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Course info
KMA / 6TEC1
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Course description
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Department/Unit / Abbreviation
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KMA
/
6TEC1
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Number Theory 1
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
6
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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lecture
2
[Hours/Week]
practical class
2
[Hours/Week]
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Course credit prior to examination
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No
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Course credit prior to examination
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No
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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English
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / 0
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5 / -
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0 / 0
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Winter semester
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Semester taught
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Winter semester
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Minimum (B + C) students
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not determined
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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English
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Internship duration
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0
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| No. of hours of on-premise lessons |
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Evaluation scale |
A|B|C|D|E|F |
| Periodicity |
every year
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| Specification periodicity |
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Fundamental theoretical course |
No
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| Fundamental course |
No
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| Fundamental theoretical course |
No
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| Evaluation scale |
A|B|C|D|E|F |
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Substituted course
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None
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Preclusive courses
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KMA/TEOCI
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
,
XLS
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Course objectives:
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Student obtains the knowledge from some areas of analytic number theory.
The course is realized only every second year.
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Requirements on student
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Oral and written examination.
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Content
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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.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Being present in classes
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52
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Self-tutoring
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40
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Continuous tasks completion (incl. correspondence tasks)
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20
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Scientific text studying in a foreign language
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10
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Consultation of work with the teacher/tutor (incl. electronic)
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5
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Preparation for test
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5
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Preparation for an exam
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30
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Total
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162
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Prerequisites
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Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
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| Knowledge of elementary number theory. |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
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| 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: |
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| 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. |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
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| Written examination |
| Oral examination |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
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| Monologic (explanation, lecture, briefing) |
| Working with text (coursebook, book) |
| Dialogic (discussion, dialogue, brainstorming) |
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