This book is intended as a resource for those who wish to teach and learn mathematics through real world applications. The first part lists exercises which illustrate the use of various concepts and techniques at a level suitable for high schools and liberal arts colleges. Answers and brief notes accompany the questions. The second part of this book discusses the scientific method, mathematical modelling, and provides the background information for the exercises in the first part.
How do scientists model crowd behaviour, epidemics, earthquakes or the internet? What can we learn from the collective intelligence and adaptability of an ant colony? This book answers such questions by highlighting common themes in the study of complex systems. Topics covered include self-organisation, emergence, agent-based simulations, complex networks, phase plane plots, fractals, chaos, measures of complexity, model building, and the scientific method. Explanations are simple and concise, with common misconceptions clarified. Numerous exercises help enthusiasts consolidate their understanding through peer learning. Supplementary resources are at the companion websites www.simplicitysg.net/books and www.facebook.com/simcomty.
This book is a concise survey of the foundations of classical physics. It focuses on conceptual issues, and the various limitations that were later overcome with the development of quantum theory and Einstein's relativity. The presentation is aimed at enthusiasts in schools and beyond who have had some prior exposure to physics, but the uninitiated might also find some parts of this book to be informative. Topics covered include: Physics as information compression, the principle of relativity, cause and effect, symmetries and conservation laws, order and disorder, arrow of time, fields, waves, spontaneous symmetry breaking and emergence. Notes, exercises, and references have been included for those who are more inquisitive. Additional resources are on the book's webpage.
This book is a concise survey of the foundations of classical physics. It focuses on conceptual issues, and the various limitations that were later overcome with the development of quantum theory and Einstein's relativity. The presentation is aimed at enthusiasts in schools and beyond who have had some prior exposure to physics, but the uninitiated might also find some parts of this book to be informative. Topics covered include: Physics as information compression, the principle of relativity, cause and effect, symmetries and conservation laws, order and disorder, arrow of time, fields, waves, spontaneous symmetry breaking and emergence. Notes, exercises, and references have been included for those who are more inquisitive. Additional resources are listed on the book's webpage.
This book is for mathematics lovers, but if you are not one, we hope you soon will be. Although it mainly targets enthusiasts in high-school and liberal arts colleges, the book is structured to make learning interesting for students with different interests and backgrounds. Practice questions are of various levels of complexity and include many explorations of real-life situations: They develop understanding, build confidence and examine multiple concepts. Challenges have been included for the adventurous, while Investigations are suggested for self-study. The Escapades chapter contains stimulating puzzles to encourage experimentation, a list of unsolved mathematical problems, and a collection of wonderful theorems. The book includes simple tips to help the reader relax and re-energise. About the Authors: Adeline Ng and Dr. Rajesh Parwani are educators based in Singapore.
This book is intended as a resource for those who wish to teach and learn mathematics through real world applications. The first part lists exercises which illustrate the use of various concepts and techniques at a level suitable for high schools and liberal arts colleges. Answers and brief notes accompany the questions. The second part of this book discusses the scientific method, mathematical modelling, and provides the background information for the exercises in the first part.
This book is for mathematics lovers, but if you are not one, we hope you soon will be. Although it mainly targets enthusiasts in high-school and liberal arts colleges, the book is structured to make learning interesting for students with different interests and backgrounds. Practice questions are of various levels of complexity and include many explorations of real-life situations: They develop understanding, build confidence and examine multiple concepts. Challenges have been included for the adventurous, while Investigations are suggested for self-study. The Escapades chapter contains stimulating puzzles to encourage experimentation, a list of unsolved mathematical problems, and a collection of wonderful theorems. The book includes simple tips to help the reader relax and re-energise. About the Authors: Adeline Ng and Dr. Rajesh Parwani are educators based in Singapore.
This book is a concise survey of the foundations of classical physics. It focuses on conceptual issues, and the various limitations that were later overcome with the development of quantum theory and Einstein's relativity. The presentation is aimed at enthusiasts in schools and beyond who have had some prior exposure to physics, but the uninitiated might also find some parts of this book to be informative. Topics covered include: Physics as information compression, the principle of relativity, cause and effect, symmetries and conservation laws, order and disorder, arrow of time, fields, waves, spontaneous symmetry breaking and emergence. Notes, exercises, and references have been included for those who are more inquisitive. Additional resources are on the book's webpage.
How do scientists model crowd behaviour, epidemics, earthquakes or the internet? What can we learn from the collective intelligence and adaptability of an ant colony? This book answers such questions by highlighting common themes in the study of complex systems. Topics covered include self-organisation, emergence, agent-based simulations, complex networks, phase plane plots, fractals, chaos, measures of complexity, model building, and the scientific method. Explanations are simple and concise, with common misconceptions clarified. Numerous exercises help enthusiasts consolidate their understanding through peer learning. Supplementary resources are at the companion websites www.simplicitysg.net/books and www.facebook.com/simcomty.
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