This is the final report written by **Group 60** (FIRE) for the mathematical modelling course (**DAT026**) at Chalmers University of Technology.

Group 60 consists of:

**Mazdak Farrokhzad**901011-0279

twingoow@gmail.com

Program: IT

Time spent: \(22\) hours, \(06\) minutes

**Niclas Alexandersson**920203-0111

nicale@student.chalmers.se

Program: IT

Time spent: \(31\) hours, \(22\) minutes

The reason why some of our time differs is due to the time spent in making illustrations, which Mazdak has not measured.

**By submitting this report we confirm that the entire report is our own work, that it has been written exclusively for this course, and that we both actively participated in solving all the exercises of the course.****We will not spread our work in this course to others who take or can be expected to take the course.**

\label{section:purpose-of-this-report} During the past two months, we, the authors of this report, have been taking a course in mathematical modelling and problem solving at Chalmers university of technology. The course focuses on ways in which different aspects of reality, the world in which we live with all its details, imperfections and uncertainties, can be abstracted away and represented in simpler, more pure if you will, mathematical terms. These abstractions, these simplified representations of reality, are called *mathematical models*. Using these models, we gain the ability to take real world problems, and convert them into a form which we can then solve with the help of mathematics. If our model is good enough, the insights we gain through solving these simplified mathematical problems will then also tell us how to solve the real world problems on which our models were based. When we speak of reality, this can of course also be simulations of our realtities in computers, or other possible realities hypothesised by multiverses - but this is out of the scope of this course.

Unlike many other mathematics courses, the primary focus of this course has, perhaps counterintuitively, not been on learning mathematics. Instead, it has focused on mainly using mathematics that we already knew, in the context of solving problems from the real world. Doing this requires finding a way to model the problem using mathematics, and then solving the problem in its mathematical form. This focus on modelling and problem solving sets the course apart from other courses, which are often more theoretical and perhaps algorithmic in nature, with problems which can often be solved using well defined series of steps, such as taking the derivative of a function, multiplying two matrices, or evaluating a logical expression, while this course often requires more creativity and heuristic approaches such as trial and error.

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