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Elementary Mathematical Models: Order Aplenty and a Glimpse of Chaos
The language of mathematics has proven over centuries of application to be an indispensable tool for the expression and analysis of real problems. With numerical, graphical, and theoretical methods, this book examines the relevance of mathematical models to phenomena ranging from population growth and economics to medicine and the physical sciences. In a book written for the intelligent and literate non-mathematician, Kalman aims at an understanding of the power and utility of quantitative methods rather than at technical mastery of mathematical operations. He shows first that mathematical models can serve a critical function in understanding the world, and he concludes with a discussion of the problems encountered by traditional algebraic assumptions in chaos theory. Though models can often approximate future events based on existing data and quantitative relationships, Kalman shows that the appearance of regularity and order can often be misleading. By beginning with quantitative models and ending with an introduction to chaos, Kalman offers a broad treatment of both the power and limitations of quantitatively-based predictions.
- GenresMathematics
361 pages, Paperback
First published January 1, 1997
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November 10, 2016
I used this as the main textbook for my class called Algebraic Patterns & Functions. Some of the main goals of the course were mastery of arithmetic and geometric sequences, and fluency in working with functions and equations. Students are mostly future teachers with high school algebra experience, but likely no undergraduate math experience. I wanted to challenge them with a course that was not just a review of high school Algebra 2, but also keep the course from being proof-oriented.
I stumbled onto this book, which gave me the idea to approach my course from a modeling perspective. Overall, I was extremely pleased with the book. It is well-written, understandable for the majority of my students, and provides exercises on several different levels. The reading comprehension questions helped me gauge how much of a chapter students understood, and I prepared a follow-up lesson accordingly. Mathematical skills questions were useful to reinforce things we learned in class. Problems in context were good for in-class group work or to challenge students on their own. I didn't have time to teach all the chapters, but the material was rich and would also be adaptable for a more advanced course than mine. I might even assign some of the extra chapters to particularly advanced students.
Students found the "real-life examples" interesting and relevant. Math applications are always a tough sell, but I thought the author did an outstanding job of demonstrating real situations that can be modeled with algebra. As the author commented in his preface, stronger students will find his explanations long-winded and weaker students may still be lost. The feedback from my students agreed, but no one was completely frustrated.
I would love to see an updated revision of this book. The 1997 data, computer network problems, etc. could be updated and more engaging. Students didn't mind too much, as used copies of the book are very inexpensive.
On the negative side of things, I thought the material in Chapter 6 was a bit rushed, and Chapter 7 was extremely cursory. I expanded these chapters quite a bit with articles, videos, and worksheets. There were not enough practice problems for my students. While I realize that this book is suitable for a modeling course, and those students may not need a thorough discussion of polynomial and rational functions, I would have preferred to see these chapters either eliminated or expanded. The explanations of logarithms and lines of best fit (chapters 8 and 11) also seemed somewhat dated now that technology is so accessible. I was much more impressed with Chapters 1-5, 9, and 10.
I plan to continue using this book because it is so readable. I can supplement and clarify explanations in class, but I will let the author be the one to sit down with students at home and casually talk them through the big ideas. If you are looking for a textbook to use as a great resource, or are seeking to independently study these concepts on your own, this is a fantastic introductory book.
I stumbled onto this book, which gave me the idea to approach my course from a modeling perspective. Overall, I was extremely pleased with the book. It is well-written, understandable for the majority of my students, and provides exercises on several different levels. The reading comprehension questions helped me gauge how much of a chapter students understood, and I prepared a follow-up lesson accordingly. Mathematical skills questions were useful to reinforce things we learned in class. Problems in context were good for in-class group work or to challenge students on their own. I didn't have time to teach all the chapters, but the material was rich and would also be adaptable for a more advanced course than mine. I might even assign some of the extra chapters to particularly advanced students.
Students found the "real-life examples" interesting and relevant. Math applications are always a tough sell, but I thought the author did an outstanding job of demonstrating real situations that can be modeled with algebra. As the author commented in his preface, stronger students will find his explanations long-winded and weaker students may still be lost. The feedback from my students agreed, but no one was completely frustrated.
I would love to see an updated revision of this book. The 1997 data, computer network problems, etc. could be updated and more engaging. Students didn't mind too much, as used copies of the book are very inexpensive.
On the negative side of things, I thought the material in Chapter 6 was a bit rushed, and Chapter 7 was extremely cursory. I expanded these chapters quite a bit with articles, videos, and worksheets. There were not enough practice problems for my students. While I realize that this book is suitable for a modeling course, and those students may not need a thorough discussion of polynomial and rational functions, I would have preferred to see these chapters either eliminated or expanded. The explanations of logarithms and lines of best fit (chapters 8 and 11) also seemed somewhat dated now that technology is so accessible. I was much more impressed with Chapters 1-5, 9, and 10.
I plan to continue using this book because it is so readable. I can supplement and clarify explanations in class, but I will let the author be the one to sit down with students at home and casually talk them through the big ideas. If you are looking for a textbook to use as a great resource, or are seeking to independently study these concepts on your own, this is a fantastic introductory book.
Displaying 1 of 1 review