# Mathematical Reasoning

Course
2015-2016

## Tags

First-year programme.

LUC offers two first-year mathematics courses in parallel: Mathematical Modelling and Mathematical Reasoning. Both courses assume that students satisfy the LUC mathematics admission requirements (see ‘remarks’ below for further details).

The Mathematical Reasoning course requires less mathematical proficiency than the Mathematical Modelling course. Students who are more comfortable with basic numerical computations rather than complex symbolic manipulation and do not plan to follow higher-level mathematics and modelling courses are advised to choose the Mathematical Reasoning course.

## Description

The goal of this course is for students to understand how to apply basic mathematics to address complex – real world – problems.

The basic mathematical concepts and procedures that you have learned up to now can be considered as ‘mathematical tools’. In high school students are taught how to use these tools by applying them to carefully selected problems, where the required procedure is made explicitly clear. For instance, you may have practiced finding the maximum of a quadratic function, by determining the maximum profit of a shoe manufacturer, given sales, prices, and production costs. If all is well, you now are able to handle the mathematical tools that you have acquired at school properly and accurately.

Most real world applications, however, require a more sophisticated approach. Because the problems involved are far more complex than school textbook examples, it is usually not immediately clear which mathematical procedures are best suited to tackle complex issues. Applying mathematics to solve such problems requires an ability to reduce a problem’s complexity and select the proper tools.

Therefore, Mathematical Reasoning does not set out to teach new mathematical concepts and techniques, but instead is oriented towards showing you how to meaningfully utilize the mathematical knowledge and skills that you already possess. The course introduces you to a different way of approaching problems, from the standpoint of real world contexts and complex situations.

Mathematical Reasoning allows you to get a grip on problems that seem, at first sight, too complex, or even impossible to solve, learning from them, and posing your own questions. We will describe and exemplify the distinct phases that you encounter when developing arguments and predictions about reality, and show effective strategies for use in each of these stages. An underlying aim of the course is that you start to develop your own, individual problem solving strategies. To illustrate its application, we will study examples of mathematical reasoning in complex – real world – settings.

## Course objectives

After the course students should be able to:

• Describe the role of mathematical reasoning in the context of global challenges;

• Apply problem solving strategies to a selection of problems;

• Apply mathematical reasoning and basic mathematical procedures to gain insight in (not too complex) practical applications

• Evaluate results of applied mathematical reasoning in practical contexts.

## Timetable

Once available, timetables will be published here.

## Mode of instruction

A limited amount of lecturing. Most class time will be spent on group assignments and discussions. This course uses inquiry-based learning, where students are guided to discoveries, by working on assignments that lead step-by-step from exploration to insight.

## Assessment

In-class participation: 10%
Midterm exam: 30%
In class assignments: 30%
Individual assignment: 30%

## Blackboard

There will be a Blackboard site available for this course. Students will be enrolled at least one week before the start of classes.

Quantitative Reasoning and the Environment, Greg Langkamp and Joseph Hull, 2006 (1st edition), Pearson Education Inc. (Note: Pearson copyright is 2007)
ISBN-10: 013148527X; ISBN-13: 9780131485273

## Registration

This course is open to LUC students and LUC exchange students. Registration is coordinated by the Curriculum Coordinator. Interested non-LUC students should contact course.administration@luc.leidenuniv.nl.

## Contact

Dr. P. Haccou (convener): p.haccou@luc.leidenuniv.nl

## Remarks

It is assumed that students have a good working knowledge of the following concepts and techniques: arithmetic and algebraic computation, standard functions (polynomials, power functions, exponentials and logarithms), trigonometry, and functions and graphs. Students are advised to review these concepts and techniques before the onset of the course. If needed, students may make use of the two-week preparatory remedial course in January, and/or quantitative/math student assistants provided by LUC. Additional “self-study” materials are available in the form of online resources (for information consult the course convener).