You are here

Step into the World of Mathematics

Samuli Siltanen
Publication Date: 
Number of Pages: 
[Reviewed by
Tom French
, on
Here is the non-technical book that introduces the reader to the world of mathematical models and describes how professionals do modeling.  This book shows the hidden mathematics within models by providing a wide variety of examples of mathematical models.
The book introduces modeling by following the author through his mathematics education in primary school, high school, and university studies which shows how he got into medical imaging research and building mathematical models.  The author establishes his authority and expertise on mathematical models with this background.
The text next explores mathematical models from the specialist’s perspective. The mathematical model is a set of formulas that describe a physical phenomenon.  Each model is built for a user.  We learn that developing a model is as much an art form as it is mathematical rigor. The good model captures those features which are important to the user but can afford to be less accurate in the unimportant features.  The finished model must describe how the world works.
Our next step into the world of mathematics describes how models are used to predict weather.  The author does not go into computational or programming details but does explain the factors and instrumentation necessary for weather prediction, including ‘chaoticity’ or ‘the butterfly effect’. The read then takes us through a smooth transition from weather models to climate models which is explained simply and clearly in laymen’s terms. Many of us reference and use climate models oftentimes without a great understanding of how these models are developed or the mathematics behind these models.  This book quickly remedies that lack of understanding.
A section is also devoted to how mathematics helps doctors. Doctors rely on statistics and probabilities to test the efficacy of new medicines, treatments, and vaccinations.  Doctors also use computer tomography to diagnose and plan operations for their patients.  This book goes into detail about how tomography works and how it is still being developed and improved.  And, even though the book presents tomography some detail, the explanations can be readily understood by the lay person or those with a limited technical background.
The final chapter is devoted to the theme that mathematics belongs to everyone.  Siltanen makes the case that everyone should study mathematics.  He additionally makes the case that the field of mathematics has historically, and often still is, unfair to women.  He points out that the Mathematics Department at the University of Helsinki has hired only one woman professor of mathematics in its 379 years of existence. That woman was hired in the year 2019.  
This book is an excellent source for supplementary reading in introductory courses to computer technology, where students can be exposed to the world of mathematical models and can read for themselves about opportunities and vocations available after graduation.  This book is also can be used by professors teaching a liberal arts mathematics course because it provides students a deeper understanding of how mathematics is used and how it continually develops.  This book is a must-read for the high school teacher who is forever answering the question: “when am I going to use this math anyway?”  The author presents a myriad of examples of where mathematics is used in the everyday life of a teenager. 
This short treatise will be a welcome addition to my mathematics library.      

Tom French has a B.S. and a M.S. degree in Mathematics from Minnesota State University, Mankato.  He has 35 years of engineering and business experience with UNIVAC and its successor companies.  He has lectured on mathematics and computer systems throughout the world and has taught mathematics at a number of US colleges and universities.