An Introduction to Mathematical Modeling

Rating:
Summary: Good survey course in mathematical modeling
Review: Aimed at senior level undergraduates, the first chapter briefly discusses at a high level what mathematical models are, how they¡¯re formulated and rules of thumb as to how to evaluate them. The rest of the book surveys simple to moderately complex models applied to problems taken from a wide variety of disciplines in business, science, and engineering. As a survey course, brevity and breadth take precedent over depth and the examples are watered-down versions of problems taken from a plethora of sources cited throughout the text. However, the problems and models are not too superficial that they don¡¯t retain the essential issues modelers are likely to encounter.

Although the book is intended primarily for college seniors and first year graduate students, ¡°Part I: Elementary Methods¡± requires only first year calculus and basic probability whereas ¡°Part II: More Advanced Methods¡± also requires differential equations. Therefore, the book will appeal to various levels.

The book is rather dated as is evident by its lack of emphasis on numerical methods and no one should expect to be ready for any serious real world modeling as a result of reading this text alone. However, the book does not pretend to be anything more than what it is and the author cautions that it should merely supplement and not substitute mathematics and science coursework. (I would also add that a few courses in numerical methods and computer science would also be the order of the day.)

Although the first chapter outlines a quick four-step process for formulating mathematical models, the author stresses the role of discussion and research behind each high level step. Any attempt to provide detailed cookbook heuristics would be a sham. Professor Bender also makes a good point about addressing the ambiguity associated with complex problems raised by clients. Indeed, two themes that resonate throughout the examples are redefining the problem by clarifying objectives through discussion as well as iteratively refining a model by adding (useful) detail to an initially crude one. If nothing else, iteratively modeling elucidates the subtleties of the problem under discussion.

Success as an applied mathematician for industry thus requires excellent interpersonal skills and the author clearly reflects this sentiment by requiring group discussions for the book¡¯s exercises containing vaguely stated and open-ended problems having multiple answers. He also notes the crucial role the applied mathematician must play in helping a client clarify his/her objectives.

A must read for any aspiring industrial mathematician.

Rating:
Summary: Good survey course in mathematical modeling
Review: Aimed at senior level undergraduates, the first chapter briefly discusses at a high level what mathematical models are, how they¡¯re formulated and rules of thumb as to how to evaluate them. The rest of the book surveys simple to moderately complex models applied to problems taken from a wide variety of disciplines in business, science, and engineering. As a survey course, brevity and breadth take precedent over depth and the examples are watered-down versions of problems taken from a plethora of sources cited throughout the text. However, the problems and models are not too superficial that they don¡¯t retain the essential issues modelers are likely to encounter.

Although the book is intended primarily for college seniors and first year graduate students, ¡°Part I: Elementary Methods¡± requires only first year calculus and basic probability whereas ¡°Part II: More Advanced Methods¡± also requires differential equations. Therefore, the book will appeal to various levels.

The book is rather dated as is evident by its lack of emphasis on numerical methods and no one should expect to be ready for any serious real world modeling as a result of reading this text alone. However, the book does not pretend to be anything more than what it is and the author cautions that it should merely supplement and not substitute mathematics and science coursework. (I would also add that a few courses in numerical methods and computer science would also be the order of the day.)

Although the first chapter outlines a quick four-step process for formulating mathematical models, the author stresses the role of discussion and research behind each high level step. Any attempt to provide detailed cookbook heuristics would be a sham. Professor Bender also makes a good point about addressing the ambiguity associated with complex problems raised by clients. Indeed, two themes that resonate throughout the examples are redefining the problem by clarifying objectives through discussion as well as iteratively refining a model by adding (useful) detail to an initially crude one. If nothing else, iteratively modeling elucidates the subtleties of the problem under discussion.

Success as an applied mathematician for industry thus requires excellent interpersonal skills and the author clearly reflects this sentiment by requiring group discussions for the book¡¯s exercises containing vaguely stated and open-ended problems having multiple answers. He also notes the crucial role the applied mathematician must play in helping a client clarify his/her objectives.

A must read for any aspiring industrial mathematician.

Rating:
Summary: Eye-opener
Review: I read this book for the first time when I was in college. It addresses many fundamental and practical questions with tremendous clarity. It particularly stands out in my mind because of its simple and compelling answers to three questions: Why do we need models of reality? What are the constraints on rigorous modelling (trade-offs between precision vs. generality vs.simplicity)? How to evaluate a mathematical model?

Rating:
Summary: Eye-opener
Review: I read this book for the first time when I was in college. It addresses many fundamental and practical questions with tremendous clarity. It particularly stands out in my mind because of its simple and compelling answers to three questions: Why do we need models of reality? What are the constraints on rigorous modelling (trade-offs between precision vs. generality vs.simplicity)? How to evaluate a mathematical model?