ساختمانهای
گسسته (Discrete
Structures)
(3 واحد)
نيمسال
دوم 81 - 80
مدرس:
دکتر
محمد حسن
شيرعلی شهرضا hshirali@yazduni.ac.ir
کتاب
درس:
S. Lipschutz and M. L. Lipson, 2000
Solved Problems in Discrete Mathematics,
(Schaum's
Series), 1992.
کتاب
کمک درس:
Kenneth H. Rosen, Discrete
Mathematics and Its Applications,
Fourth Edition. WCB/McGraw-Hill, 1999
سرفصل
پيشنهادی ACM در
سال 2001 برای درس ساختمانهای
گسسته:
CS115. Discrete
Structures for Computer Science
Offers an intensive introduction to
discrete mathematics as it is used in computer science. Topics include functions, relations, sets, propositional and predicate
logic, simple circuit logic, proof techniques, elementary combinatorics,
and discrete probability.
Prerequisites: Mathematical preparation
sufficient to take calculus at the college level.
Syllabus:
• Fundamental
structures: Functions (surjections, injections,
inverses, composition); relations (reflexivity, symmetry, transitivity, equivalence relations);
sets (Venn diagrams, complements,
Cartesian products, power sets); pigeonhole principle; cardinality and countability
• Basic logic: Propositional logic;
logical connectives; truth tables; normal forms (conjunctive and
disjunctive); validity; predicate logic; limitations of predicate logic; universal and
existential quantification; modus ponens and modus tollens
• Digital logic: Logic gates,
flip-flops, counters; circuit minimization
• Proof techniques: Notions of implication,
converse, inverse, contrapositive, negation, and contradiction; the
structure of formal proofs; direct proofs; proof by counterexample; proof by contraposition; proof by contradiction;
mathematical induction; strong
induction; recursive mathematical definitions; well orderings
• Basics of counting: Counting arguments; pigeonhole
principle; permutations and combinations; recurrence relations
• Discrete probability:
Finite
probability spaces; conditional probability, independence, Bayes’ rule; random events;
random integer variables; mathematical expectation
نحوه
محاسبه نمره
درس: (Grading)
1 –
امتحان ميان
ترم(Midterm
Exam)
: 4 نمره
2 – تمرين(Assignments): 2 نمره
3 –
امتحان پايان
ترم(Final Exam) : 14
نمره