Este curso faz parte do Programa de cursos integrados Introduction to Discrete Mathematics for Computer Science

oferecido por

University of California San Diego

National Research University Higher School of Economics

Programa de cursos integrados Introduction to Discrete Mathematics for Computer Science

University of California San Diego

Informações sobre o curso

4.6

164 classificações

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36 avaliações

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.

Comece imediatamente e aprenda em seu próprio cronograma.

Redefinir os prazos de acordo com sua programação.

Sugerido: 6 weeks, 3-5 hours/week ...

Legendas: Inglês

Random VariableProbability InterpretationsProbabilityCombinatorics

Comece imediatamente e aprenda em seu próprio cronograma.

Redefinir os prazos de acordo com sua programação.

Sugerido: 6 weeks, 3-5 hours/week ...

Legendas: Inglês

Semana

1Suppose 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....

12 videos (Total 54 min), 4 leituras, 9 testes

Why counting2min

Rule of Sum3min

How Not to Use the Rule of Sum3min

Convenient Language: Sets4min

Generalized Rule of Sum3min

Number of Paths4min

Rule of Product3min

Back to Recursive Counting3min

Number of Tuples5min

Licence Plates3min

Tuples with Restrictions5min

Permutations9min

Slides1min

Slides1min

Listing All Permutations5min

Slides1min

Rule of Sum in Programming4min

Numbers Divisible by 2 or 38min

Operations with Sets10min

Generalized Rule of Sum18min

Rule of Product in Programming10min

Applications of the Rule of Product12min

Tuples5min

Counting with Restrictions20min

Semana

2In 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!...

8 videos (Total 76 min), 4 leituras, 6 testes

Number of Games in a Tournament10min

Combinations8min

Pascal's Triangle9min

Symmetries4min

Row Sums10min

Binomial Theorem12min

Practice Counting13min

Generating Combinatorial Objects: Code10min

Slides10min

Slides10min

Slides10min

Number of Segments and Diagonals20min

Forming Sport Teams15min

Number of Iterations of Nested For Loops4min

Sum of the First Six Rows of Pascal's Triangle2min

Expanding (3a-2b)^k20min

Practice Counting10min

Semana

3We 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....

8 videos (Total 36 min), 3 leituras, 8 testes

Review3min

Salad5min

Combinations with Repetitions7min

Distributing Assignments Among People3min

Distributing Candies Among Kids3min

Numbers with Fixed Sum of Digits4min

Numbers with Non-increasing Digits2min

Splitting into Working Groups4min

Salads10min

Slides1min

Slides1min

Salads10min

Combinations with Repetitions10min

Distributing Assignments Among People10min

Distributing Candies Among Kids15min

Numbers with Fixed Sum of Digits15min

Numbers with Non-increasing Digits7min

Splitting into Working Groups10min

Problems in Combinatorics45min

Semana

4The 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....

17 videos (Total 126 min), 4 leituras, 11 testes

Galton Board6min

Natural Sciences and Mathematics6min

Rolling Dice7min

More Probability Spaces10min

Not Equiprobable Outcomes4min

More About Finite Spaces6min

Mathematics for Prisoners7min

Not All Questions Make Sense10min

What Is Conditional Probability?7min

How Reliable Is The Test?8min

Bayes' Theorem8min

Conditional Probability: A Paradox7min

Past and Future8min

Independence8min

Monty Hall Paradox8min

`Our Position'6min

Slides0

Slides0

Slides0

Slides0

Concentration for Galton Board10min

Computing Probabilities for Two Dice12min

Computing Probabilities: More Examples12min

Fair Decisions and Imperfect Coins20min

Inclusion-Exclusion Formula10min

Computing Conditional Probabilities16min

Prisoner, King and Conditional Probabilities10min

More Conditional Probabilities8min

More About Independence20min

Monty Hall Gone Crazy20min

consegui um benefício significativo de carreira com este curso

por ZB•Oct 13th 2018

I really enjoyed taking this course. The teaching was pretty good and some of the quiz questions will challenge you if you haven't done Combinatorics before.

por CZ•Sep 11th 2018

The final project is hard for me cuz I don't have Python experience. and the logic is a little bit complicated. That's not for absolutely beginners!

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 (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...

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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