Course Overview

📋 Basic Information

• Course: Discrete Mathematics
• Semesters: Fall 2025 – Spring 2026
• Prerequisites: High school mathematics
• Language: Russian (lectures), English (materials)
• Instructor: Konstantin Chukharev

🎯 What You’ll Learn

By the end of this course, you will be able to:

🍁 Fall Semester:

• Work confidently with sets, operations, and cardinality
• Understand and apply binary relations (equivalence, order, functions)
• Design and analyze Boolean expressions and digital circuits
• Construct formal proofs using natural deduction

🌱 Spring Semester:

• Analyze graphs and trees using various algorithms
• Solve network flow problems
• Design and analyze finite automata and regular languages
• Apply combinatorial principles and generating functions

📚 Course Structure

Two-semester course covering 8 “modules”:

🍁 Fall Semester:

• Set Theory (Weeks 1–2, 6) Sets, operations, cardinality, axioms

• Binary Relations (Weeks 3–7) Equivalence, order, functions, lattices

• Boolean Algebra (Weeks 8–10) Logic gates, circuits, minimization

• Formal Logic (Weeks 11–16) Propositional and predicate logic, proofs

🌱 Spring Semester:

• Graph Theory (Weeks 1–4) Graphs, trees, paths, cycles, algorithms

• Flow Networks (Week 5) Max flow, min cut, applications

• Automata Theory (Weeks 6–10) Finite automata, regular languages, NFAs

• Combinatorics (Weeks 11–16) Counting principles, generating functions, recurrences

📊 Assessment Overview

In each semester, you will complete:

⚠️ Important: You must complete all homework and pass all Theoretical Minimums to receive a passing grade, regardless of total points.

🎓 Key Success Factors

• Attend all lectures - Material builds cumulatively
• Start homework early - Give yourself time to think and iterate
• Form study groups - Explain concepts to each other
• Practice regularly - Mathematical skill develops through repetition
• Ask questions - Use mentors and Telegram group actively