# Mathematical Reasoning

Vak
2021-2022

None.

This course requires less mathematical proficiency than the Mathematical Modelling course and focuses more on computations than the theory behind the mathematics. Those who do not intend to take additional mathematics courses at the LUC are encouraged to take Mathematical Reasoning.

For both courses it is assumed that students satisfy the LUC mathematics admission requirements. If needed, they may make use of the two-week preparatory remedial course in January.

Students are assumed to have a basic familiarity with polynomials, as well as in manipulating equations to isolate a variable. Those who do not feel comfortable with these topics are advised to review these subjects before the first lecture via a document to be made available on Brightspace.

## Description

This course begins with a review and introduction of the mathematical foundations needed later in the course, including functions such as the exponential and logarithmic function, and trigonometric functions. The latter half of the course is devoted to studying rates of change and optimisation problems, and serves as an introduction to differential calculus. At all points throughout the block, examples will be drawn from areas such as physics, economics, biology, chemistry, population dynamics, and the environmental sciences.

## Course Objectives

Skills
After successful completion of this course, students will be able to:

• Compute the derivatives of advanced functions and interpret the derivative as a rate of change.

• Solve optimization problems where a maximal / minimal answer is desired subject to constraints.

• Work with derivatives in the context of real-world scenarios, drawn from economics, the physical sciences, and population dynamics.

Knowledge
After successful completion of this course, students will know and understand:

• How to work with basic functions, including polynomials, trigonometric functions, exponential functions, and compositions of these functions with one another.

• The meaning of the derivative of a function both as the slope of a tangent line, and as rate of change of some phenomenon.

• The relevance and ubiquity of differential calculus in numerous fields, such as in marginal cost in economics, the relationship between distance, velocity, and acceleration in physics, and in regression models used everywhere in machine learning.

## Timetable

Timetables for courses offered at Leiden University College in 2021-2022 will be published on this page of the e-Prospectus.

## Mode of instruction

This course will be taught via live lectures, where all the new material will introduced and explained. Students will also be given an exercise sheet at the end of each lecture that they are encouraged to work through to cement their understanding of the subject. If in-person lectures are not possible, this course will be taught live over MS Teams. Students will be added to their team before the first lecture.

Short, online quizzes (

## Assessment Method

Quizzes (available after every lecture): 25%
Essay / participation: 5%
Homework assignments: 30%
Final exam: 40%

The primary reading material is typewritten notes available on Brightspace. Students are encouraged to look at the reading material for each lecture before the lecture itself.

Those who wish for additional resources are encouraged to look at Volume 1 of the Openstax Calculus textbook, available here:

https://openstax.org/details/books/calculus-volume-1

## Registration

Courses offered at Leiden University College (LUC) are usually only open to LUC students and LUC exchange students. Leiden University students who participate in one of the university’s Honours tracks or programmes may register for one LUC course, if availability permits. Registration is coordinated by the Education Coordinator, course.administration@luc.leidenuniv.nl.

## Contact

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

-