MAT3000 – Numbers, spaces and linearity
Course description
Course content
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.
Learning outcome
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.
Admission
Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.
If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.
Prerequisites
Formal prerequisite knowledge
In addition to fulfilling the Higher Education Entrance Qualification, applicants have to meet the following special admission requirements:
-
Mathematics R1 (or Mathematics S1 and S2) + R2
And in addition one of these:
- Physics (1+2)
- Chemistry (1+2)
- Biology (1+2)
- Information technology (1+2)
- Geosciences (1+2)
- Technology and theories of research (1+2)
The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies (in Norwegian).
Recommended previous knowledge
The course follows on from MAT1100 – Calculus, MAT1110 – Calculus and Linear Algebra and MAT1120 – Linear Algebra. It will be useful to have taken MAT2200 – Groups, Rings and Fields, but this is not a prerequisite for the course.
Overlapping courses
- 10 credits overlap with MAT4000
- 3 credits overlap with MA115
- 3 credits overlap with MA215
The information about overlaps is not complete. Contact the department for more information if necessary.
Teaching
4 hours of lectures/exercises every week for the duration of the semester.
Examination
Two compulsory assignments need to be passed within given deadlines to be allowed to take the final exam. Final mark based on written examination at the end of the semester.
Examination support material
No examination support material is allowed.
Language of examination
Subjects taught in English will only offer the exam paper in English.
You may write your examination paper in Norwegian, Swedish, Danish or English.
Grading scale
Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.
Explanations and appeals
Resit an examination
This subject offers new examination in the beginning of the
subsequent term for candidates who withdraw during an ordinary examination or fail an ordinary examination. For general information about new examination, see
/studier/admin/eksamen/sykdom-utsatt/mn/index.html
Evaluation
The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.