Admission requirements
Linear algebra, (abelian) groups, rings, fields, comparable to the courses Lineaire Algebra 1 and 2 and Algebra 1 and 2 of the Leiden Bachelor Wiskunde. See the lecture notes at https://websites.math.leidenuniv.nl/algebra/
Description
Polynomial rings over fields have unique factorisation, but how do you compute this factorisation efficiently? How can you do computations with abelian groups in practice? How do we find short vectors in a lattice (discrete subgroup of Rn)? How to find the minimal polynomial of an algebraic number from just a numerical approximation? How to find the set of zeroes of a system of polynomial equations?
These are natural questions after undergraduate algebra, and their answers become even more important when studying algebraic number theory, algebraic geometry, or cryptography.
This is an introductory course on computer algebra, aimed at third year BSc students and first year MSc students.
Topics include:
Complexity (fast vs slow for computers)
Hermite and Smith normal form of matrices
The LLL algorithm and applications
Polynomial factoring over finite fields
Gröbner bases
Course Objectives
Students understand the workings of the algorithms treated in the course and are able to apply and extend them. Students are better prepared for the intricacies of algorithms in algebra, including algebraic number theory, algebraic geometry, and post-quantum and public-key cryptography.
Timetable
In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.
Additionally, you can easily link MyTimetable to a calendar app on your phone, and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.
Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.
Note: Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.
Mode of instruction
Lecture, problem class, self-study, programming projects, student presentations.
Assessment method
The final grade consists of two projects (20% each) and a written (retake) exam (60%). To pass the course, the (unrounded) grade for the final exam should be at least 5 and the (unrounded) weighted average of the partial grades at least 5.5. No minimum grade is required for the projects in order to take the exam or to pass the course. The projects count as a practical and there is no retake for them.
In the projects you will apply and/or extend the algorithms from the course. You work in a group of two or three students. At the end of the project you hand in a report and present your work to your fellow students. The project grade is based on the work on the project, including the report and presentation, and the answers you and your group members give to questions asked after the presentation.
Reading list
Joachim von zur Gathen and Jürgen Gerhard, Modern Computer Algebra (Third Edition, 2013).
The book is available as a download through the library: link https://www-cambridge-org.ezproxy.leidenuniv.nl/core/books/modern-computer-algebra/DB3563D4013401734851CF683D2F03F0
Having a physical copy of the book is highly recommended. This seems to cost between EUR 130 and 160 at various bookstores or the publisher link above.
We may occasionally use other sources that are freely available electronically.
Registration
As a student, you are responsible for enrolling on time through MyStudyMap.
In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.
Extensive information about the operation of MyStudyMap can be found here.
There are two enrolment periods per year:
Enrolment for the fall opens in July
Enrolment for the spring opens in December
See this page for more information about deadlines and enrolling for courses and exams.
Note:
It is mandatory to enrol for all activities of a course that you are going to follow.
Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.
Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.
Contact
See the lecturer information column in the e-prospectus or the contact information on the Brightspace page.
Remarks
none.
Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.