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.
Programa especializado Introduction to Discrete Mathematics for Computer Science
Build a Foundation for Your Career in IT. Master the math powering our lives and prepare for your software engineer or security analyst career
ofrecido por
University of California San Diego
National Research University Higher School of Economics
Programa especializado Introduction to Discrete Mathematics for Computer ScienceUniversity of California San Diego
Acerca de este Programa Especializado
Qué aprenderás
Apply basic algorithmic techniques such as greedy algorithms, binary search, sorting and dynamic programming to solve programming challenges.
Apply various data structures such as stack, queue, hash table, priority queue, binary search tree, graph and string to solve programming challenges.
Apply graph and string algorithms to solve real-world challenges: finding shortest paths on huge maps and assembling genomes from millions of pieces.
Solve complex programming challenges using advanced techniques: maximum flow, linear programming, approximate algorithms, SAT-solvers, streaming.
Habilidades que obtendrás
Graph TheoryNumber TheoryCryptographyProbability
Cómo funciona Programa Especializado
Toma cursos
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Proyecto práctico
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Obtén un certificado
Cuando completes todos los cursos y el proyecto práctico, obtendrás un Certificado que puedes compartir con posibles empleadores y tu red profesional.
Hay 5 cursos en este Programa Especializado
Curso1
Mathematical Thinking in Computer Science
4.5
336 calificaciones
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?
In the course, we use a try-this-before-we-explain-everything approach: you will be solving many interactive (and mobile friendly) puzzles that were carefully designed to allow you to invent many of the important ideas and concepts yourself.
Prerequisites:
1. We assume only basic math (e.g., we expect you to know what is a square or how to add fractions), common sense and curiosity.
2. Basic programming knowledge is necessary as some quizzes require programming in Python.
Curso2
Combinatorics and Probability
4.6
168 calificaciones
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.
In this course we discuss most standard combinatorial settings that can help to answer questions of this type. We will especially concentrate on developing the ability to distinguish these settings in real life and algorithmic problems. This will help the learner to actually implement new knowledge. Apart from that we will discuss recursive technique for counting that is important for algorithmic implementations.
One of the main `consumers’ of Combinatorics is Probability Theory. This area is connected with numerous sides of life, on one hand being an important concept in everyday life and on the other hand being an indispensable tool in such modern and important fields as Statistics and Machine Learning. In this course we will concentrate on providing the working knowledge of basics of probability and a good intuition in this area. The practice shows that such an intuition is not easy to develop.
In the end of the course we will create a program that successfully plays a tricky and very counterintuitive dice game.
As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.
Curso3
Introduction to Graph Theory
4.6
141 calificaciones
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.
In this course, among other intriguing applications, we will see how GPS systems find shortest routes, how engineers design integrated circuits, how biologists assemble genomes, why a political map can always be colored using a few colors. We will study Ramsey Theory which proves that in a large system, complete disorder is impossible!
By the end of the course, we will implement an algorithm which finds an optimal assignment of students to schools. This algorithm, developed by David Gale and Lloyd S. Shapley, was later recognized by the conferral of Nobel Prize in Economics.
As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.
Curso4
Number Theory and Cryptography
4.6
93 calificaciones
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!
As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.
Instructores
Alexander S. Kulikov
Visiting ProfessorDepartment of Computer Science and Engineering
Michael Levin
LecturerComputer Science
Vladimir Podolskii
Associate ProfessorComputer Science Department
Socios del sector
Acerca de University of California 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.
Acerca de National Research University Higher School of Economics
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
Preguntas Frecuentes
¿Cuál es la política de reembolsos?
¿Puedo inscribirme en un solo curso?
¡Sí! Para empezar, haz clic en la tarjeta del curso que te interesa e inscríbete. Puedes inscribirte y completar el curso para obtener un certificado que puedes compartir o puedes acceder al curso como oyente para ver los materiales del curso de manera gratuita. Cuando cancelas la suscripción de un curso que forma parte de un programa especializado, se cancela automáticamente la suscripción de todo el programa especializado. Visita el panel del estudiante para realizar un seguimiento de tu progreso.
¿Hay ayuda económica disponible?
¿Puedo tomar este curso de manera gratuita?
¿Este curso es 100 % en línea? ¿Necesito asistir a alguna clase en persona?
Este curso es completamente en línea, de modo que no necesitas ir a un aula en persona. Puedes acceder a tus lecciones, lecturas y tareas en cualquier momento y cualquier lugar a través de Internet o tu dispositivo móvil.
¿Recibiré crédito universitario por completar el programa especializado?
Este programa especializado no otorga crédito universitario, pero algunas universidades pueden aceptar los Certificados del programa especializado para el crédito. Consulta con tu institución para obtener más información.
¿Cuánto tiempo se necesita para completar un programa especializado?
Time to completion can vary based on your schedule, but most learners are able to complete the Specialization in 6-8 months.
What background knowledge is necessary?
As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.
Do I need to take the courses in a specific order?
We recommend taking the courses in the order presented, as each subsequent course will build on material from previous courses.
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