Z1-PU7
COURSE DESCRIPTION
(faculty stamp)
WYDANIE N1
Strona 1 z 2
2. Course code W1A
1. Course title: NUMBER THEORY
3. Validity of course description: 2015/2016
4. Level of studies: first cycle of higher education
5. Mode of studies: intramural studies
6. Field of study: MATHEMATICS RMS
(FACULTY SYMBOL) RMS
7. Profile of studies: general
8. Programme: all
9. Semester: IV
10. Faculty teaching the course: Faculty of Applied Mathematics
11. Course instructor: prof. dr hab. Olga Macedońska-Nosalska
12. Course classification: a limited selection of items (“blok przedmiotów ograniczonego wyboru”)
13. Course status: elective
14. Language of instruction: English
15. Pre-requisite qualifications: Basic knowledge of English and linear algebra.
16. Course objectives: Developing students’ facility in reading and understanding mathematical literature in English. The course aims to
acquaint the students with various aspects of number theory, from basic notions to more advanced methods.
17. Description of learning outcomes:
A student who completes the course successfully should be able to
Nr
Learning outcomes description
Method of assessment
1. reading and understanding texts of number theory
written in English
Teaching methods
midterm test,
observation,
oral answer
2. communicating material of number theory in English oral answer
lecture, class
3. knowing basic definitions, theorems and concepts
of number theory
midterm test,
observation,
oral answer
4. applying theoretical knowledge in the investigation midterm test,
of examples and problems of number theory
observation,
oral answer
lecture, class
5. carrying out proofs of number theory in English
class
oral answer
class
lecture, class
Learning
outcomes
reference
code
K1A_U01,
K1A_K01,
K1A_K06
K1A_W05,
K1A_U36,
K1A_K02
K1A_W04,
K1A_U01
K1A_W03,
K1A_W05,
K1A_K02,
K1A_K05
K1A_W04,
K1A_U01
18. Teaching modes and hours
Lecture / Class
Lecture 30h. Class 30h.
19. Syllabus description:
Lecture: The Euclidean Algorithm, The linear Diophantine equation, The fundamental Theorem of Arithmetic, Theory of congruence, The
little Fermat’s theorem, Wilson’s theorem, Arithmetic functions, Fibonacci numbers, Pythagorean triples, Fermat Last theorem.
Class: The content of the class work will correspond to the content of the lecture. The class will be devoted to solving problems illustrating
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the theory studied during the lecture. The list of problems for students will be announced at the platform (with hints for solutions). Next week
students will present their solutions at the blackboard. The problems from the lists (or similar) will be used as the tests problems.
20. Examination: no
21. Primary sources:
1. Elementary Number Theory, D.M.Burton, Allyn and Bacon Inc. Boston-London-Sydney-Toronto 1980
22. Secondary sources:
1. Elementy teorii liczb, Wacław Marzantowicz, Piotr Zarzycki, Wydawnictwo Naukowe UAM, ISBN 83-232-0973-1
2. A. Prószyński, Algebra z teorią liczb, Wydawnictwa Uniwersytetu Kazimierza Wielkiego, Bydgoszcz 2009.
23. Total workload required to achieve learning outcomes
Lp.
Teaching mode :
Contact hours / Student workload hours
1
Lecture
30/30
2
Classes
30/59
3
Laboratory
/
4
Project
/
5
BA/ MA Seminar
/
6
Other
1/0
Total number of hours
61/89
24. Total hours: 150
25. Number of ECTS credits: 5
26. Number of ECTS credits allocated for contact hours: 5
27. Number of ECTS credits allocated for in-practice hours (laboratory classes, projects): 0
26. Comments: Assessment
Two written tests: 2x35 p.
Evaluation of responses at the blackboard: 15 p.
Activity: 8 p.
Points for attendance of lectures: 7 p.
To pass, it is necessary to acquire a total of 41 p. and achieving all learning outcomes described above (at least 30% of the maximal number of
points).
Approved:
…………………………….
(date, Instructor’s signature)
…………………………………………………
(date , the Director of the Faculty Unit signature)
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