Course syllabus - Mathematics of Internet

Objectives

The course aims to provide students with knowledge of key mathematical ideas, concepts, methods, algorithms and computational tools behind the success of the Internet and Internet-based technologies, and to explain the basic mathematical concepts and techniques with concrete examples of applications in modern information and Internet technologies and other technology and society. The course will also provide training in logical and algorithmic thinking, and in mathematical modeling and computational techniques of particular importance for applications in the Internet and information technology, as well as the ability for independent analysis of mathematical problems and models used in Internet and database technologies.

Learning outcomes

After completing the course, students should be able
- Explain basic mathematical concepts and principles that form the foundation of the Internet as a large growing network structure consisting of linked information resources
- Describe the basic mathematical principles and structures of contemporary search engines and search technology on the Internet and in databases
- Explain basic mathematical principles behind the algorithms for effective relevance ranking of information and results, including algorithms and its modifications, which are used by leading modern search engines
- Briefly explain the main mathematical structures, problems and algorithms related to the modeling of communication within social media and their impact on public opinion and decision-making processes within the business, financial markets and public institutions at national and international level
- Explain the basics for some distance-based, statistical and other mathematical methods and problems used in text mining and NLP ("Natural language processing") and describe examples of applications of these in different sectors of technology and society
- Briefly explain such mathematical concepts from matrix analysis, discrete mathematics, graph theory, stochastic processes, Markov chains, and mathematical statistics that are central to data mining in Internet and databases

Course content

- Graphs, matrices and distance mathematical foundation for the internet, databases and other information resources, and for mathematical search engine optimization
- Optimization and ranking in linked data structures
- Eigenvalues and eigenvectors of large matrices with special structural features and their central importance to searching, ranking and optimization algorithms for internet and large databases
- Google's PageRank algorithm and its modifications. Matrix iterations and matrix factorizations of numerical algorithms for the calculation of eigenvectors and eigenvalues and page rank
- Introduction to Markov chains as an alternative model for page rank and search on the internet and in other linked data structures.
- Distance, graphs and statistical techniques in text mining, NLP ("Natural Language Processing"), relevance ranking and comparison of texts.
- Graphs and matrices in models for communication and dissemination of information in social media like Facebook, Twitter and LinkedIn as well as for the relevance ranking of information as a tool to influence public opinion and decision making.

Tuition

Lectures and tutorials to work individually and in groups.

Specific requirements

At least totally 120 credits in the engineering, natural sciences, business administration or economics areas including Discrete Mathematics, 7.5 credits, Basic Vector Algebra, 7.5 credits, and either Programming, 7.5 credits, or Numerical Methods with MATLAB, 7.5 credits, or equivalent.
In addition Swedish course 3/Swedish course B and English course 6/English course A are required. For courses given entirely in English exemption is made from the requirement in Swedish course 3/Swedish course B.

Examination

Project (PRO1), 4.5 credits, marks Pass (G) or Pass with distinction (VG)
Seminars (SEM1), 3 credits, marks Pass (G) or Pass with distinction (VG)

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Grading scale: 5, 4, 3