00 / OPENING NOTE

start with the work, then follow the notes

A portfolio built like working notes.

Hi, I'm Mohammed, a recent A-Level graduate from Al Ain taking a deliberate gap year before studying mathematics. I build web and data projects, tutor mathematics, and use code to explore ideas.

This notebook brings together selected work, practical experience, and one interactive mathematical experiment.

Based inAl Ain, UAEA-LevelsMaths · Further Maths · CS2026 to 2027Focused gap year

Download CV ↓

01

INDEX / CONTENTS

What's inside?

Portfolio evidence comes first. The mathematics experiment follows after the projects, experience, and profile.

interactive selected work personal note

use the folded corners, ← → keys, or swipe

02

03 / PROFILE

Mohammed Yousif
Al Ain, UAE

A deliberate year before university.

I'm Mohammed, a recent A-Level graduate based in Al Ain.

I completed Mathematics, Further Mathematics, and Computer Science in 2026. I chose a gap year from a position of momentum. The goal is to enter university with stronger mathematical maturity, more independent work, and clearer evidence of how I think, build, and explain.

FoundationMathematics · Further Mathematics · Computer ScienceThis yearProof · computational notebooks · tutoring · projectsNext stepUniversity-level mathematics

break it down · test it · explain it

07

THE GAP YEAR PLAN

Make the year count.

This is an active year with specific academic and practical outcomes.

1

Deepen the mathematics

Develop stronger foundations in proof, analysis, and problem-solving.

2

Publish independent work

Turn mathematical questions into reproducible notebooks and clear explanations.

3

Teach and build

Keep tutoring while completing selected web and data projects.

pure
math

computation

teaching

me

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04 / MATH LAB

Stirling, but touchable.

Adjust n to see how Stirling's approximation improves as factorials grow.

Experiment 01

When does Stirling get convincing?

Move n and watch a famously compact approximation close in on the exact factorial.

n! ≈ √(2πn) · (n/e)ⁿ

Choose nn = 24

Focus the slider and use the arrow keys for one-step changes.

Exact n!6.20448 × 10^23

Stirling estimate6.18298 × 10^23

Relative error0.347%

Error falls as n growslogarithmic vertical scale

At n = 24, the compact formula recovers 99.653% of n!. Values are compared in log-space, so the experiment remains stable even near 170!, the edge of ordinary JavaScript numbers.

Read the Python notebook 09

OBSERVATION LOG

What the experiment shows.

01

The error shrinks

Even the leading approximation improves steadily as n increases.

02

Log space matters

Factorials grow too quickly for ordinary arithmetic; logarithms keep the comparison stable.

why it belongs here

The calculation is reproducible.
The graph makes the error visible.
The code supports the mathematics.

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01 / SELECTED WORK

Projects across maths, data, and web.

Open a card for the question, process, and result.

03

MORE WORK

Applied tools and experiments.

matheducationdatasystems

04

02 / EXPERIENCE

Experience & practical work.

2025 to present

Co-founder & Web Developer

Sharp Studios · Remote

Build and maintain responsive websites, from early requirements through deployment.

ongoing

Mathematics Tutor

Independent · Al Ain

Teach school and A-Level mathematics through structured steps, verification, and clear explanation.

Jan 2025 to Feb 2026

Data & Reporting Intern

QRS Engineering · Al Ain

Supported reporting by cleaning spreadsheet data, consolidating trackers, and improving repeatable workflows.

Sep 2024 to Jan 2025

Technical Intern

INTEGRES · Al Ain

Assisted with software tasks, technical documentation, and project coordination.

05

FOUNDATIONS

Education & working tools.

2026Al Ain English Speaking School

A-Levels completed

Mathematics
Further Mathematics
Computer Science

Next direction: university-level mathematics and deeper computational work.

Mathematics & data

Numerical methods · mathematical logic · Python · Pandas · Matplotlib · Excel

Web engineering

TypeScript · JavaScript · React · Node.js · HTML · CSS

Delivery

Responsive design · Git · deployment · hosting · technical documentation

helloEnglish · Arabic

06

05 / NOW

A gap year with a plan.

updated · August 2026

01
Mathematical maturity
Moving beyond exam technique into proof, analysis, and deeper problem-solving.
02
A visible body of work
Publishing mathematical experiments, clear plots, and explanations that can be checked.
03
Responsibility and experience
Tutoring consistently and continuing selected web and data work through Sharp Studios.

the notebook is never really finished

11

CONTACT

Want to get in touch?

For projects, tutoring, opportunities, collaboration, or simply to say hello, feel free to email me.

Send an email

GitHub@krezio ↗LinkedInMohammed Yousif ↗Studiosharpstudios.dev ↗Curriculum vitaePDF ↓

Mohammed YousifAl Ain · UAE

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