Required in stage
Optional in stage
First term
Second term
Both terms
Not organised
This year
Next year
Alternating years
External
Prerequisites
Taught by
Language of instruction
Duration
Identical coursesAims
Introducing the basic results and methods from elementary number theory. Applications and computational aspects are extensively discussed.
Previous knowledge
Courses G0N27A Lineaire Algebra, G0T45A Algebraïsche Structuren and G0N88A Algebra I.
Is included in these courses of study
Activities
4 ects. Number Theory (B-KUL-G0P61a)
Content
Review of basic arithmetics: Euler function, congruences of Euler and Wilson, Chinese Remainder Theorem.
Structure of the unit group of Zn.
Solubility of congruences: Lemma Hensel-Rychlik.
Quadratic reciprocity laws of Gauss and Jacobi.
Fast algorithms for congruences and primality testing.
The field of p-adic numbers.
p-adic numbers and the Hilbert symbol.
Rational points on a conic. The Hasse principle.
Quadratic rings.
Whole points on conic sections.
Applications in cryptography.
Prime numbers and the Riemann zeta function (introductory).
Elliptic curves
Course material
Syllabus
Format: more information
Lectures
2 ects. Number Theory: Exercises (B-KUL-G0P62a)
Content
Same as lectures.
Course material
Same as lectures + Toledo.
Format: more information
Exercises.
Evaluation
Evaluation: Number Theory (B-KUL-G2P61b)
Explanation
The evaluation consists of:
- a written exam during the examination period (with grade E).
- 3 (non-obligatory) assignments during the semester (with grade T).
The final grade is calculated according to the formule max{E,(3E+T)/4}.
It is not possible to retake the assignments for the second examination attempt, but the previously submitted assignments do count for the final grade.