Master
2019/2020

## Research Seminar ''Intelligent Systems and Structural Analysis''

Type:
Compulsory course (Data Science)

Area of studies:
Applied Mathematics and Informatics

Delivered by:
School of Data Analysis and Artificial Intelligence

When:
1 year, 1-4 module

Mode of studies:
Full time

Master’s programme:
Data Science

Language:
English

ECTS credits:
4

### Course Syllabus

#### Abstract

The discipline goal is to develop students' professional skills in applied fields of the computer science. As part of the Scientific Seminar, the course "Introduction to the Number Theory and its Applications" will be read during the first semester and the course “Introduction to the Semantic Web Technologies” during the second semester. The course "Introduction to the Number Theory and its Applications" is aimed at the formation and development of theoretical-numerical thinking, as well as the understanding of the fundamental concepts of number theory and the ways in which they can be used in cryptography. The course “Introduction to the Semantic Web Technologies” is a gentle introduction to the theory and practice of the Semantic Web, an extension of the current Web that provides an easier way to find, share, reuse and combine information. It is based on machine-readable information and builds on XML technology's capability to define customized tagging schemes, RDF's (Resource Description Framework) flexible approach to representing data, the OWL (Web Ontology Language) schema language and SPARQL query language. The Semantic Web provides common formats for the interchange of data (where on the Web there is only an interchange of documents). It also provides a common language for recording how data relates to real world objects, allowing a person or a machine to start off in one database, and then move through an unending set of databases which are connected not by wires but by being about the same thing. Important applications of the Semantic Web technologies include Healthcare (SNOMED CT), Supply Chain Management (Biogen Idec), Media Management (BBC), Data Integration in the Oil & Gas industry (Chevron, Statoil), Web Search and E-commerce.

#### Learning Objectives

- know some algorithms used in cryptography and based on the use of number- theoretic constructions
- to understand the fundamental concepts of number theory and the ways in which they can be used in cryptography.
- know the fundamental concepts of the Semantic Web, the structure of RDF and related technologies, such as RDFa and SPARQL
- know the ontology language OWL 2 and its profiles, principles of ontology- based data access, the foundations of the basic representation of knowledge and formalisms of reasoning, such as the description logic
- use terminology and methods for writing queries using SPARQL, writing ontologies in OWL 2

#### Expected Learning Outcomes

- Students should be able to evaluate the greatest common divisor of two integers using Euclidean algorithm.Students should be able to solve linear equation ax+by=c using Euclidean algorithm.
- Students should be able to find a continued fraction expansion of rational numbers and of quadratic irrationals. Students should be able to evaluate quadratic irrational by knowing its continued fraction expansion.
- Students should be able to work with congruences and to apply theorem of Ferma and Euler
- Students should be able to evaluate the value of Legendre symbol.
- Students understand fundamental concepts, advantages and limitations of Semantic Technologies.
- Students understand the principles of ontology-based data access and integration.
- Students understand the basics of knowledge representation with description logics.
- Students understand and use the ontology language OWL 2 and its profiles.

#### Course Contents

- Euclidean algorithm.Euclidean algorithm, solution of linear equation ax+by=c in integers
- Continued fractionsContinued fractions
- Prime NumbersBasic factos of the theory of prime numbers
- Multiplicative functionsMobius and Euler totient function
- The ring of integers modulo NCongruences modulo N. The Chinese Remainder Theorem. Theorems of Ferma and Euler. Theorem of Wilson
- The Quadratic reciprocity lawQuadratic residue and nonresidue. Legendre and Jacobi symbol. The Quadratic reciprocity law
- Primitive roots.Primitive roots and discrete logarithm
- Introduction to mathematical cryptographyThe RSA cryptosystem, Diffie-Hellman anElGamal cryptosystem
- Integer factorizationDifferent algorithms for factorization of integrs
- The Semantic Web and Knowledge Graphs introduction.The history of the Semantic Web. Syntactic vs semantic web. Ontologies in (Computer) Science. The layered approach to the Semantic Web. XML, the tree model of XML documents, XML Schema. Querying XML documents, XPath.
- Ontologies in Description Logics. Lightweight description logic EL and Snomed CT. Syntax and semantics.
- DL-Lite and Schema.org.
- Expressive description logics ALC and its extensions.
- The Web Ontology Language OWL.
- First-Order Predicate Logic (FOPL) as an Ontology Language.
- Query answering over data and knowledge bases.
- Ontology Based Data Access.Instance data as ABoxes. Entailment regimes for SPARQL queries. Ontology-based data access with Ontop.

#### Assessment Elements

- контрольная работа
- In-class testIn-class written tests. Preparation time – 80 min.<br />3rd module.
- ExamWritten exam. Preparation time– 120 min.<br />4th module. Оценка за дисциплину выставляется в соответствии с формулой оценивания от всех пройденных элементов контроля. Экзамен не проводится.

#### Interim Assessment

- Interim assessment (4 module)0.3 * Exam + 0.3 * In-class test + 0.4 * контрольная работа

#### Bibliography

#### Recommended Core Bibliography

- J.H. Silverman, Jill Pipher, Jeffrey Hoffstein. An Introduction to Mathematical Cryptography. Springer-Verlag New York 2008
- William Stein. Elementary Number Theory: Primes, Congruences, and Secrets. Springer, New York, NY

#### Recommended Additional Bibliography

- Staab S., Studer R. Handbook on ontologies. – Springer, 2009. – 811 pp.