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.

Offered By

## Combinatorics and Probability

University of California San Diego## About this Course

## Skills you will gain

- Random Variable
- Probability Interpretations
- Probability
- Combinatorics

## Offered by

### 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.

## Syllabus - What you will learn from this course

**5 hours to complete**

## Basic Counting

Counting is one of the basic mathematically related tasks we encounter on a day to day basis. The main question here is the following: can we count the number of objects without listing all of them? This question arises naturally in various scenarios both in real life and in Computer Science. What is the number of different phone numbers or license plates? What is the number of different combinations one needs to brute force in order to crack a password? Is there a way to tell that an 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 consider the basic building blocks of combinatorics. All of them are easy to understand and at the same time are powerful enough to handle various non-trivial questions. To help you to develop an intuition, we consider short Python code snippets for generating the objects to be counted.

**5 hours to complete**

**4 hours to complete**

## 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 most 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 hours to complete**

**3 hours to complete**

## Advanced Counting

We have already considered most of the 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 hours to complete**

**5 hours to complete**

## 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 hours to complete**

## Reviews

- 5 stars70.48%
- 4 stars20.42%
- 3 stars6.97%
- 2 stars1.12%
- 1 star0.99%

### TOP REVIEWS FROM COMBINATORICS AND PROBABILITY

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.

the dainty old dude was the worst lecturer who rambled non-coherent nonsense. the younger folks were much better verbal communicators. overall great course!

Thank you for your course. The content was engaging, teachers were great. I was doing last exercise for long 5 hours to realize there was a simple mistake in my code, pure pleasure, excellent

Great lessons, great instructors, literacy slides, this course has everything. I'm so proud to complete two out of five courses in this specialization!

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