Artificial Intelligence
This course, "Mathematics for Machine Learning," offers a thorough yet accessible introduction to the mathematical foundations of machine learning. The focus is on understanding, application, and implementation: each mathematical concept is linked to practical examples and exercises in Python.
Machine learning is inextricably linked to mathematics. Mathematical principles underlie every predictive model, every optimization step, and every form of learning from data. Yet for many professionals, this mathematical foundation remains abstract and difficult to grasp. This course provides an overview, context, and understanding of the mathematics behind machine learning, and shows how this mathematics enables various forms of learning.
Machine learning isn’t about magic, but about formulating and optimizing mathematical models. In this course, you’ll learn how data is represented mathematically, how models learn from examples, and how they generalize to new situations. The focus is on understanding and insight, supported by Python exercises that make the mathematics concrete and accessible.
Different forms of machine learning—such as supervised, unsupervised, semi-supervised, and reinforcement learning—differ in their approach but share the same mathematical foundations. In this course, you’ll learn how these forms relate to one another and what role linear algebra, calculus, and probability theory play in each of these approaches.
The Mathematics for Machine Learning course is not an abstract math training program, but a fundamental introduction to the mathematical thinking behind machine learning models. You’ll gain a better understanding of what happens “under the hood,” so that algorithms and models no longer remain a black box.
Dive into the mathematics that makes machine learning possible and discover how different learning paradigms are mathematically structured. You won’t learn how to program complete models, but rather how to recognize and understand the underlying mathematics.
In supervised learning, you’ll learn how models are trained on labeled data and how optimization and error minimization play a central role in this process.
In unsupervised learning, you’ll discover how mathematical structures are used to find patterns and relationships in unlabeled data.
Semi-supervised learning demonstrates how limited labels are combined with assumptions about data structure.
Reinforcement learning introduces learning through interaction, with rewards and optimization at its core.
By studying these approaches side by side, you’ll develop an understanding of when each approach is mathematically sound and appropriate.
For professionals, this offers a different perspective on machine learning: not from the standpoint of algorithms or tools, but from that of principles. You’ll learn when mathematical assumptions are realistic and when they are not.
All forms of machine learning are based on the same fundamental mathematical principles. Understanding these principles is essential for interpreting and evaluating models:
Key concepts you’ll learn:
By understanding these principles, you’ll develop a clear mental model of the mathematical foundations of machine learning.
In this course, you’ll combine insight with practical application. Among other things, you’ll develop the following skills:
The course focuses heavily on understanding and application. Python is used to explore and visualize mathematical concepts:
You’ll learn to use Python as a tool for thinking and analysis, not as a black box.
Choosing this course means you’ll learn to understand machine learning at its very foundation: mathematics. This will enable you to better comprehend, evaluate, and apply models in a world where data and AI are becoming increasingly central.
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Contact usThe first day is entirely devoted to the mathematical foundations of machine learning. We start with the core question: what does it actually mean for a model to learn from data? Building on that question, we explore how data, models, and learning processes are described mathematically.
You’ll learn how data is represented using vectors, matrices, and functions, and why virtually all machine learning models can be traced back to these concepts. Linear algebra turns out not to be an abstract subject, but a practical tool for describing relationships in data and understanding what a model can and cannot learn.
Next, we explore calculus and optimization as the driving forces behind machine learning. You’ll learn why learning boils down to minimizing an error and how derivatives and gradients guide the learning process. Instead of memorizing formulas, you’ll develop an intuitive understanding of how optimization works and why it sometimes gets stuck or fails.
Uncertainty and variation are also addressed. Using probability and statistics, we examine how models handle noise, incomplete data, and random patterns. You’ll learn why generalization is more important than perfect performance on training data and what assumptions come into play.
Throughout the day, these concepts are supported by Python. Python serves as a tool to make mathematics visible: through simple calculations and visualizations, you’ll see what’s happening, without programming becoming the goal in itself.
By the end of Day 1, you will have built a solid foundation and understand how mathematics forms the basis of all forms of machine learning.
On the second day, we’ll connect the mathematical building blocks from Day 1 to the various forms of machine learning. You’ll discover that supervised, unsupervised, semi-supervised, and reinforcement learning aren’t separate techniques, but variations on the same underlying mathematical idea: learning through optimization under certain assumptions.
We’ll start with supervised learning and show how regression and classification arise from optimizing a loss function on labeled data. You’ll learn what assumptions are made in this process and why generalization is often more challenging than it seems.
Next, the focus shifts to unsupervised learning, in which no labels are available. You’ll explore how mathematical structures, distances, and probabilistic models are used to discover patterns and relationships in data. This clarifies when unsupervised learning is useful and when it is not.
Next, we cover semi-supervised learning, in which limited labeled data is combined with large amounts of unlabeled data. You’ll learn the underlying mathematical assumptions and why this approach works only under specific conditions.
Finally, we’ll look at reinforcement learning, in which learning occurs through interaction and reward. You’ll discover how optimization works over time and how this form of learning relates mathematically to the other approaches.
On this day as well, Python is used to explore and visualize processes. By comparing different learning paradigms side by side, their similarities and differences become clear and understandable.
By the end of Day 2, you will be able to place the various forms of machine learning within a mathematical framework, identify their assumptions, and critically evaluate which approach is best suited to a particular problem.
The participant:
Do you have questions about the course content? Or are you unsure whether the course aligns with your learning goals or preferences? Would you prefer an in-house or private course? We’d be happy to help.
At their core, machine learning models are mathematical models. Concepts such as vectors, matrices, derivatives, and probability distributions determine how a model learns, optimizes, and makes predictions. Without an understanding of this mathematics, machine learning remains a “black box,” and it becomes more difficult to assess why a model works or fails.
In this course from Geo-ICT Training Center, you will work with:
Together, these components form the basis of virtually all modern machine learning algorithms.
This course assumes that you:
This corresponds to the HAVO level of mathematics. Without this foundation, following the explanations will require a disproportionate amount of effort, and the focus on understanding machine learning itself will be lost.
Yes, provided you have a solid grasp of basic high school math. The course does not cover the entire high school math curriculum, but explains concepts in an intuitive and practical way, often supported by Python visualizations. If you don’t have that foundation, we recommend brushing up on your math skills first.
