# Introduction to Discrete Mathematics for Computer Science

University of California San Diego

Discover the language of Computer Science with the Introduction to Discrete Mathematics for Computer Science course. This online specialization, offered by the University of California San Diego, delves into the fundamental principles of discrete mathematics and their applications in various IT fields. You will explore mathematical thinking, combinatorics, probability, graph theory, number theory, and cryptography, while also developing programming skills in Python. The course promotes a try-this-before-we-explain-everything approach, allowing you to solve interactive puzzles and gain a deeper understanding of the underlying ideas. By the end of the course, you will be equipped to tackle real-world computational problems and understand their theoretical foundations.

• Gain a deep understanding of mathematical thinking in computer science, including induction, recursion, and logic.
• Explore the principles of combinatorics and probability, essential for algorithmic implementations and machine learning.
• Discover the elegance and practical applications of graph theory, including its use in GPS systems and integrated circuit design.
• Unlock the potential of number theory and cryptography, understanding the basics of encryption and decryption.
• Tackle the challenging travelling salesman problem and understand the P versus NP problem, a fundamental question in computer science.

Certificate Available ✔

##### Course Modules

The Introduction to Discrete Mathematics for Computer Science course comprises modules on mathematical thinking, combinatorics and probability, graph theory, number theory and cryptography, and the travelling salesman problem.

#### Mathematical Thinking in Computer Science

Mathematical Thinking in Computer Science introduces crucial tools used in discrete mathematics, such as induction, recursion, and logic. By solving interactive puzzles, you will develop a deep understanding of these concepts and their applications in programming and real-world problem-solving. Prerequisites include basic math knowledge and familiarity with Python programming.

#### Combinatorics and Probability

Combinatorics and Probability explores the fundamental principles of counting and the application of combinatorial settings in algorithmic problems. Additionally, it delves into the basics of probability theory, essential for statistics and machine learning. The course emphasizes the development of practical skills and intuition in these areas, targeting individuals working or planning to work in IT.

#### Introduction to Graph Theory

Introduction to Graph Theory takes learners on a fascinating journey into the world of graph theory, demonstrating its applications in various fields such as GPS systems, integrated circuit design, and genome assembly. The course equips you with the ability to implement algorithms for real-world problems, including the optimal assignment of students to schools. It is suitable for individuals interested in IT, including motivated high school students.

#### Number Theory and Cryptography

Number Theory and Cryptography explores the basics of number theory and its application in cryptographic protocols. By the end of the course, participants will be capable of encrypting and decrypting messages, as well as understanding the RSA algorithm. This module is designed for individuals working in IT, starting from motivated high school students.

#### Delivery Problem

Delivery Problem focuses on implementing efficient programs, using Python, for the travelling salesman problem. While no provably efficient algorithms exist for this problem, the course demonstrates how to apply discrete mathematics concepts to develop practical solutions. Learners will rely on proof techniques, combinatorics, probability, and graph theory to design and implement these solutions.

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