Course syllabus

Welcome to the introductory course in mathematics for language technology! This course is given, together with programming, to introduce (or remind) you of the basic skills needed for working with computational methods. The goal will be to ensure that everyone has a sufficient understanding of the fundamentals of mathematics for natural language processing (which is both a field and a course starting in November). All content is chosen to be useful in our future courses. While some concepts will be directly applicable already in November, other parts are aimed toward training your mathematical thinking. Usually, spread of skill level between students is between not having studied (or hardly used) maths for years to having taken university courses recently. As this course aims to prepare you for coming courses, we will focus mostly on you who are feeling nervous while reading this. Good luck! :)

"Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. One goes into the first room, and it’s dark, completely dark. One stumbles around bumping into the furniture, and gradually, you learn where each piece of furniture is, and finally, after six months or so, you find the light switch. You turn it on, and suddenly, it’s all illuminated. You can see exactly where you were." - Andrew Wiles

This course is, roughly, split into four parts defined by the learning outcomes from the "course syllabus with course literature". Every course at Uppsala University has a legally binding syllabus that, in the abstract, defines the course content (not to be confused with the studium syllabus page which you are looking at right now).

Lecture format

The lectures will be given as a pragmatic mix of traditional lecturing, exercises, and labs. You will find lecture content, code, slides etc. in the lecture plan.

The lectures will primarily be given as IRL events. However, if you for whatever good reason can't join us physically, please join via video stream. You can find the zoom room invitation here. Also, feel free to use the zoom room as a place for a digital study group. Contact the lecturer to ensure that the lecture will be streamed.

There is a preliminary plan to hire a TA and have some type of support sessions.

Course literature

All literature can be downloaded for free.

ST: David M Diez, Christopher D Barr, Mine Çetinkaya-Rundel (2019), OpenIntro Statistics. Free pdf from

LA: Géza Schay (2012), A Concise Introduction to Linear Algebra, Birkhäuser. Free pdf, for UU students, at the UU library (direct link).

PSA (optional): Géza Schay (2016), Introduction to Probability with Statistical Applications, Birkhäuser. Free pdf, for UU students, at the UU library

OpenIntro Statistics has video clips on their website and even a book in high school statistics. Use these extra resources if you need them. When it comes to basic mathematical concepts, you can find plenty of useful introductory material on the web, e.g. lectures on YouTube, Khan academy, wolfram alpha, 3blue1brown, slides from other courses, and many good textbooks.

The code shown in the lectures will (or is already) available at Please experiment to your heart's content.


All lectures will be given by Fredrik Wahlberg, whom you can find in office 9-2041 or reach by email.

All lessons are given by Paloma García de Herreros García, whom you can reach by email.

Assessment and grading

You complete the course by doing two two-hour written tests: Dugga 1 (covering Sets & Probability) and Dugga 2 (covering Statistics & Linear algebra). The tests have equal weight. Pass (G): at least 60% correct on each test. Pass with distinction (VG): at least 80% correct on the two tests added. There will be a second opportunity to take both tests on the 24th of November, with four hours for both parts (i.e. as one four-hour test). You cannot retake a test which you have passed.

For each exam, you will likely be allowed to bring any notes you have written yourself (by hand, with a pen) and a simple calculator (see slides for details). You will also be provided with necessary distribution tables etc. We will discuss the details closer to the exams and find a way for a fair exam given future potential COVID problems and remote participation.

Old exams

Usually, the easiest way to pass a mathematics course is to look at old exams (caution: older exams reflect an older curriculum). The old exams are good for checking your skill, but don't be alarmed when you see content you are not familiar with from this iteration of the course. Please ask at the lectures if you are unsure of what is included this year.

Course summary:

Date Details Due