## Admission requirements

Students are expected to have followed Wiskunde B in their middle schools, or an equivalent course if from abroad. That is, students are expected to know elementary functions such as polynomials, rational functions, exponentials and logarithms, and trigonometric functions. Students are also expected to have been exposed to differential and integral calculus beforehand.

## Description

In this course we will learn the foundational calculus that is needed for any statistician. The material taught will come up repeatedly in future courses in the Statistics and Data Science programme.

After a brief review of basic functions, sets, and important mathematical notation, students will learn about continuity of functions and then what it means for a function to be differentiable. We'll continue to discuss differentiation and how it's used to explain important properties of functions such as maxima/minima and the shape of graphs. We'll conclude this first part by looking at approximations of functions and briefly discuss Taylor's theorem.

The second part is focused on integration. We'll learn what an integral is and techniques of integration, and relate the integral to derivatives via the Fundamental Theorem of Calculus.

We will conclude by briefly looking at multivariate calculus, i.e. calculus of functions with more than one variable. This is needed in the most elementary applications in statistics, such as finding the line of best fit of a data set. We'll cover partial derivatives and how they can inform us about local maxima/minima.

## Course objectives

- Students will be able to use elementary functions and mathematical notation in applied problems, where they directly model a scenario using mathematics and use the equations to understand more about the scenario.
- Students will understand the meaning of the derivative and be able to compute derivatives of diverse functions.
- Students can use the derivative to find maxima and minima of functions, including in applied scenarios, and can use the derivative to draw functions.
- Students will be able to approximate functions using Taylor polynomials and use Taylor's theorem to interpret how good an approximation is.
- Students will understand the meaning of the integral and be able to compute integrals using various techniques.
- Students can use the integral in applied scenarios to find the total rate of change of something via the Net Change Theorem.
- Students will be able to compute partial derivatives of multivariate functions. They will be able to find the local minima/maxima of multivariate functions and use this to be able to compute a line of best fit of a small data set.

## Timetable

In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.

Additionally, you can easily link MyTimetable to a calendar app on your phone, and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.

Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.

**Note:** Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.

## Mode of Instruction

This course is taught in-person. Students will have 2 hours of lectures and 2 hours of tutorials each week. It is expected that students go through a weekly reading before each lecture and that they are active in their learning process via trying practice problems.

## Assessment method

The final grade is the best of the following marking schemes:

Scheme 1: Exam: 100%

Scheme 2: Exam: 70%, Homework: 30%

## Reading List

Course notes, plus additional optional readings from:

Calculus a complete course – tenth edition,

Robert A. Adams & Christopher Essex, 2021, Pearson Education Canada ISBN 9780135732588

## Registration

As a student, you are responsible for enrolling on time through MyStudyMap.

In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.

Extensive information about the operation of MyStudyMap can be found here.

There are two enrolment periods per year:

Enrolment for the fall opens in July

Enrolment for the spring opens in December

See this page for more information about deadlines and enrolling for courses and exams.

**Note:**

It is mandatory to enrol for all activities of a course that you are going to follow.

Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.

Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.

## Contact

Garnet Akeyr, g.j.akeyr@math.leidenuniv.nl

## Remarks

This course is one of the two homologation courses of the master Statistics and Data Science, the other homologation course is Empirical Research in the Life and Behavioural Sciences. It is mandatory to follow at least one of the two homologation courses. Students with a substantive Bachelor’s degree such as bachelor degrees in the life and behavioral sciences, need to follow this course Mathematics for Statisticians.

**Software**

Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.