Math106
Discrete Mathematics
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
In this course, students will learn how to formally write mathematical ideas via notions of logic, quantifiers and basic set theory. They will also have an overview of Number Theory and discrete probability.
The continuation of this course of Discrete Mathematics is the course of Combinatorics and Graphs. It's important for the students to take both courses. After these two courses, the students will have enough skills to apply them in other courses like Intro to Probabilities and Statistics, and Algorithms and Data Structures.
Learning highlights
- Understanding and using logic statements in mathematics.
- Basics of set theory.
- Formally proving a mathematical concept.
- Basics of group theory, applicable in number theory.
- Basic results from Number Theory that are applicable in Cryptography.
- Elements of discrete probabilities.
Course outline
15 classes
Session 1
Set Theory
Session 2
Set Relations
Session 3
Logic
Session 4
Set functions
Session 5
Logical functions
Session 6
Review of proof techniques
Session 7
Midterm + Review
Session 8
Recursion
Session 9
Intro to Number Theory
Session 10
Group theory and applications in number theory
Session 11
More about Number Theory
Session 12
Discrete Probabilities
Session 13
General review
Session 14
Final exam
Session 15
Snow Summit
Course materials
Books
Prerequisites
The students must have algebraic and proving skills, thus it’s a requirement that they have passed the course ‘Intro to higher mathematics’ successfully.
Methodology
Each class will consist of a theoretical part illustrated by examples and exercises. Students are encouraged to try and solve these exercises during class and to ask as many questions as possible; there will be room for open discussion and questions.
There will be daily assignments, to be submitted after each class. At the end of each week, there will be a discussion of the assignments of the week.
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
Discrete Mathematics
by Anier Velasco Sotomayor
Total hours
42 Hours
Dates
Jan 13 - Jan 30, 2025
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.