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.
Este curso forma parte de Programa Especializado - Introduction to Discrete Mathematics for Computer Science
ofrecido por
Universidad de California en San Diego
National Research University Higher School of Economics
Programa Especializado - Introduction to Discrete Mathematics for Computer ScienceUniversidad de California en San DiegoAcerca de este Curso
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Fechas límite flexibles
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Nivel principiante
Aprox. 20 horas para completar
Inglés (English)
Subtítulos: Inglés (English), Griego, Chino (simplificado)
Habilidades que obtendrás
Random VariableProbability InterpretationsProbabilityCombinatorics
Resultados profesionales del estudiante
33%
consiguió un beneficio tangible en su carrera profesional gracias a este curso
50%
consiguió un aumento de sueldo o ascenso
Certificado para compartir
Obtén un certificado al finalizar
100 % en línea
Comienza de inmediato y aprende a tu propio ritmo.
Fechas límite flexibles
Restablece las fechas límite en función de tus horarios.
Nivel principiante
Aprox. 20 horas para completar
Inglés (English)
Subtítulos: Inglés (English), Griego, Chino (simplificado)
ofrecido por
Universidad de California en 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.
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 communicamathematics, engineering, and more.
Programa - Qué aprenderás en este curso
3 horas para completar
Basic Counting
Suppose we need to count certain objects. Can we do anything better than just list all the objects? Do we need to create a list all phone numbers to check whether there are enough phone numbers for everyone? Is there a way to tell whether 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 module we will give an introduction to this field that will help us to answer basic versions of the above questions.
3 horas para completar
12 videos (Total 54 minutos), 4 lecturas, 9 cuestionarios
12 videos
Rule of Sum3m
How Not to Use the Rule of Sum3m
Convenient Language: Sets4m
Generalized Rule of Sum3m
Number of Paths4m
Rule of Product3m
Back to Recursive Counting3m
Number of Tuples5m
Licence Plates3m
Tuples with Restrictions5m
Permutations9m
4 lecturas
Slides1m
Slides1m
Listing All Permutations5m
Slides1m
8 ejercicios de práctica
Rule of Sum in Programming4m
Numbers Divisible by 2 or 38m
Operations with Sets10m
Generalized Rule of Sum18m
Rule of Product in Programming10m
Applications of the Rule of Product12m
Tuples5m
Counting with Restrictions20m
4 horas para completar
Binomial Coefficients
In how many ways one can select a team of five students out of ten students? What is the number of non-negative integers with at five digits whose digits are decreasing? In how many ways one can get from the bottom left cell to the top right cell of a 5x5 grid, each time going either up or to the right? And why all these three numbers are equal? We'll figure this out in this module!
4 horas para completar
8 videos (Total 76 minutos), 4 lecturas, 6 cuestionarios
8 videos
Number of Games in a Tournament10m
Combinations8m
Pascal's Triangle9m
Symmetries4m
Row Sums10m
Binomial Theorem12m
Practice Counting13m
4 lecturas
Generating Combinatorial Objects: Code10m
Slides10m
Slides10m
Slides10m
6 ejercicios de práctica
Number of Segments and Diagonals20m
Forming Sport Teams15m
Number of Iterations of Nested For Loops30m
Sum of the First Six Rows of Pascal's Triangle30m
Expanding (3a-2b)^k20m
Practice Counting30m
3 horas para completar
Advanced Counting
We have already considered most of the most standard settings in Combinatorics, that allow us to address many counting problems. However, successful application of this knowledge on practice requires considerable experience in this kind of problems. In this module we will address the final standard setting in our course, combinations with repetitions, and then we will gain some experience by discussing various problems in Combinatorics.
3 horas para completar
8 videos (Total 36 minutos), 3 lecturas, 8 cuestionarios
8 videos
Review3m
Salad5m
Combinations with Repetitions7m
Distributing Assignments Among People3m
Distributing Candies Among Kids3m
Numbers with Fixed Sum of Digits4m
Numbers with Non-increasing Digits2m
Splitting into Working Groups4m
3 lecturas
Salads10m
Slides1m
Slides1m
8 ejercicios de práctica
Salads10m
Combinations with Repetitions10m
Distributing Assignments Among People10m
Distributing Candies Among Kids15m
Numbers with Fixed Sum of Digits15m
Numbers with Non-increasing Digits7m
Splitting into Working Groups10m
Problems in Combinatorics45m
5 horas para completar
Probability
The word "probability" is used quite often in the everyday life. However, not always we can speak about probability as some number: for that a mathematical model is needed. What is this mathematical model (probability space)? How to compute probabilities (if the model is given)? How to judge whether the model is adequate? What is conditional probability and Bayes' theorem? How our plausible reasoning can be interpreted in terms of Bayes' theorem? In this module we cover these questions using some simple examples of probability spaces and real life sutiations.
5 horas para completar
17 videos (Total 126 minutos), 4 lecturas, 11 cuestionarios
17 videos
Galton Board6m
Natural Sciences and Mathematics6m
Rolling Dice7m
More Probability Spaces10m
Not Equiprobable Outcomes4m
More About Finite Spaces6m
Mathematics for Prisoners7m
Not All Questions Make Sense10m
What Is Conditional Probability?7m
How Reliable Is The Test?8m
Bayes' Theorem8m
Conditional Probability: A Paradox7m
Past and Future8m
Independence8m
Monty Hall Paradox8m
`Our Position'6m
4 lecturas
Slides
Slides
Slides
Slides
10 ejercicios de práctica
Concentration for Galton Board10m
Computing Probabilities for Two Dice12m
Computing Probabilities: More Examples12m
Fair Decisions and Imperfect Coins20m
Inclusion-Exclusion Formula10m
Computing Conditional Probabilities16m
Prisoner, King and Conditional Probabilities10m
More Conditional Probabilities8m
More About Independence20m
Monty Hall Gone Crazy20m
Revisiones
Principales revisiones sobre COMBINATORICS AND PROBABILITY
por MT31 de jul. de 2020
Great course. The final Project unclear had instructions on how to provide input. I spent a lot of time trying to troubleshoot it even though I already have a correct solution
por UV22 de ene. de 2020
This course provided me with new ways to confront the problems of combinatorics. I am very grateful to the faculty for their content and coursera for giving me financial aid.
por KB25 de dic. de 2019
Great course, lots of good info, not too long. Some of the coding assignments and quizzes are challenging, but the staff respond very quickly to questions in the forums.
por PR2 de ago. de 2019
Had loads of fun during most part of the course. Frequent quizzes keep the learner on toes. Thoroughly enjoyed the final programming quiz to implement a dice game.
Acerca de Programa especializado: Introduction to Discrete Mathematics for Computer Science
Discrete Mathematics is the language of Computer Science. One needs to be fluent in it to work in many fields including data science, machine learning, and software engineering (it is not a coincidence that math puzzles are often used for interviews). We introduce you to this language through a fun try-this-before-we-explain-everything approach: first you solve many interactive puzzles that are carefully designed specifically for this online specialization, and then we explain how to solve the puzzles, and introduce important ideas along the way. We believe that this way, you will get a deeper understanding and will better appreciate the beauty of the underlying ideas (not to mention the self confidence that you gain if you invent these ideas on your own!). To bring your experience closer to IT-applications, we incorporate programming examples, problems, and projects in the specialization.
Preguntas Frecuentes
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¿Qué recibiré si me suscribo a este Programa especializado?
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Sí, Coursera ofrece ayuda económica a los estudiantes que no pueden pagar la tarifa. Solicítala haciendo clic en el enlace de Ayuda económica que está debajo del botón “Inscribirse” a la izquierda. Se te pedirá que completes una solicitud. Recibirás una notificación en caso de que se apruebe. Deberás completar este paso para cada uno de los cursos que forman parte del Programa especializado, incluido el proyecto final. Obtén más información.
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