Physics & Applied Mathematics

Mathematical Proof Construction

Required. Construct a complete formal proof in continuous mathematics (real analysis, linear algebra, differential equations, or probability). The proof may be original or a reconstruction of a named non-trivial result with all steps explicit. Reviewed by a mathematician or physicist who confirms logical validity and presents an unseen claim for the student to work through live. Requires no equipment — mathematical foundations underpin all subsequent physics steps.

Physics Experiment Execution and Analysis

Elective. Design and execute a real physics experiment: testable prediction from theory, raw data with documented measurement uncertainty, error analysis (systematic + random, error propagation), and quantitative comparison to theoretical prediction. Accessible alternative: full methodology analysis of a named real dataset from CERN Open Data Portal, NASA Exoplanet Archive, SDSS, or LIGO Open Science Center — documentation requirements are identical to lab work.

Computational Physics Modelling

Elective. Build a real computational physics model using numerical methods (finite difference, Monte Carlo, molecular dynamics, or numerical ODE/PDE integration) in code (Python with NumPy/SciPy, Julia, or equivalent). Submitted code must be runnable as-is. Reviewer runs the code independently, then asks you to modify a specific parameter and predict the outcome during the review session. All tools are free and open source.

Physics Open Data Analysis

Elective. Analyse a named real publicly available physics dataset from CERN Open Data Portal, NASA Exoplanet Archive, IPAC Infrared Science Archive, SDSS, or LIGO Open Science Center. Full methodology documentation: data source and version, preprocessing, statistical analysis with uncertainty quantification, conclusions with physical interpretation. Code or methodology sufficient for reproducibility. Reviewer challenges the uncertainty interpretation and asks whether alternative explanations are consistent with the data.

Physics Derivation from Primary Literature

Elective. Work through a key derivation from a named primary physics paper step by step — filling in all algebraic and physical reasoning steps the authors compressed. Document each step with physical justification, identify approximations and their domain of validity. Accessible via arXiv (free) and Physical Review Letters open access. Reviewer selects a second related paper during the review session and asks you to identify the key derivation step.

Free access to petabytes of real particle physics data from LHC experiments (ATLAS, CMS, LHCb, ALICE), including collision event records, processed datasets, and analysis software. Use for the physics open data analysis step — real LHC data with documented provenance and citable DOIs. The portal also provides analysis tools and tutorials for getting started with high-energy physics data.

Free access to real gravitational wave strain data from all LIGO, Virgo, and KAGRA observational runs, including the GW150914 first detection. Use for the open data analysis step — the data is real, the signal is real, and tutorials are available in Python. Reviewers can independently verify your analysis methodology.

Free access to physics preprints across all subfields — condensed matter, quantum physics, astrophysics, mathematical physics, and more. Use for the primary literature derivation step: select a named paper in your area of interest and work through a derivation from it step by step. arXiv papers are citable and widely used by professional physicists.

Free visual explanations of the continuous mathematics covered in the proof construction step — linear algebra, real analysis, and differential equations. Use to build geometric intuition for the structures you are proving statements about. Not a substitute for the proof itself, but excellent preparation for understanding why the theorems are true before proving they are.