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Office: SA-130 Phone: x2135
Final exam is to be held
on Wednesday, May 28, at 15:30,
at rooms EB203 (Agah -- Öztürk) and EB102 (Satir --Yildirim).
Using a wrong room may result in a penalty!
These problems
are highly recommended for self-study.
A common make-up is to be held on Monday, May 31st, at 10:00-12:00.
`Common' means that it is for ALL exams missed and
ALL topics covered
during the semester are included!Important announcements/assignments/grades etc.
are to be placed here. Check often to be informed![Top][Home]
Formulas for the number of linear
arrangements (without or with repetitions), circular arrangements (without
repetitions), and combinations (without or with repetitions).
Algebraic properties of binomial coefficients; identities; applications.
The concept of (closed) statement =
Boolean variable. Elementary Boolean operations and Boolean expressions, properties (identities),
simplification. Disjunctive normal form. Applications.
Open statements;
quantifiers and their simplest properties.
Sets, elements, subsets. Sets as open statements.
The number of subsets; applications (counting and combinatorial identities).
Set operations (union, intersection,
complement, difference, symmetric difference) and their properties.
Venn diagrams; applications to counting.
Well ordering and its applications; induction.
Divisibility of integers, primes,
greatest common divisor, Euclidean algorithm, prime factorization and its
uniqueness.
Cartesian product. Relation as a subset. Functions. Counting relations, functions,
injections, and surjections. Stirling numbers.
Properties of relations (mainly, the terminology: reflexive,
(anti-)symmetric, and transitive relations).
Partial orders: definition and properties;
Hasse diagrams; maximal/minimal and greatest/least elements;
least upper bound and greatest lower bound; lattices;
extending a partial order to a total order.
Equivalence relations and partitions.
The pigeonhole principle and related tricks
(extensive practice is highly recommended).
The principle of inclusion and exclusion: the basic formula, the formulas for
E_{k} and
L_{k}, applications to counting,
the Euler function.
Generating function:
choosing and writing down the function related to a problem, computing
the coefficients (whenever possible) and related tricks (including
a few `known' functions and partial fractions).
Linear recurrence relations with constant coefficients: homogeneous
(both methods) and nonhomogeneous (via generating functions).
Applications to counting: setting a recurrence relation for a sequence
in question, examples (Fibonacci numbers, compositions of integers, etc).
Grading policy *
I will take off a few (2-3) points for arithmetical mistakes. However,
a lot of points will be taken off for `obvious'
mistakes, i.e., either those that you can easily avoid or those
showing a deep misunderstanding of the subject. This includes, but
is not limited to, the following: