Entry requirements

Algebra I

Learning outcomes

In order to pass the course (grade 3) the student should be able to

• solve linear Diophantine equations;
• solve polynomial congruence equations;
• be familiar with the Möbius inversion formula;
• be familiar with the parametrisation of primitive Pythagorean triples;
• decide whether a given number is a quadratic residue modulo p;
• cary out computations with continued fractions and find solutions to Pell's equation.

Content

Divisibility; ideals in the ring of integers, Linear Diophantine equations, groups of units in quotients of the ring of integers, Hensel's lemma. Cyclic groups of units and primitive roots, order. Quadratic residues and quadratic reciprocity. Arithmetic functions and the Möbius inversion formula. Sums of squares, Pythagorean triples. Continued fractions, rational approximation. Pell's equation.

Instruction

Lectures and problem solving sessions.

Assessment

Oral examination at the end of the course combined with written assignments during the course according to instructions provided at course start.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.