Math109
Combinatorics & Probability
Faculty
Anier Velasco Sotomayor
Lead at the ML Theory group at Cohere for AI Open Science community.
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
Combinatorics and probabilities are important topics in any modern technical program in higher education. They’re relevant in many other areas, such as statistics or algorithms.
Learning highlights
- With this course, students will develop an understanding of modelling, counting methods, and combinatorial structures and will start their journey in probabilities by discussing fundamental topics like independence, linearity of expectation, conditional probabilities, and Bayes’ theorem.
Course outline
15 classes
Session 1
Proofs. Mathematical induction. Pigeonhole Principle.
Session 2
Set Theory summary. Inclusion-exclusion Principle.
Session 3
Modelling. Addition and multiplication principles. Inclusion-Exclusion Principle in counting.
Session 4
Permutations. Combinations. Binomial coefficients. Binomial Theorem.
Session 5
Recurrence relations. Telescopic sums and products. Famous recurrences.
Session 6
Generating functions. Catalan numbers, Stirling numbers, Bernoulli numbers.
Session 7
Graphs.
Session 8
Practice day.
Session 9
Midterm exam.
Session 10
Discrete and continuous probabilities. Random variables.
Session 11
Geometric probabilities.
Session 12
Conditional probability. Bayes’ Theorem.
Session 13
Expectancy. Linearity of expectation. Variance.
Session 14
Probability distributions. Common distributions.
Session 15
Final exam.
Methodology
There will be theoretical lectures and practice seminars. Participation by the students is highly encouraged
Grading
Anier started in computer science by doing programming Olympiads in high school, during which he obtained a gold medal in the Cuban National Olympiad and a bronze medal in the Ibero-American Olympiad in Informatics.
He has a BSc. in Computer Science and Data Science from Harbour.Space University. His main professional interest is Machine Learning Theory Research, and he’s an independent researcher.
See full profileApply for this course
Combinatorics & Probability
by Anier Velasco Sotomayor
Total hours
45 Hours
Dates
Apr 08 - Apr 26, 2024
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.