LETI - Mr. Posov

1. ETU Courses:
● Discrete mathematics
● Mathematical logic
and theory of
algorithms
● At Faculty of
Computer Science
and Technology
(FSCT)
Saint Petersburg Electrotechnical University "LETI"
Ilya Posov, assistant lecturer, iposov@gmail.com
Department of Higher (Further) Mathematics #2

2. TEMPUS project monitoring
● 1st of December 2014, Saint Petersburg, ETU
● pozdnkov@gmail.com
Поздняков Сергей Николаевич

3. History
● About 20 years by Sergei Pozdniakov (Поздняков
Сергей Николаевич)
– also by Sergey Rybin (Рыбин Сергей Витальевич)
– Assistant lectures: Ilya Posov (Посов Илья Александрович),
Anton Chukhnov (Чухнов Антон Сергеевич), Sergey Ivanov
(Иванов Сергей Георгиевич), and others
● Theory + Practice
– Now: 2h + 2h
– Previously: 3h + 1h
– Previously: 4h + 1h
– ...
● A textbook by Rybin and Pozdniakov:
Discrete Mathematics, 2007, 422 pages.

4. Directions at FSCT
● Pozdniakov:
– System Analysis and Control
– Control in Technical Systems
– Information Systems and Technologies
– Computer Systems Engineering and Informatics
● Rybin:
– Applied Mathematics and Computer Science
– Software Engineering
– Computer Security

5. Course structure
● 2nd semester (1st year)
Discrete mathematics:
– Number theory
– Combinatorics
– Binary relations
● 3rd semester (2nd year)
Mathematical logic and theory of algorithms
– Logic
– Formal languages
– Graph Algorithms

6. Discrete mathematics, Number theory
● Euclid's algorithm (basic, extended)
● Diophantine equations
● Modular arithmetic, linear modular equations
● Chinese remainder theorem
● Fast modular exponentiation
● Euler function, Euler theorem
● RSA
● Continued fractions

7. Number theory test

8. Discrete mathematics, Combinatorics
● Rule of sum, rule of product
● Balls and walls
● Lucky tickets (by means of inclusion-exclusion
principle)
● Discrete probability
● Enumeration of words and permutations

9. Combinatorics test

10. Discrete mathematics, Binary relations
● Properties of binary
relations
● Orders, equivalence
relation
● Graph and matrix
representation
● Transitive closure

11. MatLog & AlgTh, Logic
● Propositional logic
– Algebraic transformations
– Normal forms, Zhegalkin polinomial
– Closed classes, Post's theorem
– Resolution method
● Predicate logic
– Definition
– Normal forms
– Resolution method, unification

12. Propositional logic test

13. MatLog & AlgTh, formal languages
● Regular expressions
● Finite automaton
● Turing machines
● Context-free grammars, LL(1) parser
– Second individual homework on LL-1 parser
implementation

14. Second test

15. MatLog & AlgTh, graph algorithms
● Prim's algorithm, Kruskal's algorithm
● Dijkstra's algorithm
● Floyd–Warshall algorithm
● Bellman–Ford algorithm

16. Problems generation
● Generation system by Alexey Stepanov
(Степанов Алексей Владмирович)
– A set of problems covering almost all courses of the
department
– Problems may be arranged into printable LaTeX
tests
– Implementation of generators open for everybody
– Optional domain specific language to implement
generators
● Generators going online
– Under development

17. Assessment
● Practice
– Individual homework assignments (generated)
– Tests (usually very close to individual homework)
● Theory
– Individual homeworks
– Web sites with homeworks (google sites)
– Short assignments at the end of every lecture
– Lecture notes discussion for those who missed a lot
of lectures.

18. Google sites of students

19. Examination
● Written examination
● Non-standard problems that test understanding
– How many transitive relations are there on the set
of two elements {a,b}?
● Assess the statement (true, false, unknown)
– Example: a symmetric, transitive relation is anti-
reflexive. Answer: unknown

20. Alternative Examination
● A good mark for the first test may be converted
to an alternative examination
● 1st type. Programming
– Generate all irreducible polynomials of a given
degree over Zp for a given p. (link to a book)
● 2nd type. Solve problems
– Read a certain book with excersises, solve them
● 3rd type. Essay
– Tell us about some certain variant of temporal logic