Spécialisation Introduction to Discrete Mathematics for Computer Science
Learn the language of Computer Science. Learn the math that defines computer science, and practice applying it through mathematical proofs and Python code
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Compétences que vous acquerrez
À propos de ce Spécialisation
Projet d'apprentissage appliqué
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.
Aucune connaissance prérequise.
Aucune connaissance prérequise.
Comment fonctionne la Spécialisation
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Une Spécialisation Coursera est une série de cours axés sur la maîtrise d'une compétence. Pour commencer, inscrivez-vous directement à la Spécialisation ou passez en revue ses cours et choisissez celui par lequel vous souhaitez commencer. Lorsque vous vous abonnez à un cours faisant partie d'une Spécialisation, vous êtes automatiquement abonné(e) à la Spécialisation complète. Il est possible de terminer seulement un cours : vous pouvez suspendre votre formation ou résilier votre abonnement à tout moment. Rendez-vous sur votre tableau de bord d'étudiant pour suivre vos inscriptions aux cours et vos progrès.
Projet pratique
Chaque Spécialisation inclut un projet pratique. Vous devez réussir le(s) projet(s) pour terminer la Spécialisation et obtenir votre Certificat. Si la Spécialisation inclut un cours dédié au projet pratique, vous devrez terminer tous les autres cours avant de pouvoir le commencer.
Obtenir un Certificat
Lorsque vous aurez terminé tous les cours et le projet pratique, vous obtiendrez un Certificat que vous pourrez partager avec des employeurs éventuels et votre réseau professionnel.

Cette Spécialisation compte 5 cours
Mathematical Thinking in Computer Science
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: induction, recursion, logic, invariants, examples, optimality. We will use these tools to answer typical programming questions like: How can we be certain a solution exists? Am I sure my program computes the optimal answer? Do each of these objects meet the given requirements?
Combinatorics and Probability
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 create a list of all phone numbers to ensure that there are enough phone numbers for everyone? Is there a way to tell that our algorithm will run in a reasonable time before implementing and actually running it? All these questions are addressed by a mathematical field called Combinatorics.
Introduction to Graph Theory
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 mathematical results, and insights into the deep theories behind them.
Number Theory and Cryptography
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 thousands of years. And for thousands of years it was more or less just a game that was only interesting for pure mathematicians. Famous 20th century mathematician G.H. Hardy once said “The Theory of Numbers has always been regarded as one of the most obviously useless branches of Pure Mathematics”. Just 30 years after his death, an algorithm for encryption of secret messages was developed using achievements of number theory. It was called RSA after the names of its authors, and its implementation is probably the most frequently used computer program in the word nowadays. Without it, nobody would be able to make secure payments over the internet, or even log in securely to e-mail and other personal services. In this short course, we will make the whole journey from the foundation to RSA in 4 weeks. By the end, you will be able to apply the basics of the number theory to encrypt and decrypt messages, and to break the code if one applies RSA carelessly. You will even pass a cryptographic quest!
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Université de Californie à San Diego
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.

Université HSE
HSE University 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 communicamathematics, engineering, and more.

Foire Aux Questions
Puis-je obtenir des crédits universitaires si je réussis la Spécialisation ?
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Puis-je suivre le cours gratuitement ?
Ce cours est-il vraiment accessible en ligne à 100 % ? Dois-je assister à certaines activités en personne ?
Quelle est la durée nécessaire pour terminer la Spécialisation ?
Do I need to take the courses in a specific order?
Will I earn university credit for completing the Specialization?
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