🧠 Algorithms and Programming

YMT112 - Spring Semester 2025

📚 About the Course

This Discrete Mathematics course introduces the core mathematical language and reasoning skills used across computer science. Students develop fluency with formal logic and proof techniques, sets, functions and relations, induction and recursion, counting and basic combinatorics, graphs and trees, and modular arithmetic. Emphasis is placed on writing clear, correct proofs, analyzing simple algorithms and their complexity, and modeling real problems with discrete structures. The course connects theory to applications in data structures, cryptography, networks, and automata, preparing students for upper-level CS courses and rigorous problem solving.

Course Philosophy

We approach Discrete Mathematics as a language for precise thinking. The course prioritizes conceptual understanding over rote manipulation, and cultivates habits of clear reasoning, careful definitions, and well-structured proofs. Students learn by doing: short problem-centered activities, frequent low-stakes practice, and guided proof writing build confidence steadily.

Our philosophy emphasizes:

• Clarity before formality: develop intuition with examples, then generalize and prove
• Multiple proof strategies: direct, contrapositive, contradiction, and induction, chosen to fit the problem
• Modeling and connection: use discrete structures to frame real CS problems in data structures, algorithms, cryptography, and networks
• Productive struggle: challenge is expected; feedback, collaboration, and reflection help convert confusion into insight
• Ethical scholarship: integrity in reasoning, attribution, and reuse of ideas

The goal is not just to pass an exam, but to think like a computer scientist—able to read and write rigorous arguments, analyze algorithms, and communicate mathematical ideas clearly.

Learning Objectives

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

• Understand formal logic and apply proof techniques including direct, contrapositive, and contradiction
• Work with fundamental discrete structures including sets, relations, functions, and modular arithmetic
• Apply mathematical induction to prove properties of recursively defined sequences and algorithms
• Solve counting problems using combinatorial principles and techniques