Computational Mathematician

EduRankAI; Kolkata District; Presencial; INR 900.000 - 1.800.000; Jornada completa

Descripción de la vacante

EduRankAI in Kolkata seeks an Engineer/Scientist specializing in mathematical foundations for high-precision computing. You will develop numerical methods, analyze convergence and stability, and ensure rigorous error budgeting for conditioning and floating point correctness.

The role involves designing algorithms, supporting cross-division modelling, and proudly reporting limits of validity with robust verification and reproducibility.

Formación

• Ability to state and use the definition of convergence for a numerical scheme.
• Linear algebra to conditioning, decompositions and ill-conditioned problems.
• Real analysis: limits, continuity, well-posedness.
• Implemented a numerical method from a paper and verified convergence order.
• Probability and statistics to explain what a confidence interval does.
• Proficiency in Python, Julia and C++.

Responsabilidades

• 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 characterize failure modes.
• Support modelling across divisions and identify ill-posed models.
• Review colleagues' numerical work for method-supported results.
• Own a problem end to end: framing, execution, reporting limits.

Conocimientos

Convergence analysis

Linear algebra

Real analysis

Numerical methods

Python

Julia

C++

Probability and statistics

Documentation

Herramientas

Python

Julia

C++

Descripción del empleo

Where the mathematics and the machine meet: conditioning, floating point, and what the computed answer is worth.

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: Where the mathematics and the machine meet: conditioning, floating point, and what the computed answer is worth. Scale range for this work: 10^-100 m to 10^100 m. Research classification: Computational. Computing quantities that cannot be obtained in closed form, from established physics. Evidential standing: Computational research. Computed from established physics. A computed number is a prediction, and it is only as good as its convergence, its error budget, and whatever data it can be checked against. 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 3 (Engineer and Scientist). A whole problem end to end: framing it, doing the work, and reporting the result with its limits.

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.
• Own a whole problem end to end: framing it, doing the work, and reporting the result with its limits.
• Review a colleague's work when asked, and say plainly when a result is not supported by its method.

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