Darshan P.

Darshan P.

"If something is intriguing and complex, it must hold a certain beauty."

Research Work

At this point, I don't believe I have produced anything that could significantly impact the world. However, I am continuously working on various projects and research areas that I am passionate about.

From the Summation of the Quotient Function to the Partition of Integers

Paper introduces a recursive formula for the partition of integers and validates the results against Eulers Identity of Integer Partition.

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An Alternative Proof of the Fundamental Theorem of Algebra

This note presents an alternative proof of the fundamental theorem of algebra. Specifically, we demonstrate that the degree of an irreducible polynomial.

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Impact of Mixed Traffic on the Capacity of Two-Lane Roads: A Case Study of Indian Highways

This study investigates the effects of mixed traffic on two-lane road capacity, highlighting the role of slower vehicles and introducing the concept of dynamic passenger car units.

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Design Papers

Creativity is the way I share my soul with the world. Here are some of the design papers that reflect my passion for visual storytelling and innovation.

Blockchain and Urban Governance

Blockchain technology is increasingly shaping urban governance, enabling local governments to enhance transparency, accountability, and efficiency. By leveraging decentralized systems, cities can address key challenges in infrastructure, resource management, and citizen engagement, leading to more innovative and responsive governance models.

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A Deep Dive into Secure Shell

This deep dive explores how SSH works under the hood, from key exchange to encrypted communication, and explains the different layers and mechanisms that ensure secure data transmission.

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Sustainable Design: Balancing Aesthetics and Environmental Impact

This paper discusses how sustainable design practices can be integrated into the creative process without compromising on aesthetic quality, focusing on eco-friendly materials and production techniques.

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Blog

My reflections span finance, mathematics, technology, law, philosophy, and beyond—threads of a curious mind.

The 2008 Financial Crisis: A Decade of Consequences and Lessons for the Future

An in-depth analysis of the 2008 financial crisis, its long-lasting impact on the global economy, and the critical lessons we must remember for the future.

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C: The Language that Changed the World

A comprehensive overview of the C programming language, its history, impact, and the critical role it has played in software development across generations.

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Fly Too Close to the Sun

Exploring the myth of Icarus, its implications for ambition and risk-taking, and how the story resonates in modern contexts of human aspiration.

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Areas of Interest

Combining diverse fields of knowledge could become the key to solving bigger problems.

Computer Science

Computers are amazing machines. Exploring different programming languages is something that never gets old. Depending on the project, I've worked with Assembly (x86), Bash, C, C++, Fortran, Golang, Haskell, Java, Python, R, SQL, TypeScript, and more.

Economics & Finance

Economics is about understanding how small changes can have big impacts. The 2008 crisis sparked an interest in how economic policies and human behavior interact. I see this as an opportunity to blend math, programming, and an understanding of human nature.

Mathematics

I enjoy teaching Linear Algebra in an intuitive way. Playing with Calculus and Geometrical Analysis for things like Celestial Objects is something I do for fun. Number Theory can be addictive, and I like to challenge myself by solving problems on Project Euler.

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My Bookshelf

My collection spans nearly every area of interest you could imagine. I began with books on mathematics, but over time, I realized the power of blending diverse knowledge. Today, my bookshelf holds 70+ folders and over 550+ books and research papers each contributing to an ever evolving web of understanding.

Contact

Feel free to reach out for collaborations, queries, or just to say hello.

Have an idea or a project in mind? Drop me a message, and I'll get back to you!