Elementaire getaltheorie

Course goals

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Content

Course Content 
In this course, we will study many of the main topics from elementary number theory. These include:

• modular arithmetic
• Euclid’s algorithm
• prime numbers and factorization
• continued fractions
• Diophantine equations
• Gaussian primes
• polynomial rings
• the law of quadratic reciprocity
• arithmetic functions and their properties
• sums of squares 

Learning Objectives 
By the end of this course, you will be able to:

• Build up the basic theory of the integers from a list of axioms
• Improve your written and oral communication skills
• Compose clear, precise mathematical proofs
• Learn to work collaboratively

Teaching Methods 
Two times 4 hours of class per week.
This course will be taught using an Inquiry-Based Learning (IBL) model. The format will be very different from that of a typical math course. In particular, the lectures will be short and there will not be any assigned reading. A typical class period will consist primarily of working on problems in small groups. Rather than being presented with neatly-packaged theorems and proofs, in this course you will be asked to devise your own conjectures and then prove them for yourself! 

Assessment
The grades in this course will be calculated according to the following scheme:

• 15% Class Participation
• 25 % Hand-in Exercises
• 30% Quizzes
• 30% Final Project

Resit and Effort Requirement 
Students with an insufficient final mark of at least 4, can repair at most one quiz. 

Language
The course is taught in English.