Customer Reviews

Applied Algebra and Functional Analysis (Dover Books on Mathematics)

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This book was recommended to me as a starting point to both review and learn advanced mathematics useful for robotics scientists and engineers. It covers linear differential equations, algebras (including Lie algebra), and metric spaces.

I found the text reasonable readable, and would recommend it to anyone looking to improve their understanding of the mathematical fundamentals useful for robotics and control research.

My advanced mathematical training is in statistics, which is a field that relies HEAVILY on linear algebra. One undergraduate course in linear algebra is really insufficient to understand the mathematics necessary for the more advanced courses and some knowledge of functional analysis is also useful. This book is--thanks to Dover--an inexpensive way to fill the gap through self-study. It is highly useful for explaining a number of more advanced results without being too technical. Enhancing its utility to people working in applied fields, it has a number of useful examples and applications illustrating the utility (well, mathematical utility :) of the concepts discussed, e.g., applications to least squares problems, Fourier series, etc.

I have recently obtained my PhD in control systems from UC Berkeley. Controls is higly mathematical area of applied science. It mainly relies on linear algebra, real and complex analysis which all constitue the unifying functional analysis framework. This book, which happens to be written by controls professors, is indeed a very useful reference to the subject. The book's style is very balanced between deep theory and applications. From my experience taking math courses on functional analysis, the book is also very comprehensive in the amount of topics it covers. In conclusion, anyone interested in seeing applied functional analysis (Banach and Hilbert spaces techniques), this book is good.

I specialize in Dynamics and Controls. I found this book great for acquiring (some of) the necessary mathematics to get into a more serious study of mathematical control theory. It also boosted my capacity to closely follow some journal articles in control theory. People with the average graduate preparation in controls may skip the first four chapters and start with metric spaces. The book is not, however, adequate for studying Lie algebra as needed in controls (and robotics) as pointed out by the reviewer from Japan. It only defines Lie algebra in a very general way, and does not get into Lie algebras of vector fields, which is what we need for geometric control. The book contains, however, valuable applications of the theory to optimal control and estimation, as well as a clear exposition of existence and uniqueness of solutions to ODEs.