The course "Mathematical Foundations of Machine Learning" is a program for those who want to systematically understand the mathematics necessary for studying machine learning, data analysis, and artificial intelligence. You will master the key tools of linear algebra and integral calculus, learn to understand the mathematical ideas underlying ML algorithms, and be able to more confidently transition to practical tasks in Data Science.
About the course
Mathematics in machine learning helps not only to use ready-made libraries but to understand why models work, how to interpret results, and what limitations algorithms have. This course focuses on basic topics most often encountered in the study of ML: vectors, linear transformations, eigenvalues, eigenvectors, integrals, and the relationship of integration with differentiation.
The training combines theoretical explanations, recorded lectures, practical exercises, interactive consultations, and projects. This format helps reinforce mathematical concepts with examples and see their application in machine learning tasks.
What you will learn
- Understand the role of mathematics in machine learning and artificial intelligence.
- Work with basic concepts of linear algebra: vectors, matrices, and linear transformations.
- Analyze the dot product as a tool for measuring similarity and as part of linear operations.
- Understand the meaning of eigenvalues and eigenvectors and their application in data analysis.
- Differentiate between definite and indefinite integrals.
- Understand the relationship between integral calculus and differentiation.
- Apply mathematical methods in the study of machine learning algorithms.
Course program
Linear Algebra for Machine Learning
This section is dedicated to fundamental concepts of linear algebra used in machine learning models, neural networks, optimization methods, and multidimensional data analysis.
- Vectors and operations with them.
- Matrices and linear transformations.
- Dot product and its geometric meaning.
- Dot product as a linear transformation.
- Eigenvalues and eigenvectors.
- Practical significance of linear algebra in ML tasks.
Integral Calculus
This block covers the basics of integral calculus necessary for understanding continuous models, probabilistic distributions, loss functions, and methods of mathematical analysis.
- Concept of an indefinite integral.
- Concept of a definite integral.
- Geometric interpretation of the integral.
- Relationship between integration and differentiation.
- Application of integrals in data analysis and machine learning tasks.
Who the course is for
- Beginning specialists in Data Science who need a solid mathematical foundation for further learning.
- Students of technical and natural science fields studying machine learning and artificial intelligence.
- Developers who want to understand ML algorithms more deeply rather than just using ready-made tools.
- Analysts planning to transition to modeling, forecasting, and working with ML models.
- Self-learners who need a structured course on the mathematical foundations of machine learning.
Learning format
The course combines several formats to make the theory understandable and applicable in practice:
- Recorded lectures for self-study of the material;
- Practical exercises to reinforce topics;
- Interactive consultations for clarifying complex questions;
- Practical projects that help connect mathematics with machine learning tasks.
What skills you will acquire after completion
After completing the course, you will be able to more confidently study machine learning algorithms, read technical materials on ML, and better understand mathematical notations found in textbooks, articles, and documentation.
- Strengthen your base in linear algebra and mathematical analysis.
- Learn to see the connection between formulas and practical ML tasks.
- Prepare for studying optimization, statistics, probability, and neural networks.
- Be able to work more consciously with machine learning models and analyze their behavior.
Why study the mathematical foundations of machine learning
Machine learning is built on mathematical principles. Without understanding linear algebra, derivatives, integrals, and transformations, it is difficult to comprehend the operation of models, training methods, and quality assessment of algorithms. This course helps fill in the gaps and create a foundation for further development in the field of artificial intelligence.
Understanding mathematics makes studying machine learning more conscious: you begin to see not only the code but also the principles on which algorithms operate.
Conclusion
“Mathematical Foundations of Machine Learning” is a course for those who want to prepare for a serious study of ML and AI. It will help master linear algebra, integral calculus, and key mathematical ideas necessary for confident work with modern machine learning algorithms.
