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Browse IS/STAG (S025)

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Courses found, count: 1

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  Abbreviation unit / Course abbreviation Title Variant
Item shown in detail - course KMA/6TEC1  KMA / 6TEC1 Number Theory 1 Show course Number Theory 1 2023/2024

Course info KMA / 6TEC1 : Course description

  • Course description , selected item
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Department/Unit / Abbreviation KMA / 6TEC1 Academic Year 2023/2024
Academic Year 2023/2024
Title Number Theory 1 Form of course completion Exam
Form of course completion Exam
Accredited / Credits Yes, 6 Cred. Type of completion Combined
Type of completion Combined
Time requirements lecture 2 [Hours/Week] practical class 2 [Hours/Week] Course credit prior to examination No
Course credit prior to examination No
Automatic acceptance of credit before examination No
Included in study average YES
Language of instruction English
Occ/max Status A Status A Status B Status B Status C Status C Automatic acceptance of credit before examination No
Summer semester 0 / - 0 / - 0 / - Included in study average YES
Winter semester 0 / 0 5 / - 0 / 0 Repeated registration NO
Repeated registration NO
Timetable Yes Semester taught Winter semester
Semester taught Winter semester
Minimum (B + C) students not determined Optional course Yes
Optional course Yes
Language of instruction English Internship duration 0
No. of hours of on-premise lessons Evaluation scale A|B|C|D|E|F
Periodicity every year
Specification periodicity Fundamental theoretical course No
Fundamental course No
Fundamental theoretical course No
Evaluation scale A|B|C|D|E|F
Substituted course None
Preclusive courses KMA/TEOCI
Prerequisite courses N/A
Informally recommended courses N/A
Courses depending on this Course N/A
Histogram of students' grades over the years: Graphic PNG ,  XLS
Course objectives:
Student obtains the knowledge from some areas of analytic number theory.
The course is realized only every second year.

Requirements on student
Oral and written examination.


Content
1.-2. Arithmetic functions, multiplicativity, convolution.
3.-4. Factorization methods.
5.-6. Cantor series, expression of numbers.
7.-8. Continued fractions.
9.-10. Diophantine approximations, linear independence, transcendence.
11.-12. Asymptotic density and other densities.


Activities
Fields of study


Guarantors and lecturers
  • Guarantors: prof. RNDr. Jaroslav Hančl, CSc. (100%), 
  • Lecturer: prof. RNDr. Jaroslav Hančl, CSc. (50%), 
  • Tutorial lecturer: Mgr. Lukáš Novotný, Ph.D. (100%), 
Literature
  • Extending: Niven, Zuckermann. An Introduction to the theory a Numbers. John Wiley, New York, 1967. ISBN 1492093823.
  • Recommended: Serre. A Course in Arithmetc. New York, 1996. ISBN 978-0-387-90040-7.
  • Recommended: Keng, H., L. Introduction to Number Theory. Springer-Verlag, 1982. ISBN 3-540-10818-1.
  • On-line library catalogues
Time requirements
All forms of study
Activities Time requirements for activity [h]
Being present in classes 52
Self-tutoring 40
Continuous tasks completion (incl. correspondence tasks) 20
Scientific text studying in a foreign language 10
Consultation of work with the teacher/tutor (incl. electronic) 5
Preparation for test 5
Preparation for an exam 30
Total 162

Prerequisites

Competences - students are expected to possess the following competences before the course commences to finish it successfully:
Knowledge of elementary number theory.

Learning outcomes

Knowledge - knowledge resulting from the course:
He obtains basic knowledge from specific areas of analytic and algebraic number theory. He knows different methods of expressing real numbers. He knows basic theorems from the theory of densities of sets of natural numbers.
Skills - skills resulting from the course:
He is able to apply relations between arithmetic functions. He knows how to express real numbers with the help of series of real numbers. He knows how to write a number with the help of continued fractions.

Assessment methods

Knowledge - knowledge achieved by taking this course are verified by the following means:
Written examination
Oral examination

Teaching methods

Knowledge - the following training methods are used to achieve the required knowledge:
Monologic (explanation, lecture, briefing)
Working with text (coursebook, book)
Dialogic (discussion, dialogue, brainstorming)
 

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