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Math for AI & ML

The math behind every ML algorithm, built in code rather than on paper

5 phases. 22 lessons. 22 labs. 1 capstone. The mathematical foundations of AI and ML — linear algebra, calculus, probability, optimization, and advanced math — every concept implemented in NumPy and PyTorch, not just written on paper. You build a personal math library with tested, visualized modules for every concept, and graduate understanding exactly what happens inside every ML algorithm you'll ever use.

5 phases · 22 lessons · 22 labs · 1 capstone

Take Quantitative Foundations first — this course builds on it.

Outcomes you will have by the end

• A personal math library — A complete, tested, documented Python package with modules for linear algebra, calculus, probability, optimization, and advanced math — every function implemented from scratch and verified against production libraries.
• A working mental model of what happens inside every ML algorithm — When you use PyTorch, scikit-learn, or any ML library, you'll know exactly what the math is doing underneath — because you built it yourself. No more black boxes.
• An autodiff engine you built from scratch — The mini autodiff engine from Phase 2 is the same mechanism PyTorch uses for backpropagation — understanding it at this level makes every neural network you build later transparent.
• Verified certificate of completion — Issued by DeVenture Academy, tied to your completion record. Lists the linear algebra, calculus, probability, and optimization skills you built.

What you will be able to do

Linear Algebra Implementation · Calculus & Automatic Differentiation · Probability & Statistics · Optimization Algorithms · Information Theory · Dimensionality Reduction · Numerical Stability

Every phase, every lesson, every project

• Linear Algebra — Vectors, Matrices & Spaces (6 lessons) — free — Vectors and vector spaces, matrices and matrix operations, matrix transformations and eigenvalues, norms and distances, singular value decomposition, tensor operations
  • Linear Algebra Intuition
  • Vectors, Matrices & Operations
  • Matrix Transformations
  • Singular Value Decomposition
  • Norms and Distances
  • Linear Systems
• Calculus & Optimization (5 lessons) — free — Derivatives and gradients, chain rule and automatic differentiation, gradient descent family (batch, stochastic, mini-batch, momentum), convex optimization, numerical stability
  • Calculus for Machine Learning
  • Chain Rule & Automatic Differentiation
  • Optimization
  • Numerical Stability
  • Convex Optimization
• Probability & Statistics (4 lessons) — Probability distributions, Bayes' theorem and statistical thinking, sampling methods, statistics for ML (mean, variance, covariance, correlation)
  • Probability and Distributions
  • Bayes' Theorem
  • Statistics for Machine Learning
  • Sampling Methods
• Advanced Math — Information, Dimensions & Signals (4 lessons) — Information theory (entropy, KL divergence, cross-entropy), dimensionality reduction (PCA, t-SNE, UMAP), Fourier transform for signal processing, graph theory for ML
  • Information Theory
  • Dimensionality Reduction
  • Complex Numbers for AI
  • The Fourier Transform
  • Graph Theory for Machine Learning
• Math to Code — Implementation Capstone (3 lessons) — Implementing math in NumPy and PyTorch, linear systems and matrix factorization, complex numbers for signal processing, stochastic processes
  • Tensor Operations
  • Stochastic Processes

The technologies you will use

NumPy · PyTorch · Matplotlib · SymPy · scikit-learn

Roles this course prepares you for

• ML Research Engineer ($140k–$220k) — Implement and extend ML algorithms from research papers, requiring deep mathematical understanding of linear algebra, calculus, and probability to translate theory into working code.
• Quantitative Developer ($130k–$250k) — Build mathematical models for finance, trading, and risk systems — where probability, statistics, and optimization are the core toolkit, not optional background.
• AI Systems Engineer ($120k–$200k) — Build the infrastructure that ML runs on — understanding the math behind tensor operations, automatic differentiation, and GPU computation to optimize at the lowest level.

What math for AI actually is

It's not abstract math — it's the specific subset of mathematics that ML and AI are built on: linear algebra (how data is represented), calculus (how models learn), probability (how models make decisions), and optimization (how models improve). Every ML algorithm is a mathematical formula translated into code. This course teaches you to do the translation.

What you do every day

You read mathematical notation and translate it into code. You debug training issues by understanding the calculus behind gradient computation. You choose the right loss function by understanding information theory. You optimize data pipelines by understanding linear algebra. You don't just call APIs — you understand what they compute.

Why this matters now

The gap between someone who can call sklearn.fit() and someone who can implement the algorithm from scratch is the gap between a junior and a senior ML engineer. As AI tools make basic ML trivial, the value shifts to engineers who understand the math deeply enough to debug, optimize, and innovate beyond what the libraries provide.

What this course is not

It is not a pure mathematics course. There are no proofs for the sake of proofs, no abstract exercises disconnected from code. Every concept is immediately implemented in Python and connected to a real ML use case. If you want to build AI systems and never get stuck on the math again, this is the course.

Common questions

Do I need a math background?

You need high school math — basic algebra and the ability to read mathematical notation. This course teaches the rest from scratch, with every concept implemented in code so you can see exactly what the symbols mean in practice.

Why implement math in code instead of just learning the theory?

Because implementing a concept in code is the only way to truly understand it. Reading about matrix multiplication is passive; writing a function that multiplies matrices and visualizing the result is active understanding. Every ML algorithm you'll ever use is just math translated into code — this course teaches you to do the translation yourself.

How is this different from the math in ML & AI Engineering?

ML & AI Engineering covers math in 5 lessons as part of a setup phase — enough to use the libraries. This course spends 22 lessons going deep: implementing every concept from scratch, building an autodiff engine, and producing a reusable math library. It's the difference between knowing what a gradient is and being able to build the thing that computes one.

What do I end up with?

A complete, tested Python math library with modules for linear algebra, calculus, probability, optimization, and advanced math — every function implemented from scratch and verified against NumPy, PyTorch, and scikit-learn. Plus the ability to read any ML paper and understand the math.

Key terms in this course

Gradient Descent

Continue your learning path

Core ML: Algorithms from Scratch · ML & AI Engineering · Deep Learning from Scratch

Start the Math for AI & ML course

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