Foundations of Mathematics

Winter Semester 2020/21
Prof. Dr. Alexander Koller
Tue 16-18, Fr 12-14; mostly online

First class: Friday, November 6

Information on COVID-19: Due to the ongoing COVID-19 pandemic, this lecture will be primarily taught online. Please let me know by October 25 (or earlier) that you would like to take this class by filling out this Google form. I will then be in touch before classes start with more details.

The course “Foundations of Mathematics” is a newly designed introductory course to mathematics for computational linguists. The goal is to equip students with the mathematical background that is necessary to understand neural networks in technical detail and not be scared of the formulas in current research papers. The course covers the fundamentals of linear algebra (vector spaces, linear transformations, matrices and matrix arithmetic, dot products and angles) and calculus (derivatives, computing derivatives, limits, integrals, gradients). These will culminate in an explanation of the backpropagation algorithm.

Who should take this course? The course is meant to provide students who did not take college-level classes on linear algebra and calculus in their first degree with the basics of these fields. Such students should treat this course as mandatory for the MSc LST/LCT, even if the study regulations don’t say it explicitly.

By contrast, students who have taken such classes in their first degrees (e.g. students with a BSc in mathematics or computer science) should not take this class. It would be a waste of your time, and we strongly encourage you to take other classes where you will learn something new.

Online learning platform. We will make heavy use of the online learning platform Moodle for all course activities. I will upload all course materials and assignments there, and I urge you to use the discussion forum. Long story short, please join the Moodle page for this course as soon as you can. (Note that this is the university’s Moodle server, and you need a university account to log in.)

Structure of the course. We will explore an inverted classroom setting, in which you do all your studying at home, and we meet twice a week to work through exercises together and discuss anything that is not clear. We will make heavy use of the fantastic Youtube channel 3Blue1Brown, in particular its playlists on the Essence of Linear Algebra and Essence of Calculus. Feel free to start watching these videos right now. I will also sometimes assign reading to cover the same topics, in order to add some more depth and familiarize you with reading mathematical texts.

Prerequisites. The course does not assume any prior knowledge beyond high-school math. We will occasionally explore Python libraries for linear algebra and calculus; for these exercises, some basic familiarity for working with Python will be useful.

Grading. This class is worth 6 credit points, which translates into 180 hours of work. Please schedule your semester accordingly.

Your grade for the course will be determined in a final written exam at the end of the semester (early February 2021, exact date TBA). You will have to be physically present in Saarbrücken for this exam.

Because of the flipped classroom format, it is extremely important to me that you participate actively in the interactive sessions.