Master's Thesis Project

Welcome to the Master's Thesis Project page for Numerical analysis: This is for students in the Computational Mathematics (COMA) track of the Applied and Computational Mathematics program (SF250X) and students of the second year of the Computer Simulations for Science and Engineering (COSSE) program (SF259X).

For inspiration and to understand the scope of suitable thesis topics, you can explore past thesis projects in the KTH database, DiVA. Former COSSE student theses are listed here. Previous thesis projects can also be found in the KTH diva (but unfortunately not through a single search).

(This is a newly written page. Old page is here: Master's Thesis in Scientific Computing)

Eligibility and Program Requirements

SF250X: Students in the Computational Mathematics (COMA) track of the Applied and Computational Mathematics master's program (TTMAM).
SF259X: Students in the second year at KTH of the master's program in Computer Simulations for Science and Engineering (COSSE). Note that the COSSE version of the thesis will be graded on an A/F scale.

Goal

The goal of the master's thesis project is to provide students with the experience of independently conducting a large-scale scientific project in scientific computing, applied mathematics and computation. This project aims to deepen your knowledge and understanding of computational mathematics and its applications.

Prerequisites

To be eligible for the master's thesis project:

SF250X: You must have completed all courses in years 1-3 of your bachelor's degree, or the courses required for the issuance of a bachelor's degree, as well as at least 60 credits of advanced-level courses. Additionally, you must satisfy the conditions concerning the compulsory and conditionally elective courses:
At least three of the courses DD2365 Advanced Computation in Fluid Mechanics, SF2524 Matrix Computations for Large-scale Systems, SF2525 Computational Methods for Stochastic Differential Equations and Machine Learning, SF2526 Numerical algorithms for data-intensive science, SF2527 Numerical Methods for Differential Equations I, SF2528 Numerical Methods for Differential Equations II, SF2529 Inverse Problems, SF2565 Program Construction in C++ for Scientific Computing. Out of these courses either SF2524 or SF2527 must have been taken. (Please note that the course catalog description /student/kurser/kurs/SF250 of requirements is currently outdated.)
SF259X: The mandatory courses for year 1 studies should be completed and registered with KTH. Contact the director of studies in case of questions.

Thesis Requirements

The master's thesis project is a 30 ECTS credit course, which corresponds to approximately five months of full-time work. For SF259X the project is individual, and group projects are not permitted. For SF250X starting Spring 2025, groups of two, might be allowed but needs to be confirmed with the examiner. The project includes the following components:

Conducting a literature search, studying relevant textbooks, articles, and reports.
Investigating a problem in scientific computing and presenting your findings in a thesis, which will be a scientific report.
Participating in seminar activities in scientific computing at KTH, particularly at the Numerical Analysis (NA) department.
Delivering an oral presentation of your thesis.
Performing opposition, which involves providing constructive criticism of another student's master's thesis.

Examination and Grading

The thesis course is examined through a written thesis, an oral presentation, and the opposition of another thesis. The quality of your report, the clarity of your presentation, the depth of your opposition, and your overall work process (for example independence and planning) will all contribute to your final grade.

For detailed grading criteria, refer to the course syllabus.

SF250X: Graded on a P/F scale.
SF259X: Graded on an A/F scale.

Practical Information

Before the Course

Before starting the course, you need to have a project approved by an examiner. Follow the checklist below:

Verify Eligibility: Ensure you meet the prerequisites mentioned above. If uncertain, consult your student counselor or program director.
Find a Project: Start by looking for a project. You can find proposals on the KTH Degree Project Portal, contact companies or research groups directly, or propose your own project. The project should focus on a nontrivial mathematical or numerical problem in scientific computing. You may want to email a professor / researcher for ideas, but keep in mind that we get a large number of emails and if you don't get a response, it does not necessarily reflect you, your email or any disinterest. (Polite reminders are usually appreciated, but you may also want approach in person after a lecture.)
Write a Preliminary Project Plan: Prepare a short description of your project, outlining the background, application, main mathematical/numerical problems, your approach, a timeline of your project work, and some initial references. This plan should be created by you, with potential feedback from a supervisor.
Find a Supervisor: Contact a researcher or teacher within the NA group and ask if they can be a supervisor for your work. If your project is external (e.g., at a company), you will need both an NA group supervisor and an external supervisor. Any faculty member or post-doc or researcher of the NA-group at KTH may be you your supervisor. Exceptionally PhD students act as supervisors, but not examiners. NA faculty members may be busy, you may have to ask several members. If you get a "no" from three persons, please contact Elias to help you proceed. Ensure your preliminary project plan is reviewed and approved by your supervisor(s) before proceeding. NA faculty are listed as examiners: https://www.kth.se/student/kurser/kurs/SF250X?l=en . Members of the division numerical analysis, optimization and systems theory is listed here https://www.kth.se/math/naost/members-1.1314516. You may want to contact a supervisor about a project before or after you have written the project plan.
Start-Up Meeting for External Projects: If your project is with a company, arrange a meeting with your external supervisors, NA supervisor, and examiner to discuss the project goals and organization. The company must also sign a contract with KTH before the project can be approved. For students participating in SF259X, please remind the company contact that the thesis will be graded A/F.
Final Approval and Course Registration: Submit the following documents to your supervisors:
- A completed master thesis application form. Please fill out as much as you can, also parts of the section that says "to be filled by supervisor".
- Your project description (PDF-file)
- A contract signed by the company and yourself (if applicable).
- For students who study CDATE: Ask for confirmation of the project’s relevance to the programme by contacting the CDATE program director.

Once your project is accepted, you will be enrolled in the course, in particular registered to this CANVAS-page. We recommend that you complete all these steps before starting your project work.

Thesis Work

Organize your thesis work with your supervisor(s) and establish a regular meeting schedule for continuous supervision throughout the project. Typically you start by reviewing literature and background material necessary for your research, leading to a finalized project plan with a clear specification and timeline. As you are leading the project, you are also expected to reach out to get the help you need from the supervisor(s), the external and/or the NA-supervisor/examiner.

Additionally, during your thesis work:

Participate in a Research Seminar: Attend a seminar relevant to scientific computing or numerical analysis. It should preferably be done in person, but digital participation may be allowed if agreed beforehand with your supervisor. Provide proof of attendance (such as a selfie) and submit in the CANVAS assignment. NA group seminar schedules can be found here. The schedule is sometimes sparse, and your supervisor may grant you the right to attend a seminar in another part of applied mathematics instead.
Opposition: You are required to be an opponent for another master's thesis, usually scheduled alongside your own presentation.

Report

Discuss the report structure with your supervisor and start writing early to receive feedback on preliminary versions.

For report formatting and templates, please refer to the following resources:

Leave the TRITA-number blank, it will be filled by the administration. Ensure the thesis has both a front and back page.

Presentation

The first round of thesis presentations takes place in early June. The exact date(s) are communicated as announcement of this CANVAS page. To participate in this presentation round, your thesis report must be at least 90% complete two weeks before your scheduled presentation date. Your NA supervisor will determine if your thesis is sufficiently ready for presentation, so it's important to plan your work well in advance. Maintain regular contact with your supervisor to ensure there are no misunderstandings about the progress of your thesis. For example, you could submit a draft (say) three weeks before the presentation and ask for readiness level. A second round of presentations will be held in August, and there may be more presentation rounds in September-December if several students want to present.

Presentations are 30 minutes long, followed by 15 minutes for opposition and audience questions. Before your presentation, submit the necessary information for final thesis reporting and registration in DiVA using this form.

Opposition

As part of your thesis requirements, you will be assigned to act as an opponent for another master's thesis. You will receive the thesis at least one week before the scheduled opposition. Your role as an opponent is crucial for providing constructive feedback and engaging in scholarly discussion.

Your tasks as an opponent include:

Before the opposition:
- Critically review the assigned thesis, focusing on the problem statement, choice of methods, and discussion of results.
- Note any errors, unclear sections, or areas that pique your interest.
- Write a short opposition report on the thesis, following these instructions. You may use the provided LaTeX/Overleaf template to structure your report.
At the thesis seminar:
- Directly after the author's presentation: Provide an oral assessment and ask questions regarding the thesis report and presentation to stimulate discussion and further clarification. (approximately 10 minutes).
After the thesis seminar:
- Submit your opposition report in Canvas under the "Opposition" assignment within two days after the opposition.
- Send your opposition report to the author and supervisors (yours and the supervisor of the other student) by email to help improve their work.

The opposition is an essential part of the thesis process, as it allows you to critically engage with another student's work. The goal is that it enhances your skills to read and analytically evaluate results.

Finishing the Course

After the presentation, review any feedback and consider integrating it into your final report. Confirm with examiner / supervisor if there are substantial changes. Complete the publication information for your thesis using this link.

Send the finalized report to your examiner and/or supervisor by email. Include in your email:

Your name + your personnummer
Final title of your thesis (in swedish and english, or just in english)
Date of the presentation
Date of opposition
Final report in PDF-format

He / she will submit it to the administration for registration in ladok.

When you reach this point, we are happy to congratulate you for completing your master's thesis project!

Instructions for teachers/supervisors/examiners: separate page (not accessible to students)