DEV Community: Mehfila A Parkkulthil

SageMath

Mehfila A Parkkulthil — Thu, 05 Mar 2026 23:12:16 +0000

What is SageMath?

SageMath is a free, open-source mathematics software system built on top of Python. Rather than building everything from scratch, it integrates dozens of well-established mathematical libraries — NumPy, SciPy, PARI/GP, Maxima, R, and many more — under one unified Python-based interface. The goal, as its creator William Stein put it, was to create a "viable free open source alternative to Magma, Maple, Mathematica, and MATLAB."

It means you can do symbolic algebra, number theory, algebraic geometry, combinatorics, graph theory, linear programming, and numerical computation all from the same environment.

Implementing Best Responses in Python

Mehfila A Parkkulthil — Thu, 05 Mar 2026 23:09:21 +0000

The concept of a best response is one of the most fundamental ideas in game theory.
Given what your opponent is doing, what's the best you can do? That's your best response.
If both players are playing best responses to each other simultaneously, then its a Nash equilibrium.

What Is a Best Response?

In a two-player game with a payoff matrix,finding player 1's best response to a specific pure strategy of player 2.

import numpy as np

# Payoff matrix for Player 1
# Rows = Player 1's strategies, Columns = Player 2's strategies
payoff_matrix = np.array([
    [3, 0],
    [0, 3],
    [1, 1]
])

def best_response_to_pure(payoff_matrix, opponent_strategy_index):
    """Returns the best response to a pure strategy of the opponent."""
    payoffs = payoff_matrix[:, opponent_strategy_index]
    return np.argmax(payoffs)

print(best_response_to_pure(payoff_matrix, 0))  # Best response when opponent plays strategy 0
print(best_response_to_pure(payoff_matrix, 1))  # Best response when opponent plays strategy 1

Best responses to Mixed Strategies

When your opponent plays a mixed strategy — let's say they play strategy 0 with probability p and strategy 1 with probability (1-p) your expected payoff for each of your strategies is a weighted average. You pick whichever gives you the highest expected value.

def best_response_to_mixed(payoff_matrix, opponent_mixed_strategy):
    """
    opponent_mixed_strategy: list of probabilities over opponent's strategies.
    Returns the index of the best responding pure strategy.
    """
    expected_payoffs = payoff_matrix @ np.array(opponent_mixed_strategy)
    return np.argmax(expected_payoffs)

# Opponent plays [0.5, 0.5]
br = best_response_to_mixed(payoff_matrix, [0.5, 0.5])
print(f"Best response: strategy {br}")

Using Gambit's Best Response Tools

Gambit's pygambit library can compute best responses directly on a Game object. Once you define your game and a mixed strategy profile, you can ask which pure strategies are in the support of the best response:
python import pygambit as gbt

g = gbt.Game.new_table([2, 2])
# ... (set up payoffs as before)

profile = g.mixed_strategy_profile()
# Set opponent's probabilities
profile[g.players[1].strategies[0]] = 0.4
profile[g.players[1].strategies[1]] = 0.6

# Get payoffs under this profile for each strategy of player 0
for s in g.players[0].strategies:
    payoff = profile.payoff(g.players[0])
    print(s.label, profile[s])

Once you understand best responses, Nash equilibrium stops feeling like a definition and starts feeling inevitable.

What is Game Theory?

Mehfila A Parkkulthil — Fri, 27 Feb 2026 22:35:46 +0000

What is Game Theory?

Game Theory is the formal study of strategic interaction.
In game theory, “strategic form” (or “normal form”) and “extensive form” are ways of representing games. In a strategic setting the actions of several agents are independent. Each agent's outcome depends not only on his actions , but also the actions of his opponents.
So the goal is to "How to predict opponents play and respond optimally."

Key elements of a Game:

Players
Strategies : Strategies are a complete plan or the options of each player or in what order do players act.
Payoffs : Payoffs are how strategies translate into outcomes and what are players preferences over possible outcomes.

Normal Form Games

A normal (or strategic) form game is a triplet (N,S,u).
where,

N ={1,2,...,n}: finite set of players
Si: set of pure strategies of player i S =S1×···×Sn ;s =(s1,...,sn): set of pure strategy profiles
ui : S →R: payoff function of player i; u = (u1,...,un). Outcomes are interdependent.

Eg: Prisoner's Dilemma
Imagine two persons are arrested for a crime.There is not enough evidence to convict either.Differnt rooms, no communication.
After being caught by the police for committing a crime, the two prisoners are separately offered a deal:

If both stay silent (cooperate), they get light sentences.

If one defects (betrays the other) while the other stays silent, the defector goes free and the silent one gets a heavy sentence.

If both defect, they both get moderate sentences.
eg: To qualify as a Prisoner’s Dilemma, the payoffs must satisfy:
Temptation > Reward > Punishment > Sucker
T (Temptation to defect) = 3 → you defect while the other cooperates
R (Reward for mutual cooperation) = 2
P (Punishment for mutual defection) = 1
S (Sucker’s payoff) = 0 → you cooperate while the other defects
Higher numbers = better outcome.

where, c=cooperation and d=defect

Extensive form games

Represents a game as a tree showing the order of moves.Useful for sequential games, where players move one after another.Captures timing, information sets, and chance events.

N: finite set of players; nature is player 0 ∈ N
tree: order of moves
payoffs for every player at the terminal nodes
actions available at every information set
description of how actions lead to progress in the tree

Day 1 : Introduction of DSA

Mehfila A Parkkulthil — Wed, 28 Jan 2026 10:01:53 +0000

Hey everyone!
I'm excited to announce that I'm starting a blog series focused on Data Structures and Algorithms (DSA). I'll be sharing tutorials based on what I've learned and know.
I'll be using the C++ language for these tutorials, and I'll also be posting C++ language tutorials for those who are new to it.

While DSA can be solved either using C++ , Java or Python.

Here I am using C++ .

So guys this is just an introduction , you don't need to worry if you don't understand I will be covering these topics on upcoming blogpost.
This is just to make sure that these are the topics we are gonna cover.
If you are new to C++ I would suggest first its must to know C++ if you are known with java , thats fine.
Yes, my blogs are structured to help you learn both C++ and DSA simultaneously..

Primitive Data Structure

Primitive data structures are the most basic forms of data representation in programming languages.
Here are the common primitive data structures:

Integer (int)
Represents whole numbers without any fractional part.
Examples: -1, 0, 4
Floating-Point (float, double)
Represents real numbers with fractional parts, using a fixed number of decimal places.
Examples: 3.14, -0.001, 2.71828
Character (char)
Represents a single character from a character set, typically written in quoted commas.
Examples: 'a', 'Z', '9', '#'
Boolean (bool)
Represents a binary value that can be either true or false.
Examples: true, false
Used in conditional statements, loops, and to represent binary states.
Strings (string)
Represents a sequence of characters, typically used to store text and written in quotation.
Examples: "Hello, World!", "Python", "12345"

#include <iostream>
using namespace std;
int main() {

    // Integer
    int age = 25;
    cout << "Age: " << age << endl;

    // Floating-Point
    float pi = 3.14;
    cout << "Pi: " << pi << endl;

    // Character
    char grade = 'v';
    cout << "Grade: " << grade << endl;

    // Boolean
    bool isgirl = true;
    cout << "Is Girl: " << isgirl << endl;

    // String
    string name = "Aiera";
    cout << "Name: " << name << endl;

    return 0;
}

Non - Primitive Data Structures

Non-primitive data structures, also known as composite or user-defined data structures, are more complex than primitive data structures.

They are built using primitive data structures and can store a collection of values, allowing for efficient data management and manipulation.

Arrays: A collection of elements, typically of the same type, stored in contiguous memory locations.
Linked Lists: A sequence of elements, where each element points to the next one, allowing for dynamic memory allocation.
Stacks: A linear data structure that follows the Last In, First Out (LIFO)
Example:Think of it like a stack of plates: you add and remove plates from the top.
Queues: A linear data structure that follows the First In, First Out (FIFO) principle.
Example:Imagine a line of people waiting for a bus: the first person in line is the first one to get on the bus.
Trees: A hierarchical data structure with a root element and child elements, used to represent hierarchical relationships. Common types include binary trees and binary search trees.
Graphs: A collection of nodes (vertices) connected by edges, used to represent networks, such as social networks or computer networks.
Tables: A data structure that stores key-value pairs, using a hash function to compute an index into an array of buckets or slots.

You need to learn DSA , to earn.

Mehfila A Parkkulthil — Wed, 28 Jan 2026 09:59:31 +0000

Learning Data Structures and Algorithms (DSA) is a fundamental step towards becoming a Excellent programmer.

To get started You can follow my schedule.

Understand the Basics

Introduction to Data Structures:

Arrays
Linked Lists
Stacks
Queues
Trees
Graphs
Hash Tables

Introduction to Algorithms:

Sorting Algorithms (e.g., Bubble Sort, Quick Sort, Merge Sort)
Searching Algorithms (e.g., Linear Search, Binary Search)
Recursion
Dynamic Programming

Choosing the Right Resources

Books:

"Introduction to Algorithms" by Cormen, Leiserson, Rivest, and Stein (CLRS)
"Data Structures and Algorithms Made Easy" by Narasimha Karumanchi
"The Algorithm Design Manual" by Steven S. Skiena

Online Courses:

Coursera: Data Structures and Algorithm Specialization by UC San Diego & National Research University Higher School of Economics
edX: Algorithms and Data Structures MicroMasters by University of California, San Diego
Udacity: Data Structures and Algorithms Nanodegree
YouTube Channels: MIT OpenCourseWare, MyCodeSchool, GeeksforGeeks

Interactive Platforms:

LeetCode
HackerRank
CodeSignal
GeeksforGeeks
Stack Overflow
Reddit’s
r/learnprogramming

Practice Regularly

Solve a variety of problems on platforms like LeetCode, HackerRank, and Codeforces.
Start with easy problems and gradually move to medium and hard problems.

Competitions:

Participate in coding competitions and challenges to improve your problem-solving skills.

Build Projects

Real-World Applications:

Apply what you’ve learned by building projects that solve real-world problems.

Review

Revisit Concepts:

Google Summer of Code (Gsoc)

Mehfila A Parkkulthil — Wed, 28 Jan 2026 09:55:27 +0000

Google Summer of Code (GSoC) is a program that brings new contributors into open source software development.

What is GSoC?
GSoC is a global, online program where students and beginners in open source software development work on a 12+ week programming project under the guidance of mentors from open source organizations.

Eligibility
Age: Must be at least 18 years old at the time of registration.

Residency: Must be a resident of a country not embargoed by the United States.

Application Process
Research: Identify open source organizations that interest you.

Reach Out: Contact the organizations to discuss project ideas and learn more about their community.

Register: Register on the GSoC website and submit a proposal to the organizations you're interested in.

Selection: Organizations select contributors based on their proposals.

Bonding Period: Selected contributors spend a few weeks bonding with the community and learning the codebase.

Coding Period: Work on your project for 12+ weeks, meeting milestones and receiving evaluations from mentors.

Stipend: Receive a stipend for each passed evaluation.

Benefits

Real-World Experience
Mentorship
Networking.
Earn a stipend for your contributions.

How to Apply
Visit the GSoC website for more details on eligibility, application deadlines, and tips for writing a strong proposal.
GSoC is a great opportunity to dive into open source development and build valuable skills.

Are you considering applying for GSoC this year?

AI - Threat or tool?

Mehfila A Parkkulthil — Wed, 28 Jan 2026 09:51:32 +0000

Ethical Challenges of AI in Decision-Making

AI systems are increasingly involved in decision-making processes such as hiring, credit approval, medical diagnosis, and law enforcement. While these systems promise efficiency and objectivity, they raise serious ethical concerns. One major challenge is bias. AI learns from historical data, which often reflects existing social inequalities, leading to discriminatory outcomes.

Another concern is accountability. When an AI system makes a wrong decision, it is unclear who should be held responsible—the developer, the organization, or the algorithm itself. Additionally, many AI systems operate as “black boxes,” making it difficult to understand how decisions are made, which reduces transparency and trust.

To address these challenges, ethical frameworks must be integrated into AI development. Human oversight, explainable AI, and diverse training data are essential. Ethical decision-making in AI is not optional; it is necessary to protect human rights and maintain public confidence in technology.

Can AI Replace Human Creativity?

Creativity has long been considered a uniquely human trait. With AI now generating art, music, poetry, and even films, this belief is being questioned. AI systems can analyze vast datasets and produce creative outputs that mimic human styles, often with impressive results.

However, AI creativity is fundamentally different from human creativity. AI does not experience emotions, consciousness, or lived experiences. It creates based on patterns and probabilities, not intention or meaning. Human creativity is driven by emotions, cultural context, and personal expression—qualities AI lacks.

Rather than replacing human creativity, AI is better seen as a collaborative tool. Artists and creators can use AI to enhance productivity, explore new ideas, and push creative boundaries. The future of creativity lies not in competition between humans and machines, but in meaningful collaboration.

Bias in AI: Are Algorithms Truly Neutral?

Algorithms are often perceived as neutral and objective, but in reality, they reflect human biases embedded in data and design choices. AI systems learn from historical data, which may contain prejudices related to race, gender, or socio-economic status. As a result, biased data leads to biased outcomes.

Examples include facial recognition systems performing poorly on certain ethnic groups and hiring algorithms favoring specific demographics. Such biases can reinforce inequality and discrimination at scale, making them more harmful than individual human bias.

Ensuring fairness in AI requires diverse datasets, inclusive development teams, and continuous auditing of algorithms. Algorithms are tools created by humans, and neutrality can only be achieved through conscious ethical effort.

AI in Education: Personalized Learning or Over-Dependence?

AI-powered tools are revolutionizing education through personalized learning, adaptive assessments, and intelligent tutoring systems. These technologies help address individual learning needs and improve accessibility.

However, over-dependence on AI may reduce human interaction and critical thinking. Excessive automation risks turning education into a mechanical process, neglecting emotional and social development.
A balanced approach that combines human guidance with AI assistance can create a more effective and inclusive education system.

AI - Threat or a Tool ?

Mehfila A Parkkulthil — Wed, 28 Jan 2026 09:47:54 +0000

Artificial Intelligence (AI) is one of the most transformative technologies of the 21st century. Whether it is a threat or a tool depends largely on how we design, regulate, and use it. As a tool, AI has already improved efficiency in healthcare, education, transportation, and scientific research. From early disease detection to smart traffic systems, AI enhances human capability rather than replacing it.

However, concerns arise when AI systems are deployed without ethical oversight. Job displacement, mass surveillance, biased algorithms, and autonomous weapons fuel fears that AI could harm society. The threat does not come from AI itself, but from our irresponsible use. History shows that technology amplifies human intent—good or bad.

Therefore, AI should be viewed primarily as a powerful tool. Strong governance, transparency, and human-centered design are essential to ensure that AI serves humanity’s interests. When aligned with ethical values, AI has the potential to solve global problems rather than create new ones.

Valuable ✨

Mehfila A Parkkulthil — Wed, 17 Dec 2025 17:13:21 +0000

Your Site Works in Chrome. Congrats, You've Alienated 15% of Users

Polliog ・ Dec 15

#webdev #programming #javascript #discuss

You Are Not “Less Smart” Because You Use AI or Google -An unworthy software engineer

Mehfila A Parkkulthil — Wed, 10 Dec 2025 19:56:28 +0000

You Are Not “Less Smart” Because You Use AI or Google

People in the 1970s–1990s didn’t have Google or ChatGPT, but they also had far fewer things to learn.

Back then:

Computers were simple
One language (C or assembly)
No massive frameworks
No internet
No cloud, no Git, no VS Code
No huge libraries, no documentation overload
Their world was smaller → so their brains could focus on fewer concepts.

Today:

You’re expected to learn:

C, C++, JavaScript
DSA
MERN stack
Git & GitHub
Linux
Databases
APIs
Debuggers
Deployment
Cloud
DevOps basics

Nobody can learn all that without help.
Using tools is not weakness — it’s the new normal.

Using AI ≠ Cheating

A carpenter isn’t “cheating” because they use an electric drill instead of a stone hammer.
A doctor isn’t “cheating” because they use advanced medical tools.
A pilot isn’t “cheating” because the plane has autopilot.

Tools exist so you can build faster, not feel guilty.
Your brain is still the one:

understanding the problem
deciding what to build
debugging errors
learning patterns
writing logic AI only speeds up the parts that used to waste time.

Logic is not learned by avoiding tools — it’s learned by solving

You want to develop the logic like old programmers?
You absolutely can — and you already are.
Every time you struggle with:debugging and compiling.
AI didn’t magically solve these problems for you —
you solved them step by step with guidance.

That is logic.
That is learning.
That is engineering.

The older generation used each other — that was their “Google”

Before the internet, people:

asked senior engineers
read thick manuals
asked in user groups
went to meetups
read books experimented for hours, sometimes days

Feeling “not worthy” is extremely common

Every software engineer I know — including me — has gone through this phase:

“I don't understand enough”
“Everyone knows more than me”
“I'm slow”
“I rely on tutorials/Google/AI too much”

This feeling is called Imposter Syndrome, and it hits beginners the hardest.

But here's the truth:

If you were not smart enough,
you wouldn’t even be asking this question.

People who don't care never doubt themselves.
The fact that you are worried about becoming better means you're already ahead.

You are absolutely worthy of being a software engineer

Look at what you did today !!

Didn't give up

These are the actions of someone who will definitely succeed.
If you were not capable, you would have quit long ago.
But you’re still here — struggling, learning, improving.
That’s what real engineers do.

You're not behind. You're not weak. You're not cheating.
You’re learning the way modern developers learn.
You’re adapting to the era you were born in —
and that’s exactly what every great engineer does.

How Gambit Represents Games

Mehfila A Parkkulthil — Tue, 02 Dec 2025 12:09:26 +0000

The challenge isn't playing the game — it's representing it in a way a computer can reason about.That's exactly what Gambit does.
Gambit is an open-source software toolkit for computing and analyzing game-theoretic models.
At its core, it gives you two main ways to describe a strategic situation: the normal form (also called the strategic form) and the extensive form. Each has its use, and understanding when to use which one is half the battle.

Normal Form Games

A normal form game flattens everything into a matrix. You have players, each player has a set of strategies, and the outcome is a payoff for every combination of choices. That's it.

Think of two coffee shops deciding whether to run a discount this week. Shop A can either run a promotion or hold prices. Shop B faces the same choice. The resulting 2x2 matrix captures what each shop earns depending on what the other does. In Gambit, you'd represent this as a Game object with two players, two strategies each, and four payoff entries.

import pygambit as gbt

g = gbt.Game.new_table([2, 2])
g.title = "Coffee Shop Pricing"
g.players[0].label = "Shop A"
g.players[1].label = "Shop B"

g.players[0].strategies[0].label = "Discount"
g.players[0].strategies[1].label = "Hold"
g.players[1].strategies[0].label = "Discount"
g.players[1].strategies[1].label = "Hold"

# Payoffs: (Shop A, Shop B)
g[0, 0][0], g[0, 0][1] = 3, 3   # Both discount
g[0, 1][0], g[0, 1][1] = 5, 1   # A discounts, B holds
g[1, 0][0], g[1, 0][1] = 1, 5   # A holds, B discounts
g[1, 1][0], g[1, 1][1] = 4, 4   # Both hold

Git - Github Quick Revision

Mehfila A Parkkulthil — Tue, 02 Dec 2025 12:04:43 +0000

GitHub Fundamentals

What is Git?

Git is a version control system used to track changes in your files. It allows undo, restore, and manage multiple versions ,helps multiple people work on the same project without conflict .

What is GitHub?

GitHub is a cloud platform where you can store your Git repositories online.

Git = tool on your computer
GitHub = website to store/share projects

How to install Git

Open terminal/cmd:

git --version

If not installed → download from official site.

Git Workflow Basics

Working directory → Staging → Repository

Working Directory are your actual files.

Staging — files marked to be saved.

Repository — final saved version in .git

Git Commands

Initialize Git

git init

Tell Git who you are

git config --global user.name "Your Name"
git config --global user.email "your@email.com"

Check status

git status

Add file(s) to staging

git add filename

or
add everything(all files) at a time :

git add .

Commit (save) changes

git commit -m "Write a meaningful message"

Branching

Create a branch:

git branch feature1

To Switch to branch:

git checkout feature1

Create + switch together:

git checkout -b feature1

Merge branch:

git checkout main
git merge feature1

Connecting Git to GitHub

Step 1: Create a new repository on GitHub

Do NOT initialize with README (optional but recommended)

Step 2: Connect local repo to GitHub

git remote add origin https://github.com/yourusername/repoName.git

Step 3: Push code to GitHub

git push -u origin main

After first time:

git push

Pulling and Cloning

Clone someone else’s repo:

git clone https://github.com/user/repo.git

Pull (download new changes):

git pull

GitHub Collaboration Basics

Fork → Your own copy of someone’s repo
Pull Request (PR) → Request to merge your changes
Issues → Report bugs or improvements
Actions → Automate tests/deployments