Foundations of Mathematics
Winter Semester 2021/22
Prof. Dr. Alexander Koller
Tue 16-18, Fr 12-14; mostly online
First class: Friday, October 22
Information on COVID-19: With the vaccination rate in the Saarland currently (early October 2021) just over 70%, I do not think we are quite ready to go back to meeting in person for this class. Because I am not allowed to enforce or check the 3G rules, I cannot guarantee that my classroom will be a safe and healthy environment for you. Therefore I will teach this class online for now.
I will track the development of the covid-19 incidence closely. If it remains stable despite the successively lifting of the restrictions, we may switch to physical teaching in January. I would very much like to meet you all in person, and I’m sure university is more fun for you as well when you get to meet each other, but I want to ensure we can do this safely.
This class is a newly designed introductory course to mathematics for computational linguists. It is used in two study programs:
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.
The course will be in English.
Für wen ist diese Vorlesung? Die Vorlesung ist eine Pflichtveranstaltung im BSc Computerlinguistik (Studienordnung von 2020). Wir empfehlen dringend, sie im dritten Semester zu belegen, damit Sie im vierten Semester die Vorlesung “Neural Networks: Implementation and Application” (Klakow) absolvieren können und dann die volle Auswahl unter den Seminaren haben, die Kenntnisse zu neuronalen Netzen voraussetzen.
Die Vorlesung und ihre Materialien sind auf Englisch, weil ich sie erstmals im WS 2020/21 für die Master-Studierenden gehalten habe. Wenn Sie möchten, können Sie mir dabei helfen, die Kursmaterialien auf Deutsch zu übersetzen; melden Sie sich bei Interesse gerne bei mir.
Sie können Fragen im Kurs gerne auf Deutsch stellen. Ich werde sie dann typischerweise auf Englisch beantworten. Wir werden außerdem viel Zeit in Breakout-Rooms verbringen, wo Sie gerne untereinander Deutsch sprechen können, wenn alle Anwesenden Deutsch können.
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 Google Classroom for all course activities. I will upload all course materials and assignments there, and I urge you to use the discussion forum.
Please join the Google Classroom for this course as soon as you can. You will need a free Google account to join Google Classroom.
Structure of the course. We will use an inverted classroom setting, in which you do all your studying in your own time, and we meet twice a week to work through exercises together and discuss any questions you might have.
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 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 2022, 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.