MATHS-ML.AJ1
Mathematical Foundations for AI
Begin your innovative career with the Mathematics of Machine Learning course. Learn how to design & understand the next generation of AI models.
- Practice in 36 Laboratorios prácticos — nothing to install
- 25 Lecciones interactivas y 126 topics mapped to the official exam objectives
Expert A tu propio ritmo · 1 año de acceso
36 LiveLabs prácticos
Practice real IT tasks in guided environments.
- Entornos reales
- Calificación automática
- Sin instalación
01 / Habilidades que obtendrás
What you will be able to do
Tired of treating machine learning models like black boxes? The Mathematics of Machine Learning course gives you the rigorous foundation to design and troubleshoot AI.
The power of ML lies within the mathematics of machine learning—linear algebra, calculus & probability. As quoted by Galileo: Mathematics is the language in which God has written the universe.
We turn that language into AI expertise. Mastering machine learning math is the most critical differentiator for securing high-end roles in the fields of data science & AI engineering.
- Linear Algebra & Geometry: Master vector spaces, matrices & linear algebra in practice, including eigenvalues, matrix factorizations & SVD.
- Calculus & Optimization: Conquer differentiation, integration & optimization techniques for both single & multivariable functions.
- Probability & statistics: Grasp the fundamentals of probability, random variables & expected value—the statistical backbone of all the ML models.
- Foundational Theory: Build a strong foundational theoretical base with mathematical logic, set theory, & complex numbers to fully understand the structure of Machine learning mathematics.
Course Highlights
-
25 Lecciones estructuradas Cobertura completa de los objetivos principales del curso
-
36 LiveLabs prácticos Escenarios interactivos guiados con evaluación instantánea
-
1 año de acceso completo Aprendizaje a tu propio ritmo, accesible en cualquier momento y en todos los dispositivos
02 / Lecciones y laboratorios
See exactly what you will learn and practice
Plan de estudios
25 Lecciones interactivas · 126 topics01 Introduction 4 topics +
- What is this course about?
- How to read this course
- Conventions used
- What this course covers
02 Vectors and Vector Spaces 5 topics · 2 Laboratorio en vivo +
- What is a vector space?
- The basis
- Vectors in practice
- Summary
- Problems
2 Laboratorio en vivo in this lesson — see the labs panel →
03 The Geometric Structure of Vector Spaces 4 topics · 1 Laboratorio en vivo +
- Norms and distances
- Inner products, angles, and lots of reasons to care about them
- Summary
- Problems
1 Laboratorio en vivo in this lesson — see the labs panel →
04 Linear Algebra in Practice 4 topics · 3 Laboratorio en vivo +
- Vectors in NumPy
- Matrices, the workhorses of linear algebra
- Summary
- Problems
3 Laboratorio en vivo in this lesson — see the labs panel →
05 Linear Transformations 6 topics +
- What is a linear transformation?
- Change of basis
- Linear transformations in the Euclidean plane
- Determinants, or how linear transformations affect volume
- Summary
- Problems
06 Matrices and Equations 5 topics · 5 Laboratorio en vivo +
- Linear equations
- The LU decomposition
- Determinants in practice
- Summary
- Problems
5 Laboratorio en vivo in this lesson — see the labs panel →
07 Eigenvalues and Eigenvectors 5 topics · 3 Laboratorio en vivo +
- Eigenvalues of matrices
- Finding eigenvalue-eigenvector pairs
- Eigenvectors, eigenspaces, and their bases
- Summary
- Problems
3 Laboratorio en vivo in this lesson — see the labs panel →
08 Matrix Factorizations 8 topics · 4 Laboratorio en vivo +
- Special transformations
- Self-adjoint transformations and the spectral decomposition theorem
- The singular value decomposition
- Orthogonal projections
- Computing eigenvalues
- The QR algorithm
- Summary
- Problems
4 Laboratorio en vivo in this lesson — see the labs panel →
09 Matrices and Graphs 5 topics · 1 Laboratorio en vivo +
- The directed graph of a nonnegative matrix
- Benefits of the graph representation
- The Frobenius normal form
- Summary
- Problems
1 Laboratorio en vivo in this lesson — see the labs panel →
10 Functions 4 topics · 1 Laboratorio en vivo +
- Functions in theory
- Functions in practice
- Summary
- Problems
1 Laboratorio en vivo in this lesson — see the labs panel →
11 Numbers, Sequences, and Series 5 topics · 2 Laboratorio en vivo +
- Numbers
- Sequences
- Series
- Summary
- Problems
2 Laboratorio en vivo in this lesson — see the labs panel →
12 Topology, Limits, and Continuity 5 topics · 1 Laboratorio en vivo +
- Topology
- Limits
- Continuity
- Summary
- Problems
1 Laboratorio en vivo in this lesson — see the labs panel →
13 Differentiation 4 topics · 1 Laboratorio en vivo +
- Differentiation in theory
- Differentiation in practice
- Summary
- Problems
1 Laboratorio en vivo in this lesson — see the labs panel →
14 Optimization 5 topics · 1 Laboratorio en vivo +
- Minima, maxima, and derivatives
- The basics of gradient descent
- Why does gradient descent work?
- Summary
- Problems
1 Laboratorio en vivo in this lesson — see the labs panel →
15 Integration 4 topics · 1 Laboratorio en vivo +
- Integration in theory
- Integration in practice
- Summary
- Problems
1 Laboratorio en vivo in this lesson — see the labs panel →
16 Multivariable Functions 4 topics · 2 Laboratorio en vivo +
- What is a multivariable function?
- Linear functions in multiple variables
- The curse of dimensionality
- Summary
2 Laboratorio en vivo in this lesson — see the labs panel →
17 Derivatives and Gradients 4 topics · 3 Laboratorio en vivo +
- Partial and total derivatives
- Derivatives of vector-valued functions
- Summary
- Problems
3 Laboratorio en vivo in this lesson — see the labs panel →
18 Optimization in Multiple Variables 5 topics · 1 Laboratorio en vivo +
- Multivariable functions in code
- Minima and maxima, revisited
- Gradient descent in its full form
- Summary
- Problems
1 Laboratorio en vivo in this lesson — see the labs panel →
19 What is Probability? 5 topics · 1 Laboratorio en vivo +
- The language of thinking
- The axioms of probability
- Conditional probability
- Summary
- Problems
1 Laboratorio en vivo in this lesson — see the labs panel →
20 Random Variables and Distributions 6 topics · 2 Laboratorio en vivo +
- Random variables
- Discrete distributions
- Real-valued distributions
- Density functions
- Summary
- Problems
2 Laboratorio en vivo in this lesson — see the labs panel →
21 The Expected Value 9 topics · 1 Laboratorio en vivo +
- Discrete random variables
- Continuous random variables
- Properties of the expected value
- Variance
- The law of large numbers
- Information theory
- The Maximum Likelihood Estimation
- Summary
- Problems
1 Laboratorio en vivo in this lesson — see the labs panel →
22 Appendix A: It’s Just Logic 6 topics +
- Mathematical logic 101
- Logical connectives
- The propositional calculus
- Variables and predicates
- Existential and universal quantification
- Problems
23 Appendix B: The Structure of Mathematics 5 topics +
- What is a definition?
- What is a theorem?
- What is a proof?
- Equivalences
- Proof techniques
24 Appendix C: Basics of Set Theory 5 topics +
- What is a set?
- Operations on sets
- The Cartesian product
- The cardinality of sets
- The Russell paradox (optional)
25 Appendix D: Complex Numbers 4 topics +
- The definition of complex numbers
- The geometric representation
- The fundamental theorem of algebra
- Why are complex numbers important?
Laboratorios prácticos Our edge
36 Laboratorio en vivos- Implementing Tuple and List Operations
- Performing NumPy Array and Vector Operations
- Analyzing Vectors and Distances
- Evaluating Vector Norms and Operations
- Applying Matrix Computations Using NumPy
- Representing Images and Text Using Vectors and Matrices
- Solving Linear Equations Using Gaussian Elimination
- Solving Linear Equations Using Determinants and Inverses
- Solving Linear Models in Machine Learning
- Performing LU Decomposition
- Computing the Determinant Using LU Decomposition
- Finding Eigenvalues and Eigenvectors of Matrices
- Analyzing Matrices Using Characteristic Polynomials
- Visualizing Eigenvectors and Eigenspaces in Linear Algebra
- Implementing Spectral Decomposition and PCA
- Performing Feature Extraction and Dimensionality Reduction
- Performing Singular Value Decomposition
- Implementing QR Decomposition
- Reordering Adjacency Matrices Using SCCs
- Implementing Callable Functions
- Visualizing Mathematical Sequences and Approximations
- Visualizing the Harmonic Series
- Analyzing Openness, Closedness, and Compactness of Sets
- Applying the Chain Rule
- Implementing Gradient Descent for Model Training
- Approximating Integrals Using the Trapezoidal Rule
- Plotting Multivariable Function Landscapes
- Plotting Linear Mappings and Hyperplanes for ML Models
- Evaluating Composite Functions
- Analyzing Gradients, Jacobians, and Hessians in ML Optimization
- Implementing Backpropagation in Neural Networks
- Training Machine Learning Models with Gradient Descent
- Simulating Random Outcomes for Probability Learning
- Visualizing Discrete Probability Distributions in Machine Learning
- Visualizing Continuous Statistical Distributions
- Simulating Random Processes for AI Models
03 / Preguntas frecuentes
Preguntas antes de empezar
Who should take the Mathematics of Machine Learning course? +
Data scientists, ML engineers & anyone interested in understanding the machine learning math that underpins the algorithm, like neural networks.
<
p dir="ltr">
Do I need prior experience/a degree in mathematics? +
Basic calculus & linear algebra knowledge are helpful, but the course begins with foundational concepts to ensure mastery of mathematics for machine learning.
<
p dir="ltr">
How deep does the course go into the math? < p dir="ltr"> +
It covers the full breadth of the mathematics of machine learning, including rigorous topics including topology, eigenvectors & matrix factorizations, which are essential for truly understanding modern AI.
<
p dir="ltr">
Is this course focused on theory or practice? < p dir="ltr"> +
Keep going
You might also like
Ready to Master the Math of AI?
Translate complex theories into real-world AI solutions with a machine learning mathematics program.
- 1 año de acceso completo
- 36 LiveLab incluido
- Certificado de finalización
No se requiere tarjeta de crédito