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Обычная версия сайта
2019/2020

Адаптационный курс по дискретной математике

Статус: Дисциплина общефакультетского пула
Когда читается: 1, 2 модуль
Язык: английский
Кредиты: 2
Контактные часы: 28

Course Syllabus

Abstract

The compulsory course in Discrete Mathematics is one of the key mathematical courses for data scientists and analysts. To master the subject, students will need extensive knowledge of the school programme. The tempo also provides to be challenging for some students. The main purpose of the Adaptation Course in Discrete Mathematic is to help our students follow the material of the Discrete Mathematics course by discussing its most important and challenging topics. We also aim to teach our students the correct treatment of mathematical proof and mathematical definitions as well as the right logical reasoning behind proving statements and solving problems. The course topics follow those of the Data Science and Business Analytics’ basic course but will also prove useful for Applied Mathematics and Informatics and Software Engineering students as well. Prerequisites: basic school-math knowledge.
Learning Objectives

Learning Objectives

  • help our students follow the material of the Discrete Mathematics course by discussing its most important and challenging topics.
  • teach our students the correct treatment of mathematical proof and mathematical definitions as well as the right logical reasoning behind proving statements and solving problems.
Expected Learning Outcomes

Expected Learning Outcomes

  • Students will learn to apply theorems and statements discussed at the seminars.
  • Students will practice the use of mathematical language.
  • Students will learn to give examples and counterexamples.
  • Students will learn to solve logical problems: a) using the definitions b) by contradiction.
Course Contents

Course Contents

  • Set theory. Operations with sets. Cardinality. Properties of operations with cardinalities. Countable and Uncountable Sets. The inclusion-exclusion principle for the cardinality of sets. How to prove the equivalence of sets?
  • Statements. Conditional Statements. Logical Equivalence.
  • Functions. Injections, surjections, bijections. Composition. Inverse functions. Relations of equivalence and order.
  • Type of proofs: mathematical induction, recursion, proof by counterexample, existence proofs.
  • Graphs. Types of graphs and their applications. Cycles. Spanning three.
  • An Introduction to Probability Theory. Sample Space, Outcomes, Events, Probability. Random Variables and their Distributions. Conditional Probability and Independence. Expectation of a Random Variable. Variance, Standard Deviation, Chebyshev’s Inequality. Law of Large Numbers. Central Limit Theorem.
  • Elementary generating functions. Generating functions of several variables. Pascal’s triangle.
  • Computational theory. Divisibility and modular arithmetic. The Chinese remainder theorem. Euclid's algorithm. Applications of the theory of numbers. Diophantine equations. Fundamental theorem of arithmetic.
  • Decision trees. Method of proof for lower bounds. Boolean circuits and formulas. Basis and functionally complete basis.
Assessment Elements

Assessment Elements

  • non-blocking Homework assignments
  • non-blocking In-class participation
Interim Assessment

Interim Assessment

  • Interim assessment (2 module)
    G(rade)= mean (Homework assignments)
Bibliography

Bibliography

Recommended Core Bibliography

  • Discrete mathematics, Biggs, N. L., 2004

Recommended Additional Bibliography

  • Lovász, L., Pelikán, J., & Vsztergombi, K. (2003). Discrete Mathematics : Elementary and Beyond. New York: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=108108