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Customarily, much of traditional mathematics curricula was predicated on 'by hand' calculation. However, ubiquitous computing requires us to refresh what we teach and how it is taught. This is especially true in the rapidly broadening fields of Data Mining and Artificial Intelligence, and also in fields such as Bioinformatics, which all require the use of Singular Value Decomposition (SVD). Indeed, SVD is sometimes called the jewel in the crown of linear algebra.
Linear Algebra for 21st Century Applications adapts linear algebra to best suit modern teaching and application, and it places the SVD as central to the text early on to empower science and engineering students to learn and use potent practical and theoretical techniques. No rigour is lost in this new route as the text demonstrates that most theory is better proved with an SVD.
In addition to this, there is earlier introduction, development, and emphasis on orthogonality that is vital in so many applied disciplines throughout science, engineering, computing and increasingly within the social sciences.
To assimilate the so-called third arm of science, namely computing, Matlab/Octave computation is explicitly integrated into developing the mathematical concepts and applications. A strong graphical emphasis takes advantage of the power of visualisation in the human brain and examples are included to exhibit modern applications of linear algebra, such as GPS, text mining, and image processing. Active learning is encouraged with exercises throughout that are aimed to enhance ectures, quizzes, or 'flipped' teaching.
List of contents
- 1: Vectors
- 2: Systems of linear equations
- 3: Matrices encode system interactions
- 4: Eigenvalues and eigenvectors of symmetric matrices
- 5: Approximate matrices
- 6: Determinants distinguish matrices
- 7: Eigenvalues and eigenvectors in general
About the author
A. J. Roberts is a Professor and Chair in the School of Mathematical Sciences at the University of Adelaide. He is a leader in developing and applying a branch of modern dynamical systems theory to understand the relation between detailed microscale models and average macroscale models. In conjunction with new computer algebra algorithms in scientific computing, Professor Roberts derives and interprets mathematical and computational models of complex multiscale systems, both deterministic and stochastic. He develops applications of this methodology to free surface fluid dynamics in the flow of thin fluid layers, water waves, and on to turbulent floods and tsunamis. His research programs have been supported by a dozen large research grants from the Australian Research Council.
Summary
Linear Algebra for 21st Century Applications adapts linear algebra to best suit modern teaching and application, and it places SVD as central to the text early on to empower the students in these disciplines to learn and use the best techniques.
Additional text
this is the first text I have read that uses SVD as the main operation to solve systems of linear equations instead of the traditional augmented matrix and elementary row operations to obtain a reduced row echelon form
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Highly recommended for everyone needing linear algebra competence and looking for a motivating, application oriented, comprehensible yet complete text, using modern computational tools. Dieter Riebesehl, zbMATH Open
