CTU-MATH307.AJ1
Mathematical Foundations for AI
- Practice in 31 Hands-On Labs — nothing to install
- 5 Interactive Lessons and 45 topics mapped to the official exam objectives
Self-paced · 1 year access
31 Hands-On LiveLabs
Practice real IT tasks in guided environments.
- Real environments
- Auto-graded
- No installation
5Interactive Lessons
45Topics
31LiveLab
76Flashcards
76Glossary of terms
01 / Lessons & labs
See exactly what you will learn and practice
Lessons
5 Interactive Lessons · 45 topics01 Vector and Matrix Operations 7 topics · 6 LiveLab +
- What is a vector space?
- The basis
- Vectors in practice
- Norms and distances
- Inner products, angles, and lots of reasons to care about them
- Vectors in NumPy
- Matrices, the workhorses of linear algebra
6 LiveLab in this lesson — see the labs panel →
02 Solving Systems of Linear Equations 7 topics · 5 LiveLab +
- What is a linear transformation?
- Change of basis
- Linear transformations in the Euclidean plane
- Determinants, or how linear transformations affect volume
- Linear equations
- The LU decomposition
- Determinants in practice
5 LiveLab in this lesson — see the labs panel →
03 Partial Derivatives and Gradients 15 topics · 7 LiveLab +
- Functions in theory
- Functions in practice
- Numbers
- Sequences
- Series
- Topology
- Limits
- Continuity
- Differentiation in theory
- Differentiation in practice
- Minima, maxima, and derivatives
- The basics of gradient descent
- Why does gradient descent work?
- Integration in theory
- Integration in practice
7 LiveLab in this lesson — see the labs panel →
04 Chain Rule and Composite Functions 7 topics · 6 LiveLab +
- What is a multivariable function?
- Linear functions in multiple variables
- The curse of dimensionality
- Derivatives of vector-valued functions
- Multivariable functions in code
- Minima and maxima, revisited
- Gradient descent in its full form
6 LiveLab in this lesson — see the labs panel →
05 Advanced Applications of Vector and Matrix Operations 9 topics · 7 LiveLab +
- Eigenvalues of matrices
- Finding eigenvalue-eigenvector pairs
- Eigenvectors, eigenspaces, and their bases
- Special transformations
- Self-adjoint transformations and the spectral decomposition theorem
- The singular value decomposition
- Orthogonal projections
- Computing eigenvalues
- The QR algorithm
7 LiveLab in this lesson — see the labs panel →
Hands-On Labs Our edge
31 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
- Implementing Callable Functions
- Visualizing Mathematical Sequences and Approximations
- Visualizing the Harmonic Series
- Analyzing Openness, Closedness, and Compactness of Sets
- Implementing Gradient Descent for Model Training
- Analyzing Gradients, Jacobians, and Hessians in ML Optimization
- Approximating Integrals Using the Trapezoidal Rule
- Plotting Multivariable Function Landscapes
- Plotting Linear Mappings and Hyperplanes for ML Models
- Evaluating Composite Functions
- Implementing Backpropagation in Neural Networks
- Applying the Chain Rule
- Training Machine Learning Models with Gradient Descent
- 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
Labs run in your browser — nothing to install.
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- 31 LiveLab included
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