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Available courses

B.Sc First year

Welcome!

Title: Hey everyone! 👋
Subtitle: Welcome to Topics in Algebra!
Text: I’m your instructor, and I’m thrilled to embark on this mathematical journey with you.

Course Overview

Title: Course Overview

  • Dive into fundamental yet powerful algebra concepts

  • Not just solving for x — we’ll uncover structures and relationships

  • Builds a strong foundation for mathematics, computer science, and beyond

 What We’ll Cover

Title: What We’ll Cover
Our course is divided into four key modules:
1️⃣ Sets, Functions, and Relations
2️⃣ Functions: The Heart of Relationships
3️⃣ Elementary Operations & Rank of a Matrix
4️⃣ System of Linear Equations & Cayley-Hamilton Theorem

Module I: Sets, Functions, and Relations 🔢

Title: Module I (08 Lectures)

  • Sets: Definitions, operations, Cartesian Product

  • Relations: Types of relations, focus on Equivalence Relations

  • Why it matters: These are the building blocks of modern mathematics

Module II: Functions ❤️

Title: Module II (07 Lectures)

  • One-one, onto, bijections: Understanding mappings

  • Composition & Inverse of functions

  • Equivalence Classes & Partitions: How they connect to sets and relations

Module III: Matrices 📊

Title: Module III (07 Lectures)

  • Elementary Operations & Equivalent Matrices

  • Row Rank & Column Rank: Understanding dimensions

  • Echelon Form & Row Reduced Echelon Form: For solving systems of equations

Module IV: Linear Equations & Cayley-Hamilton 💡

Title: Module IV (08 Lectures)

  • System of Linear Equations: Homogeneous & Non-Homogeneous

  • Characteristic Values & Vectors (Eigenvalues & Eigenvectors)

  • Cayley-Hamilton Theorem: How a matrix relates to its characteristic polynomial

Why Study Algebra? 🤔

Title: Why Study Algebra?

  • The language of problem-solving

  • Applications: Computer graphics, cryptography, data analysis, algorithms

  • Develops logical thinking and real-world problem-solving skills

Getting Started

Title: Getting Started

  • No advanced algebra needed — high school math is enough

  • Be ready to think critically and engage with abstract ideas

  • Practice, practice, practice! 📝

  • Work through examples and exercises regularly

Looking Forward

Title: Let’s Unlock the Power of Algebra Together!

  • I’m excited for a great semester with you all

  • Let’s dive in and discover the beauty of algebra

  • See you in the first lecture! 🚀