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Interactive Exercise Notebook

Welcome to the Math Problems repository. This project serves as a digital notebook template designed to be your primary working tool throughout the entire course.

The repository is bilingual and designed to enable you to build your own knowledge base using a version control system.

Course Work Manifesto

This course is not about solving lists of tasks, but about building your own understanding of mathematics through systematic work with problems.

The repository you create is your personal textbook — a record of how you analyze mathematical problems, interpret results, and organize knowledge.

Tasks serve as tools for thinking: their goal is not to obtain a number, but to develop a reasoning process that you will be able to reproduce independently without technological support.

During the semester, you use digital tools and AI to deepen your understanding, while the final exam verifies the transfer of this knowledge to memory and the ability to independently reconstruct solutions.

Methodology

To correctly use the provided materials, follow the procedure below:

  1. Forking the Repository:
  2. Cloning: Download the repository to your local computer.
  3. Creating Documentation:
    • Task lists are located in the relevant sections in the menu.
    • Each topic/task file (e.g., 01_events_and_probability.md) has a dedicated solutions directory in the same section (e.g., solution_01_events_and_probability/).
    • These solution directories are your workspace — this is where you create and maintain Markdown files with solutions, proofs, and theoretical notes.
    • The structure is pre-prepared: each topic has its own solution folder containing placeholder files for individual problems (e.g., sol_prob_01.md, sol_prob_02.md, …).
    • Your task is not to create the material structure, but to systematically fill the existing files with your own reasoning, comments, and solution analysis — the repository is a ready-made workshop that you fill with content during the semester.
    • In these same directories, you can place additional materials supporting the discussion of topics (e.g., graphics, charts, HTML/JS files, input data, simulation results). For the sake of order, keep the solution for each problem primarily in its corresponding sol_prob_XX.md file, and store supporting materials in sensibly named subfolders. Messiness in the file structure will be poorly received and may be considered during grading — just like the content of the solutions and the way they are presented.
  4. Committing Changes: Regularly upload your solutions to the server (Commit & Push).

The Role of Notes in Exam Preparation

Good notes in this course serve two purposes:

  • Presentation of solutions during class: Notes are the basis for discussing tasks. A student asked to show and explain a solution should be able to display it quickly in a rendered form (e.g., Markdown preview in VS Code or as PDF/HTML) and walk through the full line of reasoning.
  • Exam preparation: The final exam is written, on-site, and takes place without access to technology. The repository is used for learning. Solutions should be developed and understood during the semester so that during the exam it is possible to independently reproduce the train of thought.

Using AI to Personalize Learning

The use of Generative AI tools (ChatGPT, Claude, Gemini) is strongly recommended at the stage of preparing materials. This technology allows for the creation of personalized notes:

  • Customization: There is no single ideal note for everyone. If a definition is unclear, ask the AI for an additional explanation, a breakdown of steps, or geometric intuition. Create material that is best for you to learn from.
  • Efficiency: Do not copy content from the HTML page. Copy the raw Markdown code from the source files into the AI prompt to maintain correct mathematical formatting.
  • Professionalism: The goal is to generate a complete, clear, and substantive note that will serve as your personal textbook.

Expectations for Classes and Student Responsibility

All task lists are available from the first day of the semester. This allows for early work planning.

  • No excuses: In the era of widespread access to AI, arguments such as "I didn't know how to start" or "I couldn't solve it" are unacceptable. Generating a base solution takes seconds and can be done anywhere (even on a phone).
  • Nature of classes: Class time is intended for discussing solutions, analyzing problems, and clarifying doubts, rather than solving tasks from scratch. It is expected that you come to class with ready materials.
  • Resourcefulness: Building and maintaining this repository is a lesson in diligence and organizing your own workshop.

For Tech Enthusiasts: Web Publication (Optional)

Students interested in technology can publish their notes as a website using GitHub Pages.

  • The mkdocs gh-deploy command is used for this.
  • Disclaimer: This is an entirely voluntary element, it does not affect the final grade, and serves only for self-development. At the same time, it is a practical asset: if you publish your notes as a public website, you do not need access to your own computer during class — a link to the repository/page (even from a phone) is enough to quickly find a solution and smoothly proceed to its discussion.

Available Sections

  • Algebra: Matrices, determinants, systems of equations.
  • Geometry: Vectors, lines, and planes.
  • Analysis: Limits, derivatives, function analysis, integrals.
  • Probabilistic Methods: Probability theory, statistics, estimation.

Select a section from the menu on the left to begin.

How to use Artificial Intelligence in this course

Artificial Intelligence is a tool supporting your understanding of mathematics, not replacing the thinking process. For AI assistance to align with the course objectives, it is necessary to provide it with the appropriate context.

At the beginning of working with AI:

  1. Share this document (index.md) with it.
  2. Explain that the repository serves as a personal textbook and reasoning notebook.
  3. Inform it that the tasks are meant to develop the analysis process, not just lead to a numerical result.
  4. Emphasize that the exam takes place without technological support, so the goal of the work is the ability to independently reproduce solutions.

Only after providing this context should you begin working on the tasks.

While working with AI:

  • ask for explanations of steps, not just the solution,
  • ask questions that deepen understanding,
  • record your own interpretations and comments in the repository,
  • treat AI as a conversational partner and tutor, not a calculator.

The goal of using AI is to develop the capacity for independent mathematical thinking and to build a coherent, personal record of knowledge.