Бакалавриат
2021/2022
Дискретная математика 2
Статус:
Курс обязательный
Направление:
01.03.02. Прикладная математика и информатика
Где читается:
Факультет компьютерных наук
Когда читается:
2-й курс, 1, 2 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для своего кампуса
Язык:
английский
Кредиты:
4
Контактные часы:
60
Course Syllabus
Abstract
The course is a natural follow up of the course Discrete Mathematics. This course covers topics that are not covered in traditional courses of calculus, algebra and linear algebra, but are part of the basic mathematic culture. The course provides theoretical foundations for courses of a more applied nature: programming, algorithms and data structures, data analysis, discrete optimization.
Learning Objectives
- After finishing this course students will be prepared to read more specialized literature on graphs and Boolean functions.
- Students will learn and analyze several important algorithms on graphs and Boolean functions.
- Students will be able to recognize hard computational problems and justify the use of heuristic and brute force algorithms for such problems.
Course Contents
- Induction and recursion on abstract sets with examples from the theory of formal languages
- Cybernetic functions, formulas and their transformations with examples from Boolean algebra
- The problem of DNF minimization and associated algorithmic obstacles
- Circuits, their complexity and methods of synthesis
- Introduction to computability theory. Decidable, semidecidable and undecidable computational problems
- The theory of complexity and P versus NP problem
Assessment Elements
- Homework assignmentsHomework problems are assigned starting from the first seminar once a week at each seminar excluding the last seminar of the course. Each student is expected to solve problems individually. Solutions must be performed in hand-written form on a piece of paper and contain the full name of the student, his group number, and the list of solved problems written in clear and recognizable manner. Each problem in the homework must contain it's respective number in the assignment, the solution and the answer explicitly given after the written word "answer". When several answers are given for a task the inspector may choose any of the specified answers to score the task. When problem is not supposed to have an answer (exercises to prove facts) then the complete proof should be provided. Each step in the solution of a task must be supported by a mathematical argument, unfounded statements may lead to lowering the score up to "0" (zero) points for the task. Only statements and theorems provided on lectures or seminars can be used without a proof. The correct answer for the task without provided solution is scored with "0" (zero) points. These rules also apply for the other written tests (midterm written test and final written test).
- Midterm written testThe planned form of conducting the midterm written test is the offline written test at the start of the second module. In the case of aggravating of epidemiologic state the midterm written test may be carried out online, in which case the rules and the form of the test are announced separately and may or may not match the rules announced for the offline form of the test. Rules for submitted solutions follow the rules described in the comment for the homework assignments.
- Final written testThe planned form of conducting the final written test is the offline written exam. In the case of aggravating of epidemiologic state the final written test may be carried out online, in which case the rules and the form of the test are announced separately and may or may not match the rules announced for the offline form of the test. Rules for submitted solutions follow the rules described in the comment section for the homework assignments.
