Modern life is increasingly relying on digital technology, which in turn runs on mathematics. However, this underlying math is hidden from us. That is mostly a good thing since we do not want to be solving equations and calculating fractions just to get things done in our everyday business. But the mathematical details do matter for anyone who wants to understand how stuff works, or wishes to create something new in the jungle of apps and algorithms. This book takes a look at the mathematical models behind weather forecasting, climate change prediction, artificial intelligence, medical imaging and computer graphics. The reader is expected to have only a curious mind; technical math skills are not needed for enjoying this text.
Author(s): Samuli Siltanen, Lauri Snellman [Translator]
Edition: 1
Publisher: Springer
Year: 2021
Language: English
Commentary: TruePDF
Pages: 127
Tags: Mathematics: General; Mathematical Modeling And Industrial Mathematics; Imaging: Radiology Machine; Learning Computer Graphics; Atmospheric Sciences
Mathematics—Our Invisible Friend
What Is in the Book?
Contents
1: My Adventures in the World of Mathematics
1.1 Primary School
1.2 High School
1.3 Engineering Studies at HUT
1.4 Thesis and Medical Imaging Research
1.5 As an Industrial Developer
2: Examples of Mathematical Models
2.1 How to Model Gender?
2.2 Natural Numbers Model Quantities
2.3 A Model for Prices in an Online Store
2.4 The Flight of a Football on PlayStation
2.5 Bringing Light to a Virtual Room
2.6 How to Build a Mathematical Model
References
3: The Big Models of Earth and Space
3.1 Weather Forecasts, Atmospheric Models and the Butterfly Effect
Dividing the World Into Boxes
Determining the Initial Conditions
The Flow Model and the Physics Model
The Butterfly Effect
3.2 Modelling Climate Change
From a Weather Model to a Climate Model
The Sources of Errors in Models
The Force of Averages in Predicting Climate Change
3.3 How to Observe the Collisions of Black Holes?
3.4 Mathematics and the Wicked Problems of Mankind
References
4: How Mathematics Helps Doctors
4.1 Why Should Children Be Vaccinated?
Alternative 1
Alternative 2
Alternative 3
4.2 The Fat Lottery and Predictions of Weight
4.3 Traditional Tomography
Ordinary X-Ray Imaging
How Tomography Works
How to Calculate the Tomographic Model from the X-Rays?
A History of Tomography
4.4 The New Low-Radiation Tomography
An Inverse Problem and Two Penalties
Using Optimization to Find the Smallest Penalty
A Low-Radiation Dental X-Ray Device
A Tomography that Uses Radiotracers
5: Is Humanity Too Just Mathematics?
5.1 A Poor Model Produces Poor Results
5.2 The High Points of AI
A Self-Taught Chess Machine
A Cat Recognition Program
Modelling the Human Tastes for Art
5.3 Will Computers Replace Artists?
References
6: Mathematics Belongs to Everyone
6.1 The Myth of Genius Is Destructive
6.2 The Properties of an Applied Modeller
6.3 A Challenge for Raising Enthusiasm: let’s Bring Everybody to the World of Mathematics!
