Math108
Combinatorics & Probability
Faculty
David Zmiaikou
PhD, Lecturer at the Belarusian State University
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
Probability theory plays a significant role in science, finance and industry. Whenever there is a non-deterministic experiment, one would like to describe possible outcomes and measure their likelihoods (in other words, to find their probabilities). During this course, we will give an elementary outline of probability with examples and applications. We will start by explaining relevant counting tools and strategies. Then we will introduce probability and give useful properties.
Learning highlights
- Get a vivid introduction to probability theory by uncovering its basic notions and techniques
- Know how to compute the number of permutations and combinations
- Know how to compute the probability of an event
- Be familiar with the notions of independent events and conditional probability
- Be able to apply Bayes’ rule
- Be familiar with the notions of random variables and their distributions
- Know how to compute the expected value and variance of a discrete random variable
Course outline
15 classes
Session 1
The Multiplication and Addition Principles The Principle of Inclusion-Exclusion
Session 2
Permutations and Combinations
Session 3
Applications of Permutations and Combinations
Session 4
The Pigeonhole Principle
Session 5
The Probability of an Event - 1
Session 6
Review and Midterm 1
Session 7
The Probability of an Event - 2
Session 8
Conditional Probability Independent Events
Session 9
Random Variables
Session 10
Expected Values
Session 11
Review and Midterm 2. Project - Modeling
Session 12
Problem Solving
Session 13
Problem Solving
Session 14
Problem Solving
Session 15
Final Exam
Course materials
Books
Methodology
Each three-hour session will consist partly of a lecture given by the professor and partly of a practical session, where students will try to solve problems (related to the subject of the day) under the professor's supervision. There will also be some classroom discussions. In order to further improve understanding of the taught material, homework will be assigned after every session. There will be two interim tests after each of the first two weeks and a final exam at the end of the module.
Grading
David Zmiaikou graduated from the Ecole Polytechnique in France, and obtained his Ph.D. degree at the University Paris-Sud under the supervision of Professor Jean-Christophe Yoccoz (Fields Medal).
After that, he did his postdoctoral research in Mathematics in Rio de Janeiro, Vienna, Zurich, Bures-sur-Yvette and Bonn, and worked in DNA Analysis at Sanger Institute near Cambridge.
See full profileApply for this course
Combinatorics & Probability
by David Zmiaikou
Total hours
45 Hours
Dates
Mar 14 - Apr 01, 2022
Fee for single course
€1500
Fee for degree students
€750
How to secure your spot
Complete the form below to kickstart your application
Schedule your Harbour.Space interview
If successful, get ready to join us on campus
FAQ
Will I receive a certificate after completion?
Yes. Upon completion of the course, you will receive a certificate signed by the director of the program your course belonged to.
Do I need a visa?
This depends on your case. Please check with the Spanish or Thai consulate in your country of residence about visa requirements. We will do our part to provide you with the necessary documents, such as the Certificate of Enrollment.
Can I get a discount?
Yes. The easiest way to enroll in a course at a discounted price is to register for multiple courses. Registering for multiple courses will reduce the cost per individual course. Please ask the Admissions Office for more information about the other kinds of discounts we offer and what you can do to receive one.