I am a Mathematics Graduate and Full-Stack Software Engineer specializing in Web Development, Backend Engineering, DSA, CP, OOP, and Software Engineering (SWE).

I design scalable, maintainable, secure, and optimized applications using mathematical reasoning, algorithmic problem-solving, object-oriented design, modern frameworks, and SWE best practices.

Core Expertise & Focus Areas:

• Mathematics & Logic: Discrete Mathematics, Linear Algebra, Probability, Statistics, Calculus, Mathematical Modelling, Algorithmic Reasoning.
• Full-Stack Development: React.js, Next.js, Redux, Node.js, Express.js, Django, Laravel, REST API, GraphQL, WebSockets, JWT Authentication, MVC Architecture, SPA, SSR, Microservices.
• Backend Engineering: API Design, CRUD, Authentication & Authorization, Middleware, Caching, ORM (Prisma, Eloquent), Database Optimization, Transactions, ACID Principles.
• Software Engineering (SWE): OOP, SOLID Principles, DRY, KISS, Design Patterns (Singleton, Factory, Observer, Strategy), TDD, BDD, Unit Testing, Integration Testing, CI/CD, Agile, Scrum, Modular Design, Clean Code.
• Databases & ORM: PostgreSQL, MySQL, MongoDB, Firebase, Redis, Query Optimization, Joins, Indexing, Normalization, Stored Procedures, Data Security, Data Integrity.
• Cloud & DevOps: AWS (EC2, S3, Lambda, IAM), Docker, Docker Compose, Nginx, Kubernetes Basics, CI/CD Pipelines, Load Balancing, Cloud Deployment, Server Scaling.
• Frontend Development: HTML5, CSS3, JavaScript, TypeScript, TailwindCSS, Bootstrap, Material UI, Responsive Design, Component-Based Architecture, State Management (Redux, Context API).
• Competitive Programming & DSA: Graphs, Trees, BFS/DFS, Shortest Path Algorithms (Dijkstra, Bellman-Ford, Floyd-Warshall), DSU, Dynamic Programming (Knapsack, LCS, LIS, LIC, DP on Trees, Segment Trees, Sparse Tables), Sliding Window, Two-Pointer, Backtracking, Recursion, Greedy, Modular Arithmetic, Bit Manipulation, PBDS, Hashing Techniques.
• Optimization & Mathematical Tricks: Binary Search & Variants, Binary Exponentiation, Prime Factorization, Sieve of Eratosthenes, Prefix Sum, Difference Array, 2D Prefix Sum, Bitset Operations, Lambda Functions, Monotonic Functions, Fermat’s Little Theorem, Goldbach Conjecture, Harmonic Series, Smallest Prime Factor, Closest Left/Right Searches, Lower Bound/Upper Bound.
• Testing & Quality Assurance: Unit Testing (Jest, Pytest, PHPUnit), Integration Testing, API Testing (Postman, Supertest), Continuous Testing, Code Coverage, Test-Driven Development (TDD).

C • C++ • Python • PHP • Laravel • JavaScript • TypeScript • Node.js • Express.js • SQL • PostgreSQL • MySQL • MongoDB • Firebase • HTML5 • CSS3 • TailwindCSS • Bootstrap • React.js • Next.js • Redux • Django • REST API • GraphQL • JWT • WebSockets • Docker • AWS • Nginx • Git • GitHub • CI/CD • Microservices • SPA • SSR • ORM • Modular Design • Clean Code

• Core Concepts: Class, Object, Encapsulation, Abstraction, Inheritance, Polymorphism.
• Advanced OOP: Interfaces, Abstract Classes, Composition, Method Overloading & Overriding, SOLID Principles, Design Patterns (Singleton, Factory, Observer, Strategy), Laravel Service Classes & MVC Architecture.
• Application: Scalable software, reusable modules, combining OOP with DSA & CP for optimized algorithms, enterprise-grade development.

Fundamental Structures: Arrays, Vector, Linked List, Stack, Queue, Map, Set, Multiset, Pair, Tuple, String, Deque.
Nested / Complex Structures: Vector of Vectors, Map of Vectors, Set of Sets, Multiset of Multisets, Nested Priority Queues.

Graph & Tree Algorithms: BFS, DFS, 2D Grid Traversal, Cycle Detection, Topological Sort, MST (Kruskal/Prim), Shortest Path Algorithms (Dijkstra, Bellman-Ford, Floyd-Warshall), DSU Operations (Union by Rank/Size, Path Compression).

Dynamic Programming (DP): Knapsack, LCS, LIS, LIC, DP on Trees, Segment Trees, Sparse Tables, Sliding Window, Backtracking, Recursion, Greedy Algorithms.

Number Theory & Math: Prime Factorization, Modular Arithmetic, GCD/LCM, Sieve of Eratosthenes, Fermat’s Little Theorem, Goldbach Conjecture, Harmonic Series, Smallest Prime Factor.

Optimization Techniques: Binary Search, Binary Search on Answer, Prefix Sum, Difference Array, 2D Prefix Sum, Bit Manipulation, Bit Masking, Bitset Operations, Lambda Functions, Monotonic Functions.

Advanced Techniques: PBDS, Single/Double Hashing, Substring Hashing, Complexity Analysis, Algorithm Optimization.

• Focus Areas: Ad-Hoc, Graphs, Trees, Recursion, Backtracking, Sliding Window, Two-Pointer, DP, Greedy, Sorting & Searching, Number Theory, Modular Arithmetic.
• CP Platforms & Ratings:
  • Codeforces: jahirul002201
  • CodeChef: jahirul002201
  • LeetCode: jahir002201
  • BeeCrowd: Profile
  • HackerRank: Profile

• Portfolio: my-portfolio-smoky-xi-63.vercel.app
• LinkedIn: Md Jahirul Islam
• GitHub: jahir002201

Mathematics sharpens logic.
DSA & CP build problem-solving efficiency.
OOP, SWE principles, Laravel MVC create scalable, maintainable software.
Full-Stack development bridges theory with real-world impact.
Optimization, algorithms, and modern frameworks enable high-performance solutions.
Continuous learning, teamwork, and problem-solving enable lifelong growth and success.