| TATA54 |
Number Theory, 6 ECTS credits.
/Talteori/
For:
CS
D
DAV
IT
Mat
Y
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Prel. scheduled
hours: 36
Rec. self-study hours: 124
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G2
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Aim:
The course should give insight into elementary number theoretic
concepts and advance ability in their use. After completing the
course the student should
- know how integers are constructed from the prime numbers and how the prime numbers are distributed among the integers
- be able to do calculations with congruences and solve certain diophantine equations
- know of certain important number theoretic functions, e.g. the Euler phi-function, and their use
- know the Möbius inversion formula and how to apply it
- have knowledge of some simple primality tests
- know the law of quadratic reciprocity
- be able to calculate with continued fractions and to use these in order to solve Pell's equation
- be able to handle the Gaussian integers and know how they are used to write integers as sums of two squares
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Basic concepts in discrete mathematics.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Organisation:
Lectures.
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Course contents:
Prime numbers, arithmetic modulo n, little Fermat, primitive roots, chinese remainder theorem, quadratic residues, reciprocity, sums of squares. Continued fractions.
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Course literature:
Rosen, K H: Elementary Number Theory and its Applications. 6th ed., Addison-Wesley.
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Examination: |
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Written examination
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6 ECTS
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Course language is Swedish/English .
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Leif Melkersson
Link to the course homepage at the department
Course Syllabus in Swedish
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