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Euclid's algorithm, prime factorization, congruence, Fermat's little theorem, Euler's theorem, Wilson's theorem, quadratic rests and quadratic sums, distribution of primes. General vector spaces, linear transformations, matrix representations and change of basis, the Caylon-Hamilton theorem, inner product spaces, spectral theory, Schur triangularization, Jordan normal form, multilinear mappings. Some applications chosen from cryptography, geometry (geometric mappings) and analysis (differential equations, discrete Fourier analysis) are also covered.
You will first be introduced to classical number theory. Then the elementary linear algebra you already have learned will be developped further in some greater generality (by considering vector spaces over fields, with emphasis on the real and the complex cases). The purpose is to provide you with a thourough understanding of the concepts and of the main results, which are of fundamental importance in most areas of modern mathematics. The abstract theory is illustrated with several concrete applications.
Students who are admitted to study programmes or individual courses at UiO must each semester register which courses and exams they wish to sign up for by registering a study plan in StudentWeb.
International applicants, if you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.
Only students admitted to the course may take part in instruction and tuition and sit for the examination.
In addition to fulfilling the minimum requirements for entrance to higher education in Norway, you must either have 2MX/2MY/3MZ and 3MX/3FY/3KJ/3BI/(2KJ+3BT)/(2BI+3BT) from Norwegian upper secondary school, or have completed equivalent studies in mathematics as well as physics, or chemistry, or biology at upper secondary school or university level at another educational institution.
The course follows on from MAT1100 - Calculus, MAT1110 - Calculus and linear algebra and MAT1120 - Linear algebra. It combines nicely with MAT2200 - Groups, Rings and Fields (which is also given in the spring semester).
This information is not complete. Contact the department for more information if necessary.
4 hours of lectures/exercises every week for the duration of the semester.
One compulsory assignment have to be handed in and approved. Final mark based on written examination at the end of the semester.
No special exam resources are allowed.
The language of examination is generally Norwegian. You can apply to the administrators of the course to be given the exam text in English. It is generally possible to submit your response in Norwegian, Swedish, Danish or English.
Course grades are awarded on a descending scale using alphabetic grades from A to E for passes and F for fail.
Information about deferred and new examination (also called repeat examination) is found here (only in Norwegian) .
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