SubjectsSubjects(version: 901)
Course, academic year 2021/2022
  
Mathematical Structures - NMAI064
Title: Matematické struktury
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: prof. RNDr. Aleš Pultr, DrSc.
doc. RNDr. Martin Klazar, Dr.
Class: Informatika Mgr. - Teoretická informatika
Informatika Mgr. - Diskrétní modely a algoritmy
Classification: Informatics > General Subjects
Is incompatible with: NMAX064
Is pre-requisite for: NMAI065, NMAI066
Is interchangeable with: NMAX064
Annotation -
Last update: G_I (11.04.2003)
Structures the students have already met (relations, algebraic structures, continuity structures), more specific facts, comparison. Various constructions (subobjects, equivalences and congruences, products, sums, etc.) in particular cases, and their common features. Particular attention will be paid to the structure of partial order, both in its general aspects and in the aspects specifically important for computer science. Some fundamental facts of category theory.
Course completion requirements -
Last update: doc. RNDr. Martin Klazar, Dr. (14.05.2020)

Oral exam, with written preparation. Exam question are/will be given on the course page,

see teacher's web page.

Prerequisity for taking exam is to get the ``zapocet''.

It will be granted for working out at least 1/2 of homeworks. There are no make up

terms for getting the ``zapocet''.

************************************************************************

As to situation caused by the current coronavirus pandemia in spring and summer 2020.

Form of exam (contact or distant) will be determined for each term in SIS

according to actual situation. Contact exam will be writen one with possible oral part.

For this course the contact form in small groups (<6, <11 people) appears probable.

Literature -
Last update: doc. RNDr. Martin Klazar, Dr. (12.10.2017)

Preliminary lecture notes in English are available from the teacher (A. Pultr) upon request.

Requirements to the exam -
Last update: doc. RNDr. Martin Klazar, Dr. (14.05.2020)

Oral exam, with written preparation. Exam question are/will be given on the course page,

see teacher's web page.

Prerequisity for taking exam is to get the ``zapocet''.

It will be granted for working out at least 1/2 of homeworks. There are no make up

terms for getting the ``zapocet''.

************************************************************************

As to situation caused by the current coronavirus pandemia in spring and summer 2020.

Form of exam (contact or distant) will be determined for each term in SIS

according to actual situation. Contact exam will be writen one with possible oral part.

For this course the contact form in small groups (<6, <11 people) appears probable.

Syllabus -
Last update: prof. RNDr. Aleš Pultr, DrSc. (11.10.2017)

1.Introduction: various structures the students have already met. Comparison, special features. Combining structures. Relations and relational

systems, some general constructions. 3. Partially ordered sets, generalities: posets, monotone maps, suprema and infima, adjunction.

4. Special posets (requiring specific or all suprema resp. infima, lattices and complete lattices. Fixed point theorems, applications. Distributive lattices, Heyting and Boolean algebras. 5. Algebraic operations, algebras, homomorphisms. Some general constructions (remarks on universal algebra). Varieties of algebras. 6. Structure of spaces. Metric spaces, topological spaces. 7. Remarks on some other types of structures. 8. Common features of some constructions: subobjects, quotients, products, sums, equalizers, etc.

 
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