Introduction to Discrete Mathematics for Computer Science Specialization

Build a Foundation for Your Career in IT. Master the math powering our lives and prepare for your software engineer or security analyst career

About This Specialization

Discrete Math is needed to see mathematical structures in the object you work with, and understand their properties. This ability is important for software engineers, data scientists, security and financial analysts (it is not a coincidence that math puzzles are often used for interviews). We cover the basic notions and results (combinatorics, graphs, probability, number theory) that are universally needed. To deliver techniques and ideas in discrete mathematics to the learner we extensively use interactive puzzles specially created for this specialization. To bring the learners experience closer to IT-applications we incorporate programming examples, problems and projects in our courses.

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5 courses

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Projects

Designed to help you practice and apply the skills you learn.

Certificates

Highlight your new skills on your resume or LinkedIn.

Projects Overview

We’ll implement together an efficient program for a problem needed by delivery companies all over the world millions times per day — the travelling salesman problem. The goal in this problem is to visit all the given places as quickly as possible. How to find an optimal solution to this problem quickly? We still don’t have provably efficient algorithms for this difficult computational problem and this is the essence of the P versus NP problem, the most important open question in Computer Science. Still, we’ll implement several efficient solutions for real world instances of the travelling salesman problem. While designing these solutions, we will rely heavily on the material learned in the courses of the specialization: proof techniques, combinatorics, probability, graph theory. We’ll see several examples of using discrete mathematics ideas to get more and more efficient solutions.

Courses

Beginner Specialization.: No prior experience required.

COURSE 1
Mathematical Thinking in Computer Science
Commitment
6 weeks, 2–5 hours/week
Subtitles
English
About the Course
Mathematical thinking is crucial in all areas of computer science: algorithms, bioinformatics, computer graphics, data science, machine learning, etc. In this course, we will learn the most important tools used in discrete mathematics: in
You can choose to take this course only. Learn more.
COURSE 2
Combinatorics and Probability
Commitment
6 weeks, 3-5 hours/week
Subtitles
English
About the Course
Counting is one of the basic mathematically related tasks we encounter on a day to day basis. The main question here is the following. If we need to count something, can we do anything better than just counting all objects one by one? Do we need to
You can choose to take this course only. Learn more.
COURSE 3
Introduction to Graph Theory
Commitment
5 weeks, 3-5 hours/week
Subtitles
English
About the Course
We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of painting and the rigor of mathematics; is simple, but not unsophisticated. Graph Theory gives us, both an easy way to pictorially represent many major math
You can choose to take this course only. Learn more.
COURSE 4
Number Theory and Cryptography
Commitment
4 weeks, 2-5 hours/week
Subtitles
English
About the Course
We all learn numbers from the childhood. Some of us like to count, others hate it, but any person uses numbers everyday to buy things, pay for services, estimated time and necessary resources. People have been wondering about numbers’ properties for t
You can choose to take this course only. Learn more.
COURSE 5
Delivery Problem
Commitment
3 weeks of study, 2–5 hours/week
Subtitles
English
About the Course
We’ll implement (in Python) together efficient programs for a problem needed by delivery companies all over the world millions times per day — the travelling salesman problem. The goal in this problem is to visit all the given places as quickly as possible
You can choose to take this course only. Learn more.

Creators

Faculty of Computer Science (http://cs.hse.ru/en/) trains developers and researchers. The programme has been created based on the experience of leading American and European universities, such as Stanford University (U.S.) and EPFL (Switzerland). Also taken into consideration when creating the faculty was the School of Data Analysis, which is one of the strongest postgraduate schools in the field of computer science in Russia. In the faculty, learning is based on practice and projects.
National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communications, IT, mathematics, engineering, and more. Learn more on www.hse.ru
UC San Diego is an academic powerhouse and economic engine, recognized as one of the top 10 public universities by U.S. News and World Report. Faculty at the Computer Science and Engineering Department at UCSD are among the leaders in the field of algorithms, bioinformatics, cryptography, machine learning, and many other areas of computer science.
UC San Diego is an academic powerhouse and economic engine, recognized as one of the top 10 public universities by U.S. News and World Report. Innovation is central to who we are and what we do. Here, students learn that knowledge isn't just acquired in the classroom—life is their laboratory.