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Faculty of Mathematics and Computer Science,
University of Łódź

Archival ECTS Information Package

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Courses for Erasmus Students

List of courses in English offered in the academic year 2008/2009

Advanced Databases
Code:
Semester: winter
Credits: 7 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: test
Description:
The lecture presents advanced techniques commonly used with relational database applications: objects, XML, stored procedures, java programming of databases, spatial data, queues, and many others. Also, there are discussed advanced methods of tuning SQL queries and techniques of using databases in applications.

Advanced Programming I
Code:
Semester: winter or summer
Credits: 6 ECTS
Format: 60 hrs computer lab.
Form of assesment: practical test
Description:
Object-oriented programming in C++. Topics: inheritance and polymorphism; containers and STL algorithms.
Prerequisites: a course equivalent to Introductory Programming II

Advanced Programming II
Code:
Semester: winter or summer
Credits: 6 ECTS
Format: 60 hrs computer lab.
Form of assesment: practical test
Description:
Topics: templates and generic programming; tools for large programs; specialized techniques.
Prerequisites: a course equivalent to Advanced Programming II

Algorithms Analysis
Code:
Semester: winter
Credits: 8 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The main purpose of algorithm analysis is to predict the behaviour of the algorithm without implementing it on a specific computer, especially we are interested in its running time. We want to present the most important tools for the investigation of the efficiency of algorithm and give simple measures for the efficiency. As a rule we are not able to predict exact behaviour of the algorithm, because there are too many influencing factors. Therefore we try to extract the main characteristics of the algorithm, ignoring many details concerning the exact implementation. It is clear that this approach leads to the approximation of the running time only. On the other hand it gives significant information about the algorithm and allows us to compare different algorithms to choose the best one for our purpose.

Algorithms and Data Structures 1
Code: AD1 ENG
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: written exam + test
Description:
Algorithms and their analysis. Elementary data structures. Dynamic data structures: lists and trees. Abstract data types. Recursion. Elementary sorting methods. Binary search trees. Non-elementary sorting methods.

Algorithms and Data Structures 2
Code: AD2 ENG
Semester: winter
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: written exam + test
Description:
Dynamic data structures: graphs. Symbol tables (dictionaries). Priority queues and cheaps. Methods of tree balancing. Hashing. Non-elementary searching methods. String searching. Graph algorithms. Prerequisites: a course equivalent to AD1 ENG

Analysis on Manifolds
Code: AR0 MMT
Semester: winter or summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: oral exam + test
Description:
This is a lecture on mathematical analysis on k-dimensional surfaces in Rn leading to such a general version of Stokes formula that the fundamental theorem of integral calculus, Green formula, divergence theorem will appear to be its special cases. The main topics are: differential forms and fields, cubes and chains, the operation of differentiation and taking the boundary, integration over manifolds, Stokes theorem, classical theorems.

An introduction to Stochastic Processes - Theory and Applications
Code:
Semester: winter or summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The course presents the following topics: random walk (gambler's ruin, expected duration of the game, recurrence and first passage), Markov chains (classification of the states, asymptotic properties, stationary distributions), branching chains (models of population), martingales with discrete time (fundamental inequalities, convergence theorems, probability of ruin in insurance), Poisson process, Wiener process.

Application Software
Code: AS0 ENG
Semester: winter
Credits: 3 ECTS
Format: 30 hrs computer lab.
Form of assesment: test
Description:
We offer training and tutorials in most popular computer software and office applications such as Microsoft Word, Excel, PowerPoint, Visio and others.
Prerequisites: none

Artificial Intelligence
Code:
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The lecture includes the most important problems concerning artificial intelligence such as: fundamental methods and algorithms of artificial intelligence, fundamental information about neural networks as well as fuzzy logic. The aim of the computer laboratory is to implement selected algorithms presented during the lecture and to solve artificial intelligence problems.

Automata and Formal Languages
Code:
Semester: winter
Credits: 8 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The lecture is devoted to theoretical foundations of computer science. In the lecture finite automata, pushdown automata and Turing machines are presented. In the course regular languages, context-free languages, and recursively enumerable languages are also developed. In addition some elements of computational complexity theory, i.e. computational complexity of Turing machines and formal languages, computational complexity classes, P and NP classes, NP-complete problems are shown.

Basic Computer Skills
Code: BC0 ENG
Semester: winter
Credits: 3 ECTS
Format: 30 hrs computer lab.
Form of assesment: test
Description:
The aim of this course is to develop skills in working with a computer under the Windows operating system and in using software installed in the faculty's network. Moreover, during the course there are presented basic commands of the Linux Operating System, various Internet services and some elements of HTML.
Prerequisites: none

Compiler Construction
Code:
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The course aims to acquaint students with the structure and working of a compiler of a modern structural programming language. The scope of the material includes all stages of compilation, from reading in the source code through a systematic analysis up to the generation of the result code. During the semester the students write their own complier of a simple programming language.

Computer Architecture
Code: CA0 ENG
Semester: winter
Credits: 4 ECTS
Format: 30 hrs lecture
Form of assesment: test
Description:
The lecture acquaints students with logical bases structure and operation. The main topics are the following: numerical systems (binary decimal, hexadecimal), data representation (integers, fixed-point and floating-point numbers), ASCII characters and EBCDIC), Boolean algebras, logical gates, flip-flops, clocks, counters, (binary and decimal), half adders and binary adders, parallel adding/subtracting circuit, multiplication and division, logical operations and circuits carrying them out. Memory: memory element, address decoder, addressing, SRAM, DRAM, read and write cycles, bus, control unit, phases and cycles of executing instructions, interrupts, pipelines, RISC/CISC architecture

Computer Graphics 1
Code: CG1 ENG
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: written exam + test
Description:
The aim of the lecture is a presentation of theoretical basics of computer graphic without implementation details, presentation the most important algorithms in 2D and 3D graphics. The main topics of the lecture: raster graphics, algorithm for drawing 2D primitives, properties of geometric transformation, viewing in 3D, object graphical representation. Laboratory is devoted to the realisation of algorithms of creating graphics on a computer.

Computer Graphics 2
Code: CG2 ENG
Semester: winter
Credits: 7 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The main topics of the lecture: curves and surfaces visualisation, visible surface determination, illumination and shading, colour models. Laboratory is devoted to the realisation of algorithms of creating graphics on a computer.
Prerequisites: a course equivalent to CG1

Computer Networks
Code: CN0 ENG
Semester: winter
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: written exam + test
Description:
The course aims at presenting communication rules in computer networks via discussing a layered model of networking, introducing protocols performing communication functions, discussing various network services and presenting problems related to network security. The model currently considered is the TCP/IP protocol family.

Design and Implementation of Network Systems
Code:
Semester: winter
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: written exam + test
Description:
The aim of the course is to present the basic application services based on the TCP/IP protocol. The platform used is a well-known network operating system (Unix currently). The students develop the abilities to configure network services introduced during the "Computer Networks" course, and are acquainted with some widely-used servers for these services.
Prerequisites: a course equivalent to CN0 ENG

Design of Computer Software Systems
Code: DS0 ENG
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: written exam + test
Description:
The lecture is an introduction to analysis and structural programming in CASE technology, in particular the general principles of system analysis and modelling diagrams (entity relationship diagrams, function hierarchy diagrams, data flow diagrams, Object-Relation-Attribute diagrams). It presents system development life cycle (analysis, design, implementation, testing, system exploitation). The aim of the computer laboratory is to design and implement computer software systems.

Differential Geometry
Code:
Semester: winter or summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: oral exam + test
Description:
The lecture covers classical geometry of curves and planes in three dimensional space presented in such a way that generalization to multidimensional case (of hypersurfaces in multidimensional vector space and abstract differential manifolds) becomes an easy task. The lecture is also realised at a higher level and then covers ideas presented at a lower level in the case of multidimensional geometric objects. The backgrounds of the theory of differential manifolds and Riemaniann geometry are presented. The general theory is applied to multidimensional manifolds in multidimensional Euclidean spaces. Manifold and hypersurface geometry is applied in various branches of science, for example in theoretical physics.

Discrete Mathematics
Code: DM0 ENG
Semester: winter
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The lecture covers the following issues:
- mathematical induction principle;
- recurrence - recurrence definition, recurrence formulas vs. general formulas fro sequnces,
  recurrent equations;
- notation O(ˇ) for sequence;
- graphs - definition, adjacency matrix, properties of graphs, Eulerian graph, Euler theorem;
- combinatorics - the sum rule and the product rule, definition of variation, combination and
  permutation, combinatorics formulas, nonconstructive methods in combinatorics;
- divisibility of natural number, Euclid's algorithm;
- difference equations - general and particular solutions, first order, linear equation solution;
- generating functions.

Discrete Stochastic Processes in Market Theory
Code:
Semester: winter or summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written and oral exam + test
Description:
Our aim is to present some concepts related to the stochastic processes and their applications in financial and actuarial mathematics. We will limit ourselves to the processes with values in a discrete space and the processes with discrete time. We will present the basic properties and applications of the Markov chains, Poisson process and discrete-time martingales. Finally, some elements of the ruin theory will be presented.
Prerequisites: the students who intend to participate in the course should have completed basic courses on analysis and probability theory

Distributed Systems
Code:
Semester: winter
Credits: 4 ECTS
Format: 30 hrs computer lab.
Form of assesment: test
Description:
The course is intended to acquaint students with distributed systems theory by means of analysis of their component structure and studies of the concrete prototype solutions.

Distributions Theory and its Application to Differential Equations
Code: TD0 MME
Semester: winter or summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: oral exam + test
Description:
The lecture treats distribution theory and the Fourier transform of the tempered distributions. We introduce, among other things, the notion of differentiability in a distributional sense, which enables differentiation of some irregular mappings. This apparatus is applied to the effective determination of so-called fundamental solutions of differential operators, which has a fundamental significance in the theory of differential equations both ordinary and partial.

Elements of Algebra and Number Theory
Code: EA0 ENG
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The goal of the course is to present the notions of number theory and abstract algebra which are necessary for the understanding of the modern applications of those branches of mathematics in computer science, e.g. in cryptography. The course will concentrate on the following topics: groups, permutations, cyclic groups, subgroups, normal subgroups and quotient groups, group homomorphism and isomorphism, rings, fields and ideals, divisibility, greatest common divisor, lest common multiple, Euclid's algorithm, continued fractions, prime numbers, Euler's function, congruencies, numeral systems.

Elements of Artificial Intelligence
Code: EI0 ENG
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab
Form of assesment: written exam + test
Description:
The lecture introduces into the problems related to artificial intelligence, it presents its techniques and fundamental algorithms. The aim of the computer laboratory is to implement algorithms of major importance and to solve a few simple problems of artificial intelligence.

Elements of Mathematical Economy
Code:
Semester: winter or summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
Nominal interest rate; Effective interest rate; Rate of inflation; Equilibrium; Supply; Demand; Market equilibrium; National-income model; Input-output model; Comparitive statics; Optimum timing; Profit maximalization; Elasticity; Price discrimination; Production function; Optimalization; Linear and nonlinear programming and mathematical economics (applications).
Prerequisites: Mathematical Analysis

Financial Mathematics
Code: MF0 MME
Semester: winter or summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: oral exam + test
Description:
The notion of Black-Scholes price of assets. Binary ties and the Cox-Ross-Rubinstein model. Black-Scholes formula. Martingale measures in assets pricing. A notation of arbitrage and non-arbitrage conditions. Hahn-Banach theorem, separation of convex sets and fundamental theorem on assets pricing.

Genetic Algorithms
Code:
Semester: winter
Credits: 8 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: written exam + test
Description:
The aim of the lecture is to discuss the fundamental ideas, rules and operation of genetic algorithms and their generalizations called evolutionary algorithms. These algorithms are based on imitation of evolution processes occurring in nature. The following topics are included: structure and action of genetic algorithms, schema theory, evolutionary algorithms (various representations of solutions and recombination operators), selected applications (nonlinear programming, transportation problem, travelling salesman problem, multicriteria optimisation), the simple genetic algorithm as an example of random heuristic search.

Graph Theory and Combinatorics
Code:
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The lecture covers the following topics: partition of a number, generating functions and their applications, switch off-on rule and its applications, recursive linear equation, introductory concepts from graph theory, trees in the graph (their types and applications), sections and separating vertices, isomorphism of graphs, planar and dual graphs, colouring, covering and partition.

Internet Portals
Code:
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: written exam + test
Description:
The lecture is a review of advanced methods of Internet communication, the main problems of building advanced interface for potential customer or business partner. The lecture covers issues of building applications in J2EE technology, considering also non-J2EE techniques, such as SOAP, XML transformations, etc.

Introduction to Computer Science
Code: IC0 ENG
Semester: winter
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
Lecture includes following steps: history and future of computer science, basic notions and definitions used in computer science; among others, Boolean algebra, numerical systems, conversion among different numerical systems, representation of information in computer, ASCII, BCD, floating-point, elements of architecture of computers with particular taking into consideration microprocessor, asembler Intel 8086, algorithmic, notion of algorithm, manners of records of algorithms, programming languages and their evolution, computer networks, basic features and ownership, operating systems, classification and features.
Prerequisites: none

Introduction to Databases
Code: ID0 ENG
Semester: winter
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: written exam + test
Description:
The lecture is an introduction to the world of databases, especially relational database concepts and the powerful SQL programming. During one semester students learn about SQL language and how to query database, how to design, implement and manage database structures (such as tables, views, indexes, sequences). In addition, the lecture delves into advanced querying and report techniques, and optimising data with indexes.

Introduction to Differential Equations
Code: DI0 ENG
Semester: winter
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The lecture covers the main types of differential equations and systems of equations that are effectively solved, classical existence and uniqueness theorem and behaviour of equation systems solutions. It presents applications of differential equations (differential models in biology and economics), making use of symbolic calculations computers systems.
Prerequisites: advanced calculus (a course equivalent to MA2 ENG)

Introduction to Numerical Methods
Code: IN0 ENG
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab
Form of assesment: written exam + test
Description:
Numerical methods treat construction and investigation of algorithms of approximate solving of various computational problems. The aim of the lecture is to present fundamental notions of numerical methods such as elements of the error theory, convergence of algorithm, approximation of functions, derivatives and integrals. The lecture covers also fundamental algorithms for numerical solving of nonlinear equations and linear systems. The aim of tutorials is to present examples of practical applications and to investigate properties of various methods (on the ground of self-written programs by students and with the use of known computational environments). Knowledge of programming in any language is advisable.

Introduction to Operating Systems
Code: IO0 ENG
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: written exam + test
Description:
The main aim of the course is to provide a basic knowledge about concepts and design of operating systems. The lecture is illustrated with examples from the well-known existing implementations. The laboratories concern practical aspects, i.e., usage and administration of a large operating system (now Unix, but the choice depends on the current needs and trends of the IT market).

Introduction to Programming 1
Code: IP1 ENG
Semester: winter
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: practical test + written examination
Description:
The basics of programming in C++. Topics: input/output; variables and basic types; loops and decisions; arrays and pointers; functions and header files; classes.
Prerequisites: basic computer skills

Introduction to Programming 2
Code: IP2 ENG
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: practical test + written examination
Description:
Programming in C++. Selected topics: classes; copy control; overloaded operations; object-oriented programming.
Prerequisites: a course equivalent to IP1 ENG

Introductory Programming I
Code:
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: practical test + written examination
Description:
The basics of programming in C++. Topics: input/output; variables and basic types; loops and decisions; arrays and pointers; functions and header files; classes.
Prerequisites: basic computer skills

Introductory Programming II
Code:
Semester: winter
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: practical test + written examination
Description:
Selected topics: classes; copy control; overloaded operations; object-oriented programming.
Prerequisites: a course equivalent to Introductory Programming I

Linear Algebra with Analytic Geometry
Code: LA0 ENG
Semester: winter
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The course presents main topics of the linear algebra including linear spaces, linear dependence of vectors, basis and dimension of linear spaces, bilinear forms, inner and vector products. Topics on complex numbers, matrices and determinants are also presented. Next, systems of linear equations and methods for solving linear systems of equations (Cramer and Kronecker-Capelli theorems) are developed. Finally lines, planes, hyperplanes in Rn as well as quadrics are considered.
Prerequisites: none

Linear Algebra with Geometry 1
Code: AG1 OMM
Semester: winter or summer
Credits: 12 ECTS
Format: 60 hrs lecture + 60 hrs tutorials
Form of assesment: written exam + test
Description:
Methods of solving systems of linear equations with the aid of matrices and determinants, foundations of the theory of linear and affine spaces and linear and affine transformations, analytic characterization of certain geometric figures (line, plane, circle, sphere, curves and hyperspaces of dimension 2) are considered.

Linear Algebra with Geometry 2
Code: AG2 OMM
Semester: winter or summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The most important algebraic structures (groups, rings, fields) are covered and the notions given in AG1 are generalized to the case of a linear space over any field. The theory of linear spaces and linear transformations is continued (spectral theory, Jordan canonical form, etc.) and elements of multilinear algebra (i.e. tensor calculus) are considered.
Prerequisites: a course equivalent to Linear Algebra with Geometry 1

Logic with Elements of Set Theory
Code: LS0 ENG
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The lecture covers the following issues:
- elements of logic - proposition, connectives, propositional formulas, tautologies, quantifiers, methods
  of proving theorems;
- sets - methods for sets defining, operations on sets, and their properties, finding Cartesian product
  of given sets;
- a function and a graph of function, one-to-one function (injection), onto function (surjection),
  superposition, inverse function, image and preimage;
- sequences - definition, \Sigma and \Pi symbols, O notation, recurrence definitions, connection between
  recurrence definition and general definition of a sequence, proving of theorems by induction;
- relations - definition and properties, equivalence relation, equivalence classes graphs - definition,
  paths, cycles (circuits), Eulerian graph, adjacency.
Prerequisites: none

Mathematical Analysis for Computer Science Students 1
Code: MA1 ENG
Semester: winter
Credits: 7 ECTS
Format: 30 hrs lecture + 30 hrs tutorials + 30 hrs computer lab.
Form of assesment: test
Description:
The aim of this course is to teach students the bases of mathematical analysis which is necessary for studying computer science. Topics include the algebraic, logarithmic, exponential and trigonometric functions; limits; continuity and differentiability of real-valued functionsof a single variable; derivatives; graphing and optimisation problems; sequences and series.
Prerequisites: none

Mathematical Analysis for Computer Science Students 2
Code: MA2 ENG
Semester: summer
Credits: 9 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
A continuation of "Mathematical Analysis for Computer Science Students 1". Topics include Riemann sums and the definition of the definite integral; techniques of integration; approximation techniques; improper integrals; application; the calculus of functions with several variables.
Prerequisites: a course equivalent to MA1 ENG

Mathematical Modelling
Code:
Semester: winter or summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: written exam + test
Description:
The aim of the course is to highlight with the aid of various mathematical tools the key factors that govern population development. Starting from the notorious Malthus Law the subsequent improvements in population biology are presented. The mathematical apparatus we use will depend on the mathematical background of the students for models discussed may be presented either in their full complexity or in the simplest form accessible to nonmathematics students. The generality of the presentation and conclusion to be drawn are not lost in either approach. Mathematical modelling is founded on the belief that every process in nature is governed by a certain equation. Once this equation is found it is easy to make prediction and to understand various phenomena so far not fully comprehended. But finding this equation is not as a straightforward task as it may seem. The computer laboratory class will focus on numerical approximation and phase portraits analysis of the equations considered with the aid of widely used mathematical software.

Measure and Integral
Code:
Semester: winter or summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
A presentation of classical measure theory based on the Caratheodory condition, theory of integration including theorems on passing to the limit under the integral sign, product measure and Fubini theorem.

Midrange Servers
Code: MS0 ENG
Semester: winter
Credits: 3 ECTS
Format: 30 hrs lecture
Form of assesment: test
Description:
Specificity and philosophy of an operating system for midrange servers. The rules of working with the system. System's command language. Duties of a system operator and administrator, security policy, managing system resources and user accounts. Making backups and restoring data.

Modelling and Simulation
Code:
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The aim of the course is to present mathematical models of various phenomena, e.g. of biological, medical, economical processes. For example, the prey-predator, infected-susceptible, simplex, optimal portfolio models will be covered with emphasis on simulation skills. Basic modelling and simulation tools will be discussed. All models will be analysed with the aid of computer programs.

Modern Goemetry with Applications
Code:
Semester: winter or summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:

Prerequisites:

Network Services Programming
Code:
Semester: winter
Credits: 8 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: written exam + test
Description:
The aim of the course is to introduce widely-used and standardized interfaces used in network servers and clients. The problems discussed concern: the parallel processing interface (process view and thread view), interprocess communication, methods of synchronisation, the low and the high level of distributed data transmission programming.

Neural Networks
Code:
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The lecture presents an analysis (in great part mathematized) of artificial neural networks. Computer laboratory treats application of neural networks with the aid of Matlab software and afterwards construction of simple neural networks.

Probability Methods
Code: PM0 ENG
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The lecture presents basic problems and methods of modern probability theory and mathematical statistics. The scope of the material is a necessary minimum for a student of computer science. Having this as a basis, students can study on their own more advanced probabilistic or statistical topics in accordance with their needs.

Probability Theory
Code:
Semester: winter or summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: written exam + test
Description:
The course is designed to provide students with knowledge of basic methods and applications of modern probability theory. It is a necessary basis for studying mathematical statistics as well as more advanced topics in probability theory. Content: basic notations of probability theory, random variables and their distributions, moments of random variables, random vectors, joint probability distributions and martingales, independence of events and random variables, types of convergence of random variables, laws of large numbers, characteristic functions, central limit theorems.

Programming Languages 1
Code: PL1 ENG
Semester: winter
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: test
Description:
Presentation of structural programming paradigm using C language and structural C++. Idea of structural programming, presentation programming techniques, discussion of tools and utils. Discussion of data structure in C/C++ and usage of their in structural programming. Software modularisation and creation of program in multipersonal group. Presentation of manner of escape and discovering of exceptional situation.

Programming Languages 2
Code: PL2 ENG
Semester: summer
Credits: 7 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: written exam + test
Description:
Presentation of object-oriented paradigm using C++ and Java languages. Idea of object-oriented languages, presentation programming techniques, discussion of tools and utils. Elements of object-oriented design, programming in big programmers groups. Handling exceptions and RTTI mechanism.
Prerequisites:a course equivalent to PL1 ENG

Software Engineering
Code: SI0 ENG
Semester: winter
Credits: 3 ECTS
Format: 30 hrs lecture
Form of assesment: written exam
Description:
The object of the lecture is to present the basic models of software life cycles and to give the description of individual phases of this cycle: of strategy, requirement definition, analysis, design, implementation, testing, software installation and maintenance. A structural and object oriented approach is considered and significance of documentation and Case tools is discussed.

Software Project Management
Code:
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: written exam + test
Description:
We discuss: life cycle of software, steps of the software creation, quality control and documentation, principles of creation of user documentation, scaling of the cost of the software project, software project management methodology (Prince 2, PMI, CMMI), tools used during the software process.

Text Processors 1
Code: TP1 ENG
Semester: winter
Credits: 5 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: test
Description:
In class, students learn about TeX system which is the most powerful formatting program for producing book quality scientific texts. Students learn how to prepare documents using LaTeX format. The structures of various documents, typesetting mathematical formulae, the ways of defining one's own environments will be discussed.
Prerequisites: basic computer skills

Text Processors 2
Code: TP2 ENG
Semester: winter
Credits: 3 ECTS
Format: 30 hrs computer lab.
Form of assesment: test
Description:
In class, students learn about advanced LaTeX packages. They become familiar with insertion of drawings and tables, embedding graphics in the document and using colours. In addition, packages for converting documents from LaTeX file to pdf and HTML format will be discussed.
Prerequisites: a course equivalent to TP1 ENG

Theory of Differentiation of Functions and Functionals, Generalizations and Applications
Code:
Semester: winter or summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs tutorials
Form of assesment: oral exam + test
Description:
first part of the lecture will be devoted to revising fundamental definitions related to differentiating functions in the classical sense and in the Gateaux and Frechet sense. In the second part we introduce the notion of the weak derivative, which allows us to define the Sobolev spaces and so-called weak solutions of differential equations. We prove the Sobolev and Rellich-Kondraszev embedding theorems, Lax-Milgram theorem and then we apply his apparatus to the problem of existence and uniqueness of some selected boundary value problems for differential equations.

Visual Programming
Code: VP0 ENG
Semester: summer
Credits: 6 ECTS
Format: 30 hrs lecture + 30 hrs computer lab.
Form of assesment: written exam + test
Description:
The aim of the course is to acquaint student with present-day techniques: object-oriented programming, visual programming, constructing the interface, writing programs for networks, multithreaded programming. The course is designed to develop abilities: to analyse problems in the context of objects, to use modern programming tools, design software in modern object-oriented languages (C++, Java).

Web Publishing
Code: PU0 OII
Semester: winter or summer
Credits: 3 ECTS
Format: 30 hrs computer lab.
Form of assesment: test
Description:
The topics covered in the course include: HTML forms (the anatomy forms, attributes METHOD and ACTION, tags and fields of forms). The basics of PHP syntax: variables, their types and visibility, constants, operators, conditional structures iteration instructions, and methods of imbedding of PHP scripts in an HTML code, comments, testing the state of variables, numerical and associative arrays, catching the values of form fields, storing and reading data from files, regular expressions, accessing MySQL system data from a web pages.

XML Applications in the Internet
Code: XM0 ENG
Semester: summer
Credits: 3 ECTS
Format: 30 hrs computer lab.
Form of assesment: test
Description:
The lecture is an introduction to XML, the idea of marked text and modelling semistructured data in general. During one semester students get to know advanced XML techniques used in various applications especially in the Internet. The emphasis is put on such methods as namespaces, data verification, storing and querying XML from databases, transforming XML into "more human" form (HTML or PDF), use XML in communication (AJAX, SOAP, RPC), and many others.

Last modified: 21:30:41, 28-03-2014