Teaching
Gaoxin Campus G3-109: 4(3,4,5), week 2-18.
This course is a foundational theoretical course for graduate students majoring in Computer Science and Technology. Its purpose is to enable students to learn basic mathematical skills (such as probability theory, matrix theory, etc.) and how these skills are applied in computer science. Through this course, students are expected to independently apply the learned mathematical knowledge to various applications, problem-solving, and algorithm design, including machine learning, deep learning, etc.
Syllabus
Part I Probability and Statistics and Their Applications
1.1 Fundamentals of Probability Theory [Slide]
1.2 Deviation and its Correlation Theorems [Slide]
1.3 Markov Chains and Markov Decision Processes [Slide]
1.4 Bayesian Networks [Slide]
1.5 Model Evaluation and Selection [Slide]
1.6 Clustering and Analysis [Slide]
1.7 Gaussian Mixture Models and EM Algorithm [Slide]
1.8 Random Walks [Slide]
1.9 Reinforcement Learning [Slide]
Part II Linear Algebra, Calculus, and Their Applications
2.1 Fundamentals of Matrix Algebra [Slide]
2.2 Differential and Finite difference [Slide]
2.3 Singular Value Decomposition [Slide]
2.4 Support Vector Machines [Slide]
2.5 Linear Classification and Regression [Slide]
2.6 High-dimensional Spaces [Slide]
2.7 Model Training and Model Inference [Slide]
Teaching materials and main reference books
This course is a foundational theoretical course for graduate students majoring in Computer Science and Technology. Its purpose is to enable students to learn basic mathematical skills (such as probability theory, matrix theory, etc.) and how these skills are applied in computer science. Through this course, students are expected to independently apply the learned mathematical knowledge to various applications, problem-solving, and algorithm design, including machine learning, deep learning, etc.
Syllabus
Part I Probability and Statistics and Their Applications
1.1 Fundamentals of Probability Theory [Slide]
1.2 Deviation and its Correlation Theorems [Slide]
1.3 Markov Chains and Markov Decision Processes [Slide]
1.4 Bayesian Networks [Slide]
1.5 Model Evaluation and Selection [Slide]
1.6 Clustering and Analysis [Slide]
1.7 Gaussian Mixture Models and EM Algorithm [Slide]
1.8 Random Walks [Slide]
1.9 Reinforcement Learning [Slide]
Part II Linear Algebra, Calculus, and Their Applications
2.1 Fundamentals of Matrix Algebra [Slide]
2.2 Differential and Finite difference [Slide]
2.3 Singular Value Decomposition [Slide]
2.4 Support Vector Machines [Slide]
2.5 Linear Classification and Regression [Slide]
2.6 High-dimensional Spaces [Slide]
2.7 Model Training and Model Inference [Slide]
Teaching materials and main reference books
- [1] Foundations of Data Science, Avrim Blum, John Hopcroft, Ravindran Kannan, Cambridge University Press, 2020
- [2] The Elements of Statistical Learning, Trevor Hastieļ¼Robert Tibshirani, Jerome Friedman, 2nd edition, 2017
- [3] Linear Algebra and Its Applications, David Lay, Steven Lay, Judi McDonald, Pearson, 5th edition, 2014