Schedule, syllabus and examination date

Choose semester

Exams after the reopening

As a general rule, exams will be conducted without physical attendance in the autumn of 2021, even after the reopening. See the semester page for information about the form of examination in your course. See also more information about examination at the MN Faculty in 2021.

Course content

The course gives an introduction to elliptic curves, at central topic in number theory and in algebraic geometry with applications in data security/cryptography.

Learning outcome

After completing the course:

  • you know Weierstrass curves and elliptic curves as cubic curves in the plane with coefficients in a finite or an infinite field
  • you can perform computations in the group of points on an elliptic curve
  • you know the relation between complex elliptic curves and rank two lattices in the complex plane
  • you know the endomorphism ring of elliptic curves and isogenies between these
  • you know the relation between the j-invariant and isomorphism classes of elliptic curves
  • you know the Hasse theorem for the number of points on elliptic curves over a finite field
  • you know how to present, on a scientific level, a short thesis on a chosen topic of relevance, selected in collaboration with the lecturer.

Admission to the course

PhD candidates from the Faculty of Mathematics and Natural Sciences at the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.

Overlapping courses

Teaching

3 hours of lectures/exercises per week throughout the semester.

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.

Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.

Examination

Final oral exam which counts 100 % towards the final grade.

This course has 1 mandatory assignment that must be approved before you can sit the final exam.

In addition, each PhD candidate is expected to give an oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer before you can sit the final exam.

It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: MAT4240 – Elliptic curves

Examination support material

No examination support material is allowed.

Language of examination

Courses 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 pass/fail scale. Read more about the grading system.

Resit an examination

This course offers both postponed and resit of examination. Read more:

Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Dec. 7, 2021 11:29:08 PM

Facts about this course

Credits
10
Level
PhD
Teaching

Spring 2022

Taught according to demand and resources. Contact studieinfo@math.uio.no if you are interested in this course. 

Spring semester 2022: This course will only be given as a self-study course.

Examination
Spring
Teaching language
Norwegian (English on request)