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Module 2: Calculus & Linear Algebra

Calculus and Linear Algebra - Graphs and Vectors

Goal​

Understand the mathematical foundations behind how AI models learn from data and represent information.

This module explains the core mechanics of neural networks: how they adjust themselves (calculus) and how they store and transform data (linear algebra).

Estimated Time Impact

160-180 hours total

Calculus(100h)
Linear Algebra(60h)

1. Primary Resources​

course
beginner

Calculus 1 - Khan Academy

15-20 hours
course
beginner

Linear Algebra - Khan Academy

10-12 hours

Additional Resources​

video
beginner

Essence of Calculus - 3Blue1Brown

3-4 hours
video
beginner

Essence of Linear Algebra - 3Blue1Brown

6-8 hours

Why it matters:

At its core, AI learning is optimization.

  • Calculus explains how models improve:
    • Learning is the process of adjusting parameters to reduce error, guided by derivatives and gradients.
  • Linear algebra explains what models operate on:
    • Images, text, and sound are all represented as vectors and transformed through matrix operations.

Together, these two fields form the mathematical engine of neural networks. Without them, AI training becomes a black box rather than an understandable process.

This module connects abstract math to concrete AI behavior.

What to expect:

By the end of this module, learners will:

  • Understand derivatives as measures of change and direction
  • Interpret gradients as signals telling a model how to improve
  • See learning as moving "downhill" on an error surface
  • Understand vectors as representations of data
  • Interpret matrix multiplication as transformation and combination of features
  • Build intuition for dot products as a measure of similarity

After completing this module, learners will understand how and why AI models learn, not just that they do.

Completion Checklist​

  • Completed core units in Calculus 1 - Khan Academy (limits & continuity, derivatives, applications of derivatives), with a final exam score ≥ 80%.
  • Completed core units in Linear Algebra - Khan Academy (vectors, matrices, matrix multiplication, linear transformations), with a final exam score ≥ 80%.