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