Theses

Topic areas, expectations, and best-practices for theses with the Computational Mathematics group

We supervise Bachelor's and Master's theses at the intersection of numerical mathematics, high-performance computing and scientific software engineering.

Browse open topics on the TUM Thesis Portal The portal is the only way to apply for a thesis with us, including for your own topic proposals that fit our research directions.

Who can apply

Students enrolled at the Technical University of Munich, at TUM Campus München or TUM Campus Heilbronn. Most come from Informatics, Mathematics, Computational Science and Engineering, or Information Engineering, but motivated students from related disciplines are welcome too.

Topic areas

  • High-performance computing & parallel algorithms
  • GPU programming
  • Sparse numerical linear algebra
  • Iterative solvers & preconditioning
  • Mixed-precision & communication-avoiding algorithms
  • AI for scientific computing

How it works

A thesis with us is a supervised research project: you take ownership of the work, and we provide technical guidance, compute resources, and access to our collaborators and codebases.

  1. Choose a topic

    Pick an open topic on the portal or submit your own there. We do not track theses outside the portal.

  2. Write a proposal

    Mandatory before any work begins: a LaTeX- or Typst-rendered PDF describing

    • the research question
    • possible methodologies and your planned approach
    • tools, datasets and evaluation strategy
    • a detailed weekly timeline for the full thesis

  3. Get accepted

    Once your advisor approves the proposal, you are onboarded and we register the thesis with the examination office. Only then can you start working.

  4. Kickoff

    A short presentation within the first few weeks to align on scope, methodology and success criteria.

  5. Regular meetings

    Weekly or biweekly meetings with your primary supervisor, depending on the phase, plus periodic written progress updates so blockers surface early.

  6. Final defense

    Present your work to the group at one of our Thursday seminars, in person at TUM Campus Heilbronn.

Being in touch with us about a topic does not mean you have been accepted. You join the group as a thesis student only once your advisor approves your proposal (step 3).

Thesis duration and formal steps follow the TUM examination regulations for your study program.

Guidelines

Writing

  • Write in English, in LaTeX or Typst, whichever you prefer.
  • Templates: Exzellenz TUM Thesis (Typst) or tum-thesis-latex (LaTeX).
  • Cite with BibTeX (or Typst's equivalent) and keep the bibliography file in your repository.
  • Back every claim about prior work with a citation.
  • You must be able to defend and justify each sentence in your thesis, because in effect you are the one who should have written it.
  • Generate figures from scripts, not by hand, so they can be rebuilt from raw data.
  • Attach the signed Declaration of Generative AI Use to your thesis (see Use of generative AI).

Suggested structure

  1. Abstract & introduction: motivation, research question, contributions
  2. Background & related work
  3. Methodology: the algorithms, models or systems you propose
  4. Implementation: enough detail to reproduce the work
  5. Experimental evaluation: setup, baselines, metrics, results
  6. Discussion, limitations & future work
  7. Conclusion

Code & reproducibility

Your implementation is part of the thesis, so it needs the same care we apply to our own projects.

  • Use git from day one; commit early and often.
  • Add a README with build steps, dependencies and how to reproduce the key experiments.
  • Test the core logic you introduce; continuous integration is encouraged.
  • Document datasets and benchmark problems, including source and preprocessing.
  • In our codebases (e.g. Ginkgo), follow the project's contribution guidelines and coding style.
  • Include or link an archived code snapshot matching the results in your thesis.

Use of generative AI

Generative AI tools (such as ChatGPT, Copilot, Claude Code or Grammarly) are appropriate when they support your learning, and inappropriate when they replace it. Their use in your thesis is set out in a binding agreement between you and your examiner, based on TUM's framework agreement on generative AI in written work.

Declaration of Generative AI Use (fillable PDF) ↓ For each activity, declare whether and how you used generative AI, then sign it and attach it to your thesis.

Ground rules

  • Before using AI, check that it is sensible, appropriate and allowed for the specific task.
  • AI is not a reliable or reproducible source: the same prompt can give different answers, and outputs can be wrong (hallucinations) or biased.
  • You remain responsible for the content, its factual correctness and the sources you use.
  • You must be able to defend and justify each sentence in your thesis, because in effect you are the one who should have written it.
  • AI is never a co-author.
  • Document every use of AI in a traceable way: fill in our declaration form (fillable PDF) and attach it to your thesis.
  • When in doubt about usage, ask your supervisor.

What is allowed

Your agreement marks each activity with one of three levels:

  • Permitted
  • Permitted with transparency
  • Not permitted

For theses in our group:

Permitted with transparency: you may use AI for these, but must document it.

  • Ideas & concepts
  • Literature search & analysis*
  • Coding
  • Data collection*
  • Data analysis*
  • Structuring the text
  • Translation*
  • Proofreading & editing
  • Image generation*
  • Data visualisation
  • Presentations
  • Reference list
  • Accessibility

Not permitted: these must be your own work.

  • Methodology
  • Interpretation & validation
  • Text generation

* Take extra care with copyright (others' literature, texts and images) and data protection (collecting and analysing data).

Sources: TUM framework agreement on generative AI (PDF, German) · GenAI conditions for theses in Koinon (PDF)

Before you apply

Each topic on the portal is owned by one of us. Our research, publications and people pages help you pick a project, and a supervisor, that match your interests.