Ajeet Kumar

Ajeet Kumar

Applied Mathematician with Specialization in Full Stack Machine Learning and Data Science

Sitemap

A list of all the posts and pages found on the site. For you robots out there, there is an XML version available for digesting as well.

Pages

Posts

System Design Part 9

less than 1 minute read

Published:

System Design from First Principles - The Mathematics of Attempts

System Design Part 8

less than 1 minute read

Published:

System Design from First Principles - CAP Theorem & PACELC

System Design Part 7

less than 1 minute read

Published:

System Design from First Principles - Sharding: When One Disk is Not Enough

Operational Ecosystems of LLMs in Python - Part 2

1 minute read

Published:

Module 2 : Re-Engineering and Verification Workflow

Module‑1 showed you that LLMs are not magic but a composition of code, math, and hardware, all reachable from Python if we know where to look. It traced how LLMs sit in the stack: Python as glue, PyTorch as the modeling layer, and hardware‑specific backends (CPU, GPU, etc.) as the execution engines.

Operational Ecosystems of LLMs in Python - Part 1

7 minute read

Published:

The first question came into the my mind when i started thinking about the operational ecosystem of LLM is that Why LLMs matter in the AI ecosystem ? LLMs are a core component of modern artificial intelligence. In practice, we use Python extensively for almost any task in AI and data‑driven decision‑making from simple scripts to complex production pipelines. Today, the ecosystem surrounding Python is rich and specialized for nearly every problem domain, there exist dedicated tools that can be easily integrated because they live inside Python’s operational environment. So, they are the natural evolution of this ecosystem they turn language into a computational interface but still sit on top of same stack of tools, hardware and orchastration layers that power the rest of AI.

System Design Part 6

less than 1 minute read

Published:

System Design from First Principles - The Taxonomy of Storage: How to Architect Data

System Design Part 5

less than 1 minute read

Published:

System Design from First Principles - The Physics of Persistence

System Design Part 4

less than 1 minute read

Published:

System Design from First Principles - The Anatomy of a Request (DNS, BGP, and the Edge)

System Design Part 3

less than 1 minute read

Published:

System Design from First Principles - The Cost of Communication

Mathematics

less than 1 minute read

Published:

In mathematics we study mathematical objects , relationship between objects and how relationship between objects changes w.r.t to others and many more lead to the special class of mathematical structures that mathematicians are interested to explore through geometry, algebra and analysis etc.

System Design Part 2

less than 1 minute read

Published:

System Design from First Principle - The Math of Scale

Attention Mechanisms

63 minute read

Published:

Attention Mechanisms - All You Needed To Know

Llama Lineage

7 minute read

Published:

A Study of Llama Lineage : A Transformer based LLMs

AI Model Optimization Part-1 by Applied Mathematician

1 minute read

Published:

AI Model Optimization is an interdisciplinary field that involves collaboration between researchers, system engineers, and hardware architects to make models better, cheaper, and faster with the goal of maximizing throughput and minimizing computational costs and latency.

अत्रेय महाकाव्य: शून्य से सृजन और आजमगढ़ की पावन कर्मभूमि की अमर गाथा

1 minute read

Published:

क्या आपने कभी उस ‘शून्य’ के बारे में सोचा है जहाँ से इस अनंत ब्रह्मांड का उदय हुआ? क्या आप जानते हैं कि आजमगढ़ की पवित्र नदियाँ—तमसा, मंजूषा और कुँवर—किन महान ऋषियों की साधना की साक्षी रही हैं?

Notebook : Chanakya(Kautilya) Niti Sutra

18 minute read

Published:

“Establish yourself in Self-Control, plan with Secrecy, act with Courage, and let Truth be your final destination.” — Ajeet Kumar

A Case Study of MacBook Air M4(16/256GB) for AI Model Production by Applied Mathematician

4 minute read

Published:

I was using Asus Notebook(i3/8GB/1TB-HHD) since 2021. After completion of M.Sc Mathematics and Computing degree at BHU Varanasi, went to the IIT Delhi(Cloud Computing and HIPC Lab SIT), New Delhi for the AI Research Internship. I am greatfull enough that i have worked onto the the two most interesting research problem

  1. LLM for OpenAPI Specification Generation from the given server source code.
  2. Lean4 Proof generation for the given theorem in lean4

Lean4agent

less than 1 minute read

Published:

How to become a mathematician ?

6 minute read

Published:

I don’t know from where to start to tell you about my story because i have’t become a mathematician until now, but on the track in the race of becoming a mathematician. So, whatever i will tell you that will be the my thoughts during learning and understanding in the journey of continuum hard work how i am actually transforming myself from a first class passed out master student that have a litle exposure to the research due to my masters thesis on topics of discrete differential geometry and its applications to become a researcher in mathematics after publishing papers.

MLOps for LLMs

30 minute read

Published:

Introduction to operations for Large Language Models(LLMs) also called as MLOps for LLMs.

Machine Learning Systems by

5 minute read

Published:

What does it mean to master machine learning systems—not just design models?

less than 1 minute read

Published:

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

portfolio

Vision Transformer(ViT) from Scratch - Solving Partial Differential Equations(PDE)

Mathematical Data Driven Methods for Modelling and Simulations of Science and Engineering Problems, mostly modeled as partial differential equation therefore how to solve them for performing simulation of the system. I have trained ViT model onto the Allen Cahn PDE to dataset and checked the model predicted solution for the unseen input dataset. results are close to exact solution.

Parallel and Distributed Computing

How to write and solve computation problem efficiently on different architectural devices having parallel and distributed computational frameworks

Disease Detection Web Application

The Disease Detection Web Application, developed in 2022, is a machine learning-powered platform designed to assist in the early detection of diseases.

publications

Paper Title Number 4

Published in GitHub Journal of Bugs, 2024

This paper is about fixing template issue #693.

Recommended citation: Your Name, You. (2024). "Paper Title Number 3." GitHub Journal of Bugs. 1(3).
Download Paper

The Axiomatic Genome of Number Systems

Published in Journal 1, 2025

The real number systems $\mathbb{R}$ is traditionally defined as the unique complete ordered field. However, this definition servers a pivotal midpoint in a broader numerical hierarchy. By examination of the 13 axioms of $\mathbb{R}$, we can trace how specialized number systems such as complex numbers, quarternions and and $p$-adic numbers $\mathbb{Q}_p$ emerge through deliberate axiomatic trade-offs. Our study details the transitions from discrete structures to continuous and higher-dimensional algebras, concluding with their critical applications in modern physics, robotics and cryptograph etc.

Recommended citation: Ajeet Kumar, You. (2025). "Paper Title Number 1." Journal 1. 1(1).
Download Paper | Download Slides | Download Bibtex

talks

teaching

Teaching experience 1

Undergraduate course, University 1, Department, 2014

This is a description of a teaching experience. You can use markdown like any other post.

Teaching experience 2

Workshop, University 1, Department, 2015

This is a description of a teaching experience. You can use markdown like any other post.