Discrete Mathematics 2

2023/2024

Academic Year

ENG

Instruction in English

5

ECTS credits

Delivered at:

Big Data and Information Retrieval School

Course type:

Compulsory course

When:

2 year, 1, 2 module

Instructors

Буитраго Оропеса Хуан Карлос

Danilov, Boris R.

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.

Expected Learning Outcomes

• Will master the Quine-McCluskey method of DNF minimization.
• Will know basic algorithms of searching shortest spanning trees.
• Will know the Ford-Fulkerson’s algorithm of finding the maximum flow.
• Will be able to establish equivalence of Boolean formulas.
• Will be able to establish completeness of sets of Boolean functions.
• Will be able to prove for some problems that they are computationally hard in some sense (NP-complete, NP-hard, etc.)

Course Contents

• Graph theory
• Boolean algebra
• DNF minimization and associated algorithmic obstacles
• Complexity and hard algorithmic problems, the problem P = NP

Assessment Elements

• Homework assignments <HA>
• Quizes <QZ>
• Midterm control work <MT>
• Examination control work <FT>

Interim Assessment

• 2023/2024 2nd module
  <Final grade> = min(10, round( 0.25 * <HA> + 0.15 * <QZ> + 0.25 * <MT> + 0.35 * <FT>))

Bibliography

Recommended Core Bibliography

• Bernhard Korte, Jens Vygen. Combinatorial Optimization. Theory and Algorithms. Fifth edition. Springer-Verlag, Berlin Heidelberg, 2012.
• Graph theory, Bondy, J. A., 2008
• J. A. Bondy, & U. S. R. Murty. (1976). Graph theory with applications. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.CB6871BA

Recommended Additional Bibliography

• Лекции по теории графов : учеб. пособие, Емеличев, В. А., 2009