Remote | Computational Mathematician (Scientific Computing) — Up to $60/hour

We are sharing a specialised part-time consulting opportunity for PhD-level applied mathematicians with strong expertise in scientific computing, numerical methods, computational modelling, and research-grade programming. This role focuses on designing original, executable research problems based on authentic mathematical and computational workflows. Selected experts will create challenging coding-based problems across numerical linear algebra, computational mechanics, and computational finance, develop rigorous reference solutions and grading criteria, and refine tasks through systematic testing. Key Responsibilities Applied Mathematics Problem Design Develop original research-level computational mathematics problems Build tasks from published papers, public datasets, open-source repositories, or independently designed scenarios Create problems requiring multi-step mathematical and computational reasoning Ensure tasks reflect realistic scientific or quantitative workflows rather than standard textbook exercises Design problems with precise, reproducible, and mathematically defensible solutions Numerical Linear Algebra Develop computational tasks involving matrix methods, numerical solvers, decompositions, and large-scale linear systems Design problems requiring careful consideration of numerical stability, conditioning, convergence, and computational efficiency Evaluate alternative numerical approaches and their limitations Incorporate realistic edge cases and failure modes Validate numerical results using reproducible code Computational Mechanics Create mathematical modelling and simulation tasks involving mechanics where relevant Develop problems requiring numerical treatment of physical systems, discretisation, or equation solving Evaluate modelling assumptions, boundary conditions, and computational accuracy Design tasks requiring interpretation of numerical simulation results Ensure mathematical formulations remain consistent with the underlying physical problem Computational Finance Develop quantitative tasks involving financial modelling and numerical methods Create scenarios requiring simulation, optimisation, pricing, or quantitative risk analysis Evaluate assumptions and numerical methods used in financial computations Design problems where correct conclusions depend on both mathematical rigour and computational implementation Validate outputs against authoritative reference calculations Scientific Programming Write and validate computational workflows using Python or R Develop numerical implementations, reference calculations, and solution validators Debug scientific code and identify implementation or numerical errors Build reproducible workflows suitable for automated testing Ensure code accurately implements the underlying mathematical specification Reference Solutions & Grading Criteria Produce authoritative reference solutions and supporting calculations Define clear criteria for determining whether a solution is correct Identify essential mathematical reasoning, computational steps, and numerical outputs Develop grading logic capable of distinguishing correct solutions from plausible but flawed approaches Ensure evaluation standards remain precise and consistently applicable Testing & Difficulty Calibration Test tasks against advanced computational systems Analyse failure modes and identify where reasoning or implementation breaks down Refine prompts, inputs, constraints, and expected outputs based on testing Adjust problem difficulty while preserving mathematical validity Finalise tasks only when they reliably require advanced quantitative and computational expertise Research Engineering Workflow Work through a Git/GitHub pull-request workflow Run and validate code in Docker-based environments Respond to automated quality checks and reviewer feedback Maintain clean, reproducible code and supporting documentation Collaborate effectively within structured scientific software workflows Ideal Profile PhD required in Mathematics, Applied Mathematics, Computational Mathematics, or a closely related field Demonstrated depth in at least two of the following: Numerical linear algebra Computational mechanics Computational finance Strong working proficiency in Python or R Hands-on experience using programming for mathematical modelling, numerical analysis, simulation, or quantitative research Comfortable with Git/GitHub Experience running code in Docker or other containerised environments Strong understanding of numerical accuracy, computational reproducibility, and scientific validation Ability to translate advanced mathematical concepts into clearly defined computational problems Peer-reviewed publications are advantageous Prior scientific software or research engineering experience is highly valued Strong written communication and ability to document mathematical assumptions, methods, and solutions precisely Engagement Details Part-time independent contractor engagement Fully remote 20+ hours per week Initial duration of approximately 6 weeks Immediate start Compensation: Up to $60/hour Work includes computational problem design, scientific coding, reference-solution development, grading criteria, testing, and task refinement Projects may be extended, shortened, or concluded based on project needs and performance Work must be completed without using confidential or proprietary information belonging to any employer, client, institution, or other third party H1-B and STEM OPT support is unavailable for this engagement About the Platform This opportunity is available through 24-MAG LLC. 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