence (1.2)
Quantifiers (1.3, 1.4)
Rules of Inference (1.5)
Methods of Proof (1.6, 1.7)
Basic Set Theory (2.1, 2.2)
Basic Number Theory: Divisibility and division algorithm (3.4)
Prime Numbers: GCD and LCM (3.5)
The Euclidean Algorithm (3.6)
Solving linear congruences (3.7, supplemental material from notes)
Mathematical Induction (4.1, 4.2)
The Basics
of Counting (5.1)
Permutations
and Combinations (5.3)
Binomial
Theorem and Pascal's Triangle (5.4)
Combinations
with Repetition (5.5)
Distinguishable
Permutations (5.5)
Discrete Probability (6.1)
Conditional Probability and Independent Events (6.2)
Fibonacci
Recurrence and Fibonacci Numbers (4.3)
Recurrence Relations (7.1)
Solving
Constant-Coefficient, Homogeneous Recurrences (7.2)
Generating
Functions and Counting Problems (7.4)
Principle of Inclusion/Exclusion (7.5,
7.6)
Course
Information:
Quiz Dates: The following are the dates of all of
the short quizzes we will take during recitation:
Quiz #1: Friday, January 23 or Tuesday, January 27
Quiz #2: Friday, January 30 or Tuesday, February
3
Quiz #3: Friday, February 6 or Tuesday, February 10
Quiz #4: Friday, March 6 or Tuesday, March 17
Quiz #5: Friday, March 20 or Tuesday, March 24
Quiz #6: Friday, April 10 or Tuesday, April 14
Quiz #7: Friday, April 17 or Tuesday, April 21
Office Hours
Information :
Dave Schmidt's Office Hours (in Amos
Eaton 408): Monday 10 - 11 AM and Wednesday 3:30 - 5 PM
Course Resources:
Author's
Website
Contains many resources
designed to help students learn
discrete mathematics from the Rosen text, including guides to writing
proofs
and common mistakes in discrete mathematics, links for tutoring help
and
a
useful bulletin board, as well as companion material identified by Web
icons
printed in the book. The companion material includes links to external
Web
sites, extra examples and additional steps, self-assessment on some key
topics, and interactive demonstrations of important algorithms.