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MATH 101: Linear Algebra

Linear Algebra is the first real language of modern computation. Before algorithms scale, before intelligence emerges, before systems optimize: data must be represented, transformed, and reasoned about. That language is Linear Algebra.

This course trains students to think in high dimensions, reason geometrically, and manipulate abstractions that power applied domains like Machine Learning & AI, Computer Graphics & Vision, Optimization & Control, Parallel and High-Performance Systems, and Numerical Computing & Scientific Simulation.

Course Code MATH 101
Course Name Linear Algebra
Department Mathematics
Semester Offered Odd (usually Semester 1)
Tuition Hours 20 hours
Course Level Foundational
Pre-requisite MATH 005: Cartesian Geometry
Co-requisite MATH 102: Calculus
Course Objective To learn the language of high-dimensional thinking.

Students will develop a rigorous understanding of vectors, matrices, transformations, and spaces, as conceptual building blocks for modern AI systems and computational reasoning. By the end of the course, linear algebra should feel less like a subject and more like a mental model.
Course Philosophy This course emphasizes
  • Geometric intuition before algebraic manipulation
  • Understanding before optimization
  • Reasoning before memorization
Proofs are introduced not to train mathematicians, but to teach students how to think, present and argue precisely.
Course Learning Outcomes Upon successful completion of this course, students will be able to:
  • Solve systems of linear equations and analyze the nature of their solutions (unique, infinite, or none).
  • Perform accurate and efficient calculations with vectors, matrices, eigenvalues, and eigenvectors in arbitrary dimensions.
  • Demonstrate geometric understanding of vectors and vector operations in 2D and 3D space.
  • Understand orthogonality and projection and apply these ideas in higher-dimensional settings.
  • Argue formally about linear algebraic statements, using definitions, theorems, proofs, or structured examples to prepare students for abstract vector spaces and advanced mathematics.
Course Author Sagar Udasi
MSc Statistics and Data Science with Computational Finance from The University of Edinburgh.
Contact: sagar.l.udasi@gmail.com
Course Organiser Sagar Udasi
MSc Statistics and Data Science with Computational Finance from The University of Edinburgh.
Contact: sagar.l.udasi@gmail.com
No. Lecture Title Concepts Covered
01. Why Everything Is A List Of Numbers!?
02. Yet Another Way To Look At The System Of Equations
03. Matrices Don't Just Store Vectors. They Transform Space!
04. The Geometry Hidden In This Single Number
05. How To Measure "Meaning"
06. The Hidden Coordinate System Inside Every Matrix
07. When Matrices Aren't Square
08. The Polynomial That Every Matrix Obeys
09. When Vectors Stop Looking Like Arrows
10. When Linear Algebra Stops Being Enough!
Component Weightage
Written Examination (2 hours) 60%
Assignments (2 total) 40%

Notes:

  • Assignments will emphasize problem-solving, intuition-building, and formal reasoning. Unless you have understood the concepts, students shall face trouble solving the assignments. Assignments are designed in a way that AI won't be able to help much! (You're welcome. 🙂)
  • The written exam evaluates conceptual understanding, not rote computation.
Type Resource Provider
Lecture MIT 18.06 Linear Algebra (Spring 2005) Prof. Gilbert Strang
Lecture Essence of Linear Algebra Grant Sanderson (3Blue1Brown)
Reading Linear Algebra and Its Applications Prof. Gilbert Strang

Students are strongly encouraged to watch both in parallel: Gilbert Strang for structure, 3Blue1Brown for intuition.