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Coding of diacritic chars. Making of multimedia pages. Making of dynamical elements, introduction to CGI. Introduction to Brywnt language. Wprowadzenie do Javascript online ; Rarey R. They become familiar with insertion of drawings and tables, okmbinatoryki graphics in the document and using colours. Elementy algebry abstrakcyjnej; Mostowski A. Wybrane zagadnienia algebry; Mostowski A. Zarys algebry; Browkin J.

The topics considered are elementary facts contained in modern scientific papers. Modern scientific descriptions of these topics papers and monographs and Gillman L. Rings of continuous functions; Engelking R. Measure and category; Bruckner A. Differentiation of real functions; Thomson B.

Priority queues and heaps. Methods of tree balancing. Analysis on Manifolds AR0 MMT AM4 MMT This is a lecture on mathematical analysis on k-dimensional surfaces in R n 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: Analysis on real and complex manifolds; Sikorski R.

Apprenticeship PZ0 MIZ 0 Local Credits 0 ECTS Credits 4 weeks at least hrs opinion of the institution in which the apprenticeship is served being credited with Semester 8 The apprenticeship will be organised by institutions using mathematical methods and computer techniques in their day-to-day production or services. Banks, Technology Institutes, Government Offices foll in that category. The goal of the apprenticeship is to acquaint the student with certain applications of methods of mathematics, computer science and statistics in production and science.

The apprenticeship should make choosing the future career an easier task. The aim of computer laboratory is to implement algorithms of major importance and to solve a few simple problems of artificial intelligence.

It presents fundamental ideas and models being the base for computing and computer working. In the lecture the following models are presented: There is a parallel presentation of Some formal languages and grammars generating them accepted by particular models: There are also elements of computing complexity theory: Automata and computability; Cohen D.

Introduction to computer theory; Martin J. Introduction to Languages and the Theory of Computation. It presents broaden topics from the first part of the lecture concerning: Automata and computability; Martin J. The aim of the lecture is to present foundations of the theory of Banach algebras and in particular the Gelfand theory of commutative algebras and the Gelfand-Naimark theorem.


Material provided for students. The need for the course results from the necessity of developing basic computer skills which are essential while studying other computer courses. Documentation of used software. It is a starting point for further individual studies of these issues.

There will be conducted mathematical analysis of the considered models on the one hand and simulation and verification on the basis of existing data on the other hand. Mathematical Biology; Lachowicz M. Modelowanie matematyczne zjawisk przyrodniczych; Lachowicz M.

Klasyczna ekologia matematyczna; Hastings A. Concepts and models; Fulford G. Modele matematyczne w epidemiologii i immunologii.

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Analiza matematyczna dla nauczycieli; Fichtenholz G. Taylor formula, graphs of functions, the theory of numerical series, functional series, functions of two or more variables and the applications of differential calculus. The emphasis is put on the specific methodical features of that subject and on relation to the history of the calculus of probability according to the parallelism rule.

The exercises will treat methodical solutions of problems of probability. Articles in didactic journals e. Bernoulli shift, Cantor set as attractor, various definitions of chaos, Lapunov exponent and its informative interpretation, Sharkovskii theorem, characteristics of chaotic systems.

Poincare mapping, nonlinear pendulum, Lorenz system, strange attractors, Hopf bifurcations.

Discrete Mathematics (07 74 20)

Nonlinear oscillations, dynamical systems and bifurcations of vector fields. 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. Lecture notes provided for students in an electronic way; Cytron R. Compiler construction; Aho A. It has an open character leading do multidimensional complex analysis. Characterisation of the open sets not separating the plane and an introduction to the theory of harmonic and subharmonic functions is given. Its developement has been observed since It unites nonlinear functional analysis, topology, spectral theory, operator theory and others.

Introduction to Holomorphy; Dineen S. Complex Analysis on Infinite Dimensional Spaces. The problems in question are, for example, comparison of algorithms of numerical solution of differential equations, linear algebra equation, interpolation and approximation of functions and 2D, 3D graphics. Problems and methods of their solutions provided for students.

The main topics are the following: Bartee Computer Architecture and Logic Design. The main topics of the lecture: Laboratory is devoted to the realisation of algorithms of creating graphics on a computer.


Sieci komputerowe i intersieci; Stevens R. Ochrona danych w sieci i intersieci. The following software will be considered: Derive, Cabri, Excel, Scientific Work Place and modern software being of use in the teacher s everyday routine. Matematyka z elementami informatyki w gimnazjum; Legutko M.

Wariacje na temat twierdzenia Napoleona, NiM Cabri i geometria elementarna, Matematyka 4 ; Szymczak J. Selected materials from invex and convex analysis. Theory and algorithms; Mangasarian O. Teoria i metody obliczeniowe optymalizacji; Galas Z. It contains references to combinatorial methods of computer science and to discrete mathematics. The students are being trained to analyse statistics models applied in technology, economics and medicine. The lecture refers to various branches of widely understood mathematical analysis and mathematical physics.

It is necessary for taking more specialised courses in theory of stochastic processes, theory of dynamical systems, theory of information and coding, econometrics models, financial and insurance mathematics and statistics.

A comparison with a classical construction of measure and integral is given. Applications to construction of Lebesgue measure and integral in R n are given. Creating and management of tablespace. Management of users system and object rights. Security rules, making backups. Materials provided for students; Date C. Basic structure of bases, information flow in systems integrated with transactional bases, data analysis techniques and analytic tools will be discussed.

The lecture contains also examples of abstract density topologies generated by the lower density mapping and connected with the notion of the density point with respect to the category and with the notion of a set which is rare at a point. Differentiation of Real Functions.

The course should prepare students to working on large computer systems created by teams. Projects will also treat distributed systems. Materials and documentation provided for students; Barker R. 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. Analiza funckjonalna; Szmydt Z. Differential Geometry 1 GR1 MMD tutorials 2 written tests AG2 OMM, WR0 OMM 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.