[major=AI | course_id=MAI391 | syllabus_id=13133 | semester=3 | combo=core | title=Mathematics for Machine Learning]
Course ID: MAI391
Title EN: Mathematics for Machine Learning
Title VI: Toán cho học máy
Credits: 3.0
Prerequisites: MAE101
Description: This course introduces the mathematical concepts and foundations needed to talk about the three main components of a machine learning system: data, models, and learning. Upon this course, students will be able to understand: • Foundametal concepts about matrices and matrix decomposition.
• Concepts of gradients.
• The basics of probability and some distributions.
• Optimization to find maxima/minima of functions. • Dimensionality reduction using principal component analysis.
• Classification in the context of support vector machines.
Method of teaching and learning: Lecture and project based learning
Student tasks: - Students must attend at least 80% of contact slots in order to be accepted to the final examination.
- Student is responsible for doing all exercises and assignments given by the instructor in class or at home.
- Use a laptop in class only for learning purposes
- Promptly access course websites for up-to-date course information
Tools: - Internet
- Python Programme
Course type: traditional
Decision: 932/QĐ-ĐHFPT dated 08/22/2025
Approved date: 2025-08-22
CLO0: Analytic Geometry LO 0.1 Define a norm and an inner product on a vector space LO 0.2 Determine bilinear mapping and check if a square matrix is positive definite. LO 0.3 Find the length of a vector as well as the distance between two vectors in a vector space by using inner product. LO 0.4 Find the angle between two vectors and check if they are orthogonal. Check if a square matrix is orthogonal. LO 0.5 Check if a set of vectors is an orthogonal or an orthonormal basis of a given vector space. Determine an orthogonal complement of a subspace. LO 0.6 Construct the projection onto a subspace.
[1] category=Assignments; type=on-going; weight=30.0; duration=3 hours; question_type=LO0, LO1, LO2, LO3, LO4, LO5, LO8; grading_guide=OP1: Assigment 1: Cover chapters 3, 4,5 Assignment 2: Cover chapters 6,7 Assignment 3: Cover chapters 9, 10, 12 OP2: (For Constructivism Approach only): Follow lecturer's proposal; completion_criteria=; clos=>0
[2] category=Computer Project; type=on-going; weight=20.0; duration=5 hours; question_type=LO5, LO6, LO7, LO8; grading_guide=cover chapter 9, 10,12; completion_criteria=; clos=>0
[3] category=Progress tests; type=on-going; weight=20.0; duration=30'; question_type=LO0, LO1, LO2, LO3, LO4; grading_guide=- Test 1: cover chapters 3, 4,5 - Test 2: cover chapters 6,7; completion_criteria=; clos=>0
[4] category=Final exam; type=Final exam; weight=30.0; duration=60'; question_type=LO 0, LO 1, LO 2, LO 3, LO 4; grading_guide=Selected chapters; completion_criteria=; clos=4
[1] desc=Mathematics for Machine Learning; author=M. P. Deisenroth, A. Faisal, Ch. S. Ong; publisher=Cambrige Univeristy Press; edition=1st; isbn=; main=True; online=True; note=https://mml-book.github.io/?fbclid=IwAR2WAfBUZe-E6O-pbbGL3k6E7KngL8F9sbOqraZr9LD14PAnHw6Y_e-O6Q4
[2] desc=PDF Slides; author=Instructors; publisher=; edition=; isbn=; main=; online=; note=
[3] desc=Machine Learning cơ bản; author=Vũ Hữu Tiệp; publisher=; edition=; isbn=; main=; online=True; note=https://github.com/tiepvupsu/ebookMLCB/blob/master/book_ML.pdf
[4] desc=Multivariate Calculus; author=Denis Auroux; publisher=MIT OpenCourseWare; edition=; isbn=; main=; online=True; note=https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/index.htm
[5] desc=Mathematics for machine learning; author=Mirror Neuron Chanel; publisher=; edition=; isbn=; main=; online=True; note=https://www.youtube.com/playlist?list=PLcQCwsZDEzFmlSc6levE3UV9rZ8yY-D_7
[6] desc=Mathematics for machine Learning; author=Digital Learning Hub - Imperial College London Chanel; publisher=; edition=; isbn=; main=; online=True; note=https://www.youtube.com/channel/UCSzae1ITUdw9DCdELMduaQw/playlists
[7] desc=Linear Algebra Done Right; author=Sheldon Axler; publisher=Springer; edition=3rd; isbn=; main=; online=True; note=
[8] desc=Machine Learning; author=Andrew Ng; publisher=Stanford Chanel; edition=; isbn=; main=; online=True; note=https://www.youtube.com/watch?v=UzxYlbK2c7E&list=PLA89DCFA6ADACE599&index=1
[9] desc=Mathematics for Machine Learning; author=Cousera; publisher=; edition=; isbn=; main=; online=True; note=https://www.coursera.org/specializations/mathematics-machine-learning
Session 1: Chapter 3. Analytic Geometry
3.1 Norm
3.2 Inner Products
Topic: Offline; Teaching type: CLO0; LO: T, U
ITU: Textbook Chapter 3
Download: Read Chapter 2
Exercises Chapter 3

Session 2: 3.3 Lengths and Distances
3.4 Angles and Orthogonality
Topic: Offline; Teaching type: CLO0; LO: T, U
ITU: Textbook Chapter 3
Download: Read Chapter 2
Exercises Chapter 3

Session 3: 3.5 Orthonormal Basis
3.6 Orthonormal Complement
Topic: Offline; Teaching type: CLO0; LO: T, U
ITU: Textbook Chapter 3
Download: Read Chapter 2
Exercises Chapter 3

Session 4: 3.8 Orthogonal Projections
Topic: Offline; Teaching type: CLO0; LO: T, U
ITU: Textbook Chapter 3
Download: Read Chapter 2
Exercises Chapter 3
CLO1: Matrix Decomposition LO 1.1 Compute the determinant of a square matrix, decide when a square matrix is invertible by equivalent conditions. Find the characteristic polynomial, eigenvalues and eigenvectors of a matrix. Understand some theorems concerning eigenvalues. LO1.2 Diagonalize a matrix by eigendecomposition. Decompose a matrix by singular value decomposition. LO1.3 Compute matrix approximation.
Session 1: Chapter 4. Matrix Decompositions
4.1 Determinants and Traces
Topic: Offline; Teaching type: CLO1; LO: T, U
ITU: Textbook Chapter 4
Download: Exercises Chapter 4

Session 2: 4.2 Eigenvalues and Eigenvectors
Topic: Offline; Teaching type: CLO1; LO: T, U
ITU: Textbook Chapter 4
Download: Exercises Chapter 4

Session 3: 4.4 Eigendecomposition and Diagonalization
Topic: Offline; Teaching type: CLO1; LO: T, U
ITU: Textbook Chapter 4
Download: Exercises Chapter 4

Session 4: 4.5 Singular value Decomposition
Topic: Offline; Teaching type: CLO1; LO: T, U
ITU: Textbook Chapter 4
Download: Exercises Chapter 4
CLO2: Vector Calculus LO 2.1 Revisit differentiation of a univariate function. Find Taylor expansion of a smooth function at a given point. LO 2.2 Find partial derivatives using basic formulas and the chain rule, gradients of multivariate functions. LO 2.3 Find gradients, Jacobian matrices of Vector-Valued Functions. LO 2.4 Take gradients of matrices with respect to vectors. LO 2.5 Understand the idea of backpropagation in deep learning. LO 2.6 Find the higher-order partial derivatives, linearization and multivariate Taylor series of multivariate functions.
Session 1: 4.5 Singular value Decomposition (cont.)
Topic: Offline; Teaching type: CLO1; LO: T
ITU: Textbook Chapter 4
Download: Exercises Chapter 4

Session 2: 4.6 Matrix Approximation
Topic: Offline; Teaching type: CLO1; LO: T
ITU: Textbook Chapter 4
Download: Exercises Chapter 4

Session 3: Chapter 5. Vector Calculus
5.1 Differentiation of Univariate Functions
Topic: Offline; Teaching type: CLO2; LO: T
ITU: Textbook Chapter 5
Download: Exercises Chapter 5

Session 4: 5.2 Partial Differentiation and Gradients
Topic: Offline; Teaching type: CLO2; LO: T, U
ITU: Textbook Chapter 5
Download: Exercises Chapter 5
CLO3: Probability and Distributions LO 3.1 Catch the notions of discrete variable continuous variable; find the probability mass function, the probability density function, the cumulative distribution function and their properties. LO 3.2 Calculate conditional probabilities; use multiplication rule, total probability rule and Bayes theorem to find probabilities. LO 3.3 Compute the mean and variance of a random variable, compute the covariance and the correlation between two variables. LO 3.4 Consider whether two variables are independent. LO 3.5 Describe a Gauss distribution, marginals, conditionals, sums and products of Gauss distributions.
Session 1: 5.2 Partial Differentiation and Gradients (cont.)
Topic: Offline; Teaching type: CLO2; LO: T, U
ITU: Textbook Chapter 5
Download: Exercises Chapter 5

Session 2: 5.3 Gradients of Vector-Valued Functions
Topic: Offline; Teaching type: CLO2; LO: T, U
ITU: Textbook Chapter 5
Download: Exercises Chapter 5

Session 3: 5.3 Gradients of Vector-Valued Functions (cont.)
Topic: Offline; Teaching type: CLO2; LO: T, U
ITU: Textbook Chapter 5
Download: Exercises Chapter 5

Session 4: 5.6 Backpropagation and Automatic Differentiation
Topic: Offline; Teaching type: CLO2; LO: T
ITU: Textbook Chapter 5
Download: Exercises Chapter 5
CLO4: Continuous Optimization LO 4.1 Find a local minimum of a function using gradient descent. LO 4.2 Use Lagrange multipliers to find the maximum/minimum value of a multivariate function with constraints. LO 4.3 Understand convex optimization problems and solve linear programings.
Session 1: 5.7 Higher-Order Derivatives
Topic: Offline; Teaching type: CLO2; LO: T, U
ITU: Textbook Chapter 5
Download: Exercises Chapter 5

Session 2: 5.8 Linearization and Multivariate Taylor Series
Topic: Offline; Teaching type: CLO2; LO: T, U
ITU: Textbook Chapter 5
Download: Exercises Chapter 5

Session 3: Review
Topic: Offline; Teaching type: CLO0, CLO1, CLO2, CLO8; LO: U
ITU: 
Download: Review Chapter 3, 4, 5

Session 4: Progress Test 1
Submission of Assigment 1
Topic: Offline; Teaching type: CLO0, CLO1, CLO2, CLO8; LO: 
ITU: Submit Assignment 1
CLO5: Linear Regression LO 5.1 Use maximum likelihood and maximum a posteriori (MAP) estimation to find optimal model parameters. LO 5.2 Using these parameter estimates to have a brief look at generalization errors and overfitting. LO 5.3 Discuss Bayesian linear regression.
Session 1: Chapter 6. Probability and Distributions
6.1 Construction of a Probability Space
Topic: Offline; Teaching type: CLO3; LO: T
ITU: Textbook Chapter 6
Download: Exercises Chapter 6

Session 2: 6.2 Discrete and Continuous Probabilities
Topic: Offline; Teaching type: CLO3; LO: T, U
ITU: Textbook Chapter 6
Download: Exercises Chapter 6

Session 3: 6.3 Sum Rule, Product Rule, and Bayes’ Theorem
Topic: Offline; Teaching type: CLO3; LO: T, U
ITU: Textbook Chapter 6
Download: Exercises Chapter 6

Session 4: 6.3 Sum Rule, Product Rule, and Bayes’ Theorem (cont.)
Topic: Offline; Teaching type: CLO3; LO: T, U
ITU: Textbook Chapter 6
Download: Exercises Chapter 6
CLO6: Dimensionality Reduction with PCA LO 6.1 Compute the data covariance matrix of a data set, construct m-dimensional subspace with maximum variance. LO 6.2 Find the basis of theprincipal subspace. LO 6.3 Using Low-Rank Matrix to approximate PCA. LO 6.4 Discuss PCA in high dimension and key steps of PCA.
Session 1: 6.4 Summary Statistics and Independence
Topic: Offline; Teaching type: CLO3; LO: T, U
ITU: Textbook Chapter 6
Download: Exercises Chapter 6

Session 2: 6.4 Summary Statistics and Independence (cont.)
Topic: Offline; Teaching type: CLO3; LO: T, U
ITU: Textbook Chapter 6
Download: Exercises Chapter 6

Session 3: 6.5 Gaussian Distribution
Topic: Offline; Teaching type: CLO3; LO: T
ITU: Textbook Chapter 6
Download: Exercises Chapter 6

Session 4: 6.5 Gaussian Distribution (cont.)
Topic: Offline; Teaching type: CLO3; LO: T, U
ITU: Textbook Chapter 6
Download: Exercises Chapter 6
CLO7: Classification with SVM LO 7.1 Understand binary classification by seperating hyperplane. LO 7.2 Catch mathematical ideas of support vector machine. LO 7.3 Understand the advantage of dual support vector machine. LO 7.4 Introduce non-linear classifiers by kernels. LO 7.5 Consider two different approaches for finding the optimal solution for the SVM.
Session 1: Chapter 7. Continuous Optimization
7.1 Optimization Using Gradient Descent
Topic: Offline; Teaching type: CLO4; LO: T, U
ITU: Textbook Chapter 7
Download: Exercises Chapter 7

Session 2: 7.2 Constrained Optimization and Lagrange Multipliers
Topic: Offline; Teaching type: CLO4; LO: T
ITU: Textbook Chapter 7
Download: Exercises Chapter 7

Session 3: 7.2 Constrained Optimization and Lagrange Multipliers (cont.)
Topic: Offline; Teaching type: CLO4; LO: T
ITU: Textbook Chapter 7
Download: Exercises Chapter 7

Session 4: 7.3 Convex Optimization
Topic: Offline; Teaching type: CLO4; LO: T
ITU: Textbook Chapter 7
Download: Exercises Chapter 7
CLO8: Attitude and soft skills LO 8 Develop working in group skills and self-discipline
Session 1: 7.3 Convex Optimization (cont.)
Topic: Offline; Teaching type: CLO4; LO: T, U
ITU: Textbook Chapter 7
Download: Exercises Chapter 7

Session 2: 7.3 Convex Optimization (cont.)
Topic: Offline; Teaching type: CLO4; LO: T, U
ITU: Textbook Chapter 7
Download: Exercises Chapter 7

Session 3: Review
Topic: Offline; Teaching type: CLO3, LO4, CLO8; LO: U
ITU: 

Session 4: Progress Test 2
Submission of Assignment 2
Topic: Offline; Teaching type: CLO3, LO4, CLO8; LO: 
ITU: Submit Assignment 2
Session 1: Chapter 9. Linear Regression
9.1 Problem Formulation
Topic: Offline; Teaching type: CLO5; LO: T
ITU: Textbook Chapter 9
Download: Linear Regression in Python : read and code

Session 2: 9.1 Problem Formulation (cont.)
Topic: Offline; Teaching type: CLO5; LO: T
ITU: Textbook Chapter 9
Download: Linear Regression in Python : read and code

Session 3: 9.2 Parameter Estimation
Topic: Offline; Teaching type: CLO5; LO: T
ITU: Textbook Chapter 9
Download: Linear Regression in Python : read and code

Session 4: 9.2 Parameter Estimation (cont.)
Topic: Offline; Teaching type: CLO5; LO: T, U
ITU: Textbook Chapter 9
Download: Linear Regression in Python : read and code
Session 1: Optional:
9.3 Bayesian Linear Regression
Topic: Offline; Teaching type: CLO5; LO: T
ITU: Textbook Chapter 9
Download: Linear Regression in Python : read and code

Session 2: Optional:
9.4 Maximum Likelihood as Orthogonal Projection
Topic: Offline; Teaching type: CLO5; LO: T
ITU: Textbook Chapter 9
Download: Linear Regression in Python : read and code

Session 3: Chapter 10. Dimensionality Reduction with Principal Component Analysis
10.1 Problem Setting
Topic: Offline; Teaching type: CLO6; LO: T
ITU: Textbook Chapter 10
Download: Write code that represents images as vectors

Session 4: 10.2 Maximum Variance Perspective
Topic: Offline; Teaching type: CLO6; LO: T
ITU: Textbook Chapter 10
Download: Write code that computes basic statistics of datasets
Session 1: 10.2 Maximum Variance Perspective (cont.)
Topic: Offline; Teaching type: CLO6; LO: T, U
ITU: Textbook Chapter 10
Download: Write code that computes basic statistics of datasets

Session 2: 10.6 Key Steps of PCA in Practice
Topic: Offline; Teaching type: CLO6; LO: T
ITU: Textbook Chapter 10
Download: Write code that projects image data onto a 2-dimensional subspace

Session 3: 10.6 Key Steps of PCA in Practice (cont.)
Topic: Offline; Teaching type: CLO6; LO: T, U
ITU: Textbook Chapter 10
Download: Write code that projects image data onto a 2-dimensional subspace

Session 4: Optional:
10.3 Projection Perspective
Topic: Offline; Teaching type: CLO6; LO: T
ITU: Textbook Chapter 10
Download: Write code that projects image data onto a 2-dimensional subspace
Session 1: Optional:
10.4 Eigenvector Computation and Low-Rank Approximations
Topic: Offline; Teaching type: CLO6; LO: T, U
ITU: Textbook Chapter 10
Download: Write code that implements PCA

Session 2: Optional:
10.5 PCA in High Dimensions
Topic: Offline; Teaching type: CLO5, CLO6; LO: T, U
ITU: Textbook Chapter 10
Submit Assignment 3
Download: Write code that implements PCA

Session 3: Chapter 12. Classification with Support Vector Machines
12.1 Separating Hyperplanes
Topic: Offline; Teaching type: CLO7; LO: T
ITU: Textbook Chapter 12
Download: Create a Support Vector Machine in Python

Session 4: 12.2 Primal Support Vector Machine
Topic: Offline; Teaching type: CLO7; LO: T
ITU: Textbook Chapter 12
Download: Create a Support Vector Machine in Python
Session 1: 12.2 Primal Support Vector Machine (cont.)
Topic: Offline; Teaching type: CLO7; LO: T, U
ITU: Textbook Chapter 12
Download: Create a Support Vector Machine in Python

Session 2: 12.2 Primal Support Vector Machine (cont.)
Topic: Offline; Teaching type: CLO7; LO: T
ITU: Textbook Chapter 12
Download: Create a Support Vector Machine in Python

Session 3: 12.3 Dual Support Vector Machine
Topic: Offline; Teaching type: CLO7; LO: T
ITU: Textbook Chapter 12
Download: Create a Support Vector Machine in Python

Session 4: 12.3 Dual Support Vector Machine (cont.)
Topic: Offline; Teaching type: CLO7; LO: T, U
ITU: Textbook Chapter 12
Download: Create a Support Vector Machine in Python
Session 1: Optional:
12.4 Kernels
Topic: Offline; Teaching type: CLO7; LO: T
ITU: Textbook Chapter 12
Download: Create a Support Vector Machine in Python

Session 2: Optional:
12.5 Numerical Solution
Topic: Offline; Teaching type: CLO7; LO: T
ITU: Textbook Chapter 12
Download: Create a Support Vector Machine in Python

Session 3: Presentation of Computer Project
Topic: Offline; Teaching type: CLO5, CLO6, CLO7, CLO8; LO: U
ITU: 

Session 4: Presentation of Computer Project (cont.)
Topic: Offline; Teaching type: CLO5, CLO6, CLO7, CLO8; LO: U
ITU: