Mathematics Research Intern

EduRankAI; Kolkata District; Presencial; INR 167.000 - 279.000; Jornada completa

Descripción de la vacante

EduRankAI invites applicants for an internship in mathematical and computational foundations. The role emphasizes proving results, building numerical methods, and supporting cross-division modelling with rigorous analysis.

You will work on a clearly scoped problem under a named supervisor, delivering a reproducible artefact and a short report at the end of the assignment.

Formación

• Ability to state and use the convergence definition for a numerical scheme.
• Strong linear algebra focusing on conditioning and decompositions.
• Knowledge of real analysis: limits, continuity, well-posedness.
• Experience implementing a numerical method from a paper and verifying convergence.
• Understanding of probability and statistics for confidence intervals.
• Proficiency in Python, Julia, and C++.
• Experience with symbolic mathematics.

Responsabilidades

• Develop mathematical foundations for models used by other divisions.
• Create numerical methods and establish what they converge to and under what conditions.
• Analyze convergence, stability and conditioning; report valid regimes.
• Develop optimisation algorithms and identify failure cases as well as successes.
• Support modelling across divisions; flag ill-posed proposals.
• Review others' numerical work and verify method-supported results.
• Work on a clearly scoped problem with a written final result.
• Meet a supervisor weekly and present what worked and what didn’t.

Conocimientos

Convergence definition

Linear algebra

Real analysis

Numerical method implementation

Probability and statistics

Python

Julia

C++

Symbolic mathematics

Descripción del empleo

One mathematical result reconstructed in full, including the steps its source omitted.

Department of Extreme-Scale, Nano & Fundamental Engineering, Division D09: Mathematics & Computational Foundations. This division develops the mathematics other divisions use. It builds numerical methods and proves what they converge to, designs optimisation algorithms, and supports modelling across every scale band the department declares. It is a service division and a research division at once, and it is mandatory to the department because a method nobody has analysed is a method nobody should trust. This position: One mathematical result reconstructed in full, including the steps its source omitted. Scale range for this work: 10^-100 m to 10^100 m. Research classification: Mathematical. Proving results and building the mathematical structures other work is expressed in. Evidential standing: Theoretical research. Mathematical and theoretical work. Derivation and internal consistency are the standard here; experimental confirmation is not currently available at this scale. A numerical result without a convergence statement is an opinion with decimal places. This division reports the order of a scheme, the conditions under which it is stable, and the regime where its error estimate no longer holds. Where a method is used outside the range it was analysed for, that is stated rather than hoped over. Scale bands are a research classification, not a claim of experimental reach. Most of this span cannot be probed by any apparatus that exists: nothing below about 10^-19 m has been measured directly, and anything at 10^26 m or beyond is inferred from observation rather than engineered. Every opportunity states the kind of work it actually is. Level 1 (Research and Engineering Intern). One well-defined problem, delivered with a reproducible artefact and a short written report.

Responsibilities

• Develop the mathematical foundations other divisions build their models on.
• Create numerical methods and establish what they converge to and under what conditions.
• Analyse convergence, stability and conditioning, and report the regime where the analysis holds.
• Develop optimisation algorithms and characterise where they fail as well as where they succeed.
• Support modelling across every division, including saying when a proposed model is ill-posed.
• Review other divisions' numerical work and say plainly when a result is not supported by its method.
• Work on one clearly scoped problem for the duration, with a written result at the end rather than a status update.
• Meet a named supervisor weekly and come to that meeting with what did not work as well as what did.

Skills

• Can state and use the definition of convergence for a numerical scheme, not just cite the order.
• Linear algebra to the level of conditioning, decompositions and why an ill-conditioned problem is not a bug in the solver.
• Real analysis: limits, continuity, and what makes a problem well-posed.
• Has implemented a numerical method from a paper and verified its convergence order empirically.
• Probability and statistics sufficient to state what a confidence interval does and does not claim.
• Python
• Julia
• C++
• Symbolic mathematics