Computational Mathematician (Scientific Computing)

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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