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 Hands-On Labs — nothing to install
- 25 Interactive Lessons and 126 topics mapped to the official exam objectives
Expert Self-paced · 1 year access
36 Hands-On LiveLabs
Practice real IT tasks in guided environments.
- Real environments
- Auto-graded
- No installation
01 / Skills you'll get
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
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25 Structured Lessons Comprehensive coverage of core course objectives
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36 Hands-On LiveLabs Interactive guided scenarios with instant evaluation
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1 Year Full Access Self-paced learning accessible anytime on all devices
02 / Lessons & labs
See exactly what you will learn and practice
Lessons
25 Interactive Lessons · 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 LiveLab +
- What is a vector space?
- The basis
- Vectors in practice
- Summary
- Problems
2 LiveLab in this lesson — see the labs panel →
03 The Geometric Structure of Vector Spaces 4 topics · 1 LiveLab +
- Norms and distances
- Inner products, angles, and lots of reasons to care about them
- Summary
- Problems
1 LiveLab in this lesson — see the labs panel →
04 Linear Algebra in Practice 4 topics · 3 LiveLab +
- Vectors in NumPy
- Matrices, the workhorses of linear algebra
- Summary
- Problems
3 LiveLab 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 LiveLab +
- Linear equations
- The LU decomposition
- Determinants in practice
- Summary
- Problems
5 LiveLab in this lesson — see the labs panel →
07 Eigenvalues and Eigenvectors 5 topics · 3 LiveLab +
- Eigenvalues of matrices
- Finding eigenvalue-eigenvector pairs
- Eigenvectors, eigenspaces, and their bases
- Summary
- Problems
3 LiveLab in this lesson — see the labs panel →
08 Matrix Factorizations 8 topics · 4 LiveLab +
- Special transformations
- Self-adjoint transformations and the spectral decomposition theorem
- The singular value decomposition
- Orthogonal projections
- Computing eigenvalues
- The QR algorithm
- Summary
- Problems
4 LiveLab in this lesson — see the labs panel →
09 Matrices and Graphs 5 topics · 1 LiveLab +
- The directed graph of a nonnegative matrix
- Benefits of the graph representation
- The Frobenius normal form
- Summary
- Problems
1 LiveLab in this lesson — see the labs panel →
10 Functions 4 topics · 1 LiveLab +
- Functions in theory
- Functions in practice
- Summary
- Problems
1 LiveLab in this lesson — see the labs panel →
11 Numbers, Sequences, and Series 5 topics · 2 LiveLab +
- Numbers
- Sequences
- Series
- Summary
- Problems
2 LiveLab in this lesson — see the labs panel →
12 Topology, Limits, and Continuity 5 topics · 1 LiveLab +
- Topology
- Limits
- Continuity
- Summary
- Problems
1 LiveLab in this lesson — see the labs panel →
13 Differentiation 4 topics · 1 LiveLab +
- Differentiation in theory
- Differentiation in practice
- Summary
- Problems
1 LiveLab in this lesson — see the labs panel →
14 Optimization 5 topics · 1 LiveLab +
- Minima, maxima, and derivatives
- The basics of gradient descent
- Why does gradient descent work?
- Summary
- Problems
1 LiveLab in this lesson — see the labs panel →
15 Integration 4 topics · 1 LiveLab +
- Integration in theory
- Integration in practice
- Summary
- Problems
1 LiveLab in this lesson — see the labs panel →
16 Multivariable Functions 4 topics · 2 LiveLab +
- What is a multivariable function?
- Linear functions in multiple variables
- The curse of dimensionality
- Summary
2 LiveLab in this lesson — see the labs panel →
17 Derivatives and Gradients 4 topics · 3 LiveLab +
- Partial and total derivatives
- Derivatives of vector-valued functions
- Summary
- Problems
3 LiveLab in this lesson — see the labs panel →
18 Optimization in Multiple Variables 5 topics · 1 LiveLab +
- Multivariable functions in code
- Minima and maxima, revisited
- Gradient descent in its full form
- Summary
- Problems
1 LiveLab in this lesson — see the labs panel →
19 What is Probability? 5 topics · 1 LiveLab +
- The language of thinking
- The axioms of probability
- Conditional probability
- Summary
- Problems
1 LiveLab in this lesson — see the labs panel →
20 Random Variables and Distributions 6 topics · 2 LiveLab +
- Random variables
- Discrete distributions
- Real-valued distributions
- Density functions
- Summary
- Problems
2 LiveLab in this lesson — see the labs panel →
21 The Expected Value 9 topics · 1 LiveLab +
- 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 LiveLab 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?
Hands-On Labs Our edge
36 LiveLabs- 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 / FAQs
Questions before you start
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.
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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.
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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.
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Is this course focused on theory or practice? < p dir="ltr"> +
Keep going
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Ready to Master the Math of AI?
Translate complex theories into real-world AI solutions with a machine learning mathematics program.
- 1 year of full access
- 36 LiveLab included
- Certificate of completion
No credit card required