Traditional Machine Learning

Mathematics for machine learning

Linear algebra, calculus, and geometry that make gradients, losses, and high-dimensional data intuitive.

Beginner 20 hours · Self-paced 99.0 USD · 100 lessons · ~750 min read

20 topics 100 lessons Start anywhere

What you’ll get out of this course

Build practical skill in “Mathematics for machine learning” with text-first lessons and clear checkpoints.
Level: Beginner—follow the syllabus in order or jump to the modules you need.
Reinforce ideas with end-of-topic checks and (where available) hands-on coding tasks.

Trust & quality

Content is designed and maintained by the Deep AI Minds team—structured for working adults, with frequent updates as tooling and best practices evolve.

Content currency: ~100% of lessons on the current curriculum revision

Instructor & outcomes

Deep AI Minds

Curriculum & instruction

Structured, industry-relevant paths with clear checkpoints and refresh cadence.

Satisfaction & billing

30-day satisfaction: if the syllabus or access is not as described, contact support and we will help (refunds for eligible purchases, case by case for integrations).

Common questions

You keep access for the lifetime of the catalog item you purchased, subject to fair use and our terms.

Yes—add your company name at checkout (where available) or contact us for team licensing and PO-based billing.

Review the full syllabus before buying. If something is wrong on our side, reach out and we will make it right.

Syllabus

We structured this course to build your skills step by step

Scroll through each module below—open lessons in place or jump into a topic. Everything runs in order, but you’re free to explore.

Topic 1

Learning module

Linear algebra core

Vectors, matrices, and the operations every ML library leans on.

Vectors and dimensions 8 min

Matrix–vector products 9 min

Norms and similarity 7 min

Matrix–matrix multiplication 8 min

Linear combinations and span 8 min

Topic 2

Learning module

Vectors and vector spaces

From a list of numbers to span, basis, and inner product spaces.

Vector spaces and subspaces 7 min

Linear independence 7 min

Basis and dimension 7 min

Inner product spaces 8 min

Orthogonal vectors 7 min

Topic 3

Learning module

Matrices and transformations

Matrices as functions: types, transposes, inverses, determinants, rank.

Matrices as functions 8 min

Matrix types — a quick tour 8 min

Transpose and inverse 8 min

Determinant and volume 7 min

Rank and nullity 8 min

Topic 4

Learning module

Matrix decompositions

LU, QR, Cholesky, SVD, and eigendecomposition — what each one buys you.

LU decomposition 8 min

QR decomposition 8 min

Cholesky decomposition 7 min

SVD overview 8 min

Eigendecomposition overview 8 min

Topic 5

Learning module

Eigenvalues and eigenvectors

The directions a matrix only stretches, and why ML keeps finding them.

What are eigenvalues? 8 min

Computing eigenvalues 8 min

Diagonalization 7 min

Spectral theorem 7 min

Eigenvalues in ML applications 8 min

Topic 6

Learning module

Singular value decomposition

The most useful decomposition in ML: PCA, low-rank, and beyond.

SVD fundamentals 8 min

Computing the SVD 7 min

Low-rank approximation 8 min

Principal components via SVD 8 min

SVD applications in ML 8 min

Topic 7

Learning module

Calculus for ML

Derivatives, partial derivatives, and the chain rule — the gradient toolkit.

Derivatives as slopes 7 min

Partial derivatives 8 min

Chain rule (intuition) 8 min

Limits and continuity for ML 7 min

Derivative rules toolkit 8 min

Topic 8

Learning module

Multivariable calculus

Functions of many variables: directional derivatives, tangent planes, integrals.

Functions of several variables 7 min

Directional derivatives 8 min

Tangent planes and linear approximation 8 min

Multiple integrals overview 7 min

Change of variables 8 min

Topic 9

Learning module

Gradient and Jacobian

How frameworks compute and apply derivatives at the vector and matrix level.

The gradient vector 7 min

The Jacobian matrix 8 min

Computing Jacobians 8 min

Vector–Jacobian products 8 min

Backprop as a Jacobian product 8 min

Topic 10

Learning module

Hessian and second-order methods

Curvature, definiteness, Newton, and quasi-Newton methods.

The Hessian matrix 8 min

Positive-definite matrices 7 min

Second-order conditions 8 min

Newton's method (intuition) 7 min

Quasi-Newton methods 8 min

Topic 11

Learning module

Taylor series and approximation

Local linear and quadratic models — how ML keeps approximating.

Taylor series (univariate) 7 min

Taylor series (multivariate) 8 min

Linear vs quadratic local models 7 min

Function approximation trade-offs 7 min

Perturbation analysis 7 min

Topic 12

Learning module

Geometry and optimization

Loss landscapes, gradient descent, learning rates, and momentum.

One step of gradient descent 8 min

Convexity (sketch) 6 min

High-dimensional intuition 7 min

Learning rate and step sizes 8 min

Momentum and acceleration 8 min

Topic 13

Learning module

Convex optimization

Convex sets, problems, duality, and the methods that solve them.

Convex sets and convex functions 7 min

Convex optimization problems 8 min

Lagrangian duality 8 min

KKT conditions 7 min

Projected gradient methods 7 min

Topic 14

Learning module

Constrained optimization

Equality and inequality constraints, Lagrangians, KKT, penalties.

Equality constraints 7 min

Inequality constraints 7 min

Lagrange multipliers 7 min

Penalty and barrier methods 7 min

Interior-point methods (overview) 7 min

Topic 15

Learning module

Stochastic optimization

SGD, mini-batches, variance reduction, and adaptive methods.

SGD fundamentals 8 min

Mini-batch trade-offs 7 min

Variance reduction 8 min

Adam and adaptive learning rates 8 min

SGD in deep learning 8 min

Topic 16

Learning module

Information theory basics

Entropy, cross-entropy, KL divergence, and where they appear in losses.

Entropy and uncertainty 7 min

Cross-entropy 7 min

KL divergence 7 min

Mutual information 8 min

Information theory in loss functions 7 min

Topic 17

Learning module

Probability meets linear algebra

Covariance matrices, multivariate Gaussians, whitening, projections.

Covariance matrices 7 min

Multivariate Gaussian 8 min

Whitening and PCA 8 min

Mahalanobis distance 7 min

Random projections 7 min

Topic 18

Learning module

Numerical linear algebra

Floating point, stability, conditioning, and iterative solvers.

Floating-point pitfalls 7 min

Numerical stability 7 min

Condition numbers 7 min

Iterative solvers overview 7 min

Preconditioning (intuition) 7 min

Topic 19

Learning module

Functional analysis glimpse

Function spaces, norms on functions, Hilbert spaces, kernels, and RKHS.

Function spaces overview 7 min

Norms on functions 7 min

Hilbert spaces (intuition) 8 min

Kernels and RKHS 8 min

Operator norms 7 min

Topic 20

Learning module

Math in modern ML

Where the previous 19 topics show up in attention, BatchNorm, dropout, GNNs.

The math of attention 8 min

The math of batch normalization 8 min

The math of dropout 7 min

The math of graph neural networks 8 min

Continual math learning — resources 6 min

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