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Linear Algebra for Computational Sciences and Engineering

  • Textbook
  • © 2016

Overview

Authors:
  1. Ferrante Neri

    1. Centre for Computational Intelligence, De Montfort University, Leicester, United Kingdom

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  • Covers all aspects of linear algebra from the perspective of computational science and engineering
  • Provides both a technical approach and an informal interpretation of mathematics
  • Includes examples with definitions and theorems
  • Presents a chapter where the study of an electrical network is shown as an algebraic exercise
  • Includes supplementary material: sn.pub/extras

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xxii
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  2. Foundations of Linear Algebra

    1. Front Matter

      Pages 1-1
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    2. Basic Mathematical Thinking

      • Ferrante Neri
      Pages 3-13

    3. Matrices

      • Ferrante Neri
      Pages 15-39

    4. Systems of Linear Equations

      • Ferrante Neri
      Pages 41-96

    5. Geometric Vectors

      • Ferrante Neri
      Pages 97-129

    6. Complex Numbers and Polynomials

      • Ferrante Neri
      Pages 131-158

    7. An Introduction to Geometric Algebra and Conics

      • Ferrante Neri
      Pages 159-207

  3. Elements of Linear Algebra

    1. Front Matter

      Pages 209-209
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    2. An Overview on Algebraic Structures

      • Ferrante Neri
      Pages 211-231

    3. Vector Spaces

      • Ferrante Neri
      Pages 233-281

    4. Linear Mappings

      • Ferrante Neri
      Pages 283-347

    5. An Introduction to Computational Complexity

      • Ferrante Neri
      Pages 349-362

    6. Graph Theory

      • Ferrante Neri
      Pages 363-430

    7. Applied Linear Algebra: Electrical Networks

      • Ferrante Neri
      Pages 431-449

  4. Back Matter

    Pages 451-464
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Keywords

About this book

This book presents the main concepts of linear algebra from the viewpoint of applied scientists such as computer scientists and engineers, without compromising on mathematical rigor. Based on the idea that computational scientists and engineers need, in both research and professional life, an understanding of theoretical concepts of mathematics in order to be able to propose research advances and innovative solutions, every concept is thoroughly introduced and is accompanied by its informal interpretation. Furthermore, most of the theorems included are first rigorously proved and then shown in practice by a numerical example. When appropriate, topics are presented also by means of pseudocodes, thus highlighting the computer implementation of algebraic theory.


It is structured to be accessible to everybody, from students of pure mathematics who are approaching algebra for the first time to researchers and graduate students in applied sciences who needa theoretical manual of algebra to successfully perform their research. Most importantly, this book is designed to be ideal for both theoretical and practical minds and to offer to both alternative and complementary perspectives to study and understand linear algebra.



Reviews

“In this book, Ferrante Neri elaborates on this algebraic background, providing a very good starting point for undergraduate students who wish to gain a basic understanding of the theories behind the most exciting parts of contemporary information technology (IT) technologies. … As Neri’s work is a self-contained textbook, everything is explained from scratch and all of the chapters finish with exercises to test the reader’s understanding of just the presented material.” (Piotr Cholda, Computing Reviews, May, 2017)


“This is a nice, compact treatment, especially for those individuals who have yet to take an abstract algebra course. … The topic of computational complexity is a welcome addition to any text on linear algebra. … All in all, this is a thorough, carefully written text that can be utilized for any introductory linear algebra course. Summing Up: Recommended. Lower- and upper-division undergraduates.” (R. L. Pour, Choice, Vol. 54 (6), February, 2017)

Authors and Affiliations

  • Centre for Computational Intelligence, De Montfort University, Leicester, United Kingdom

    Ferrante Neri

About the author

Ferrante Neri received a Master's degree and a PhD in Electrical Engineering from the Technical University of Bari, Italy, in 2002 and 2007 respectively. In 2007, he also received a PhD in Scientific Computing and Optimization from University of Jyväskylä, Finland. He was appointed Assistant Professor at the Department of Mathematical Information Technology at the University  of Jyväskylä, Finland in 2007, and in 2009  as a Research Fellow with Academy of Finland. Neri moved to De Montfort University, United Kingdom in 2012, where he was appointed Reader in Computational Intelligence. Since 2013, he is Full Professor of Computational Intelligence Optimisation at De Montfort University, United Kingdom. He is also Visiting Professor  at the University  of Jyväskylä, Finland. Currently, he teaches linear algebra and discrete mathematics at De Montfort University. His research interests include algorithmics, metaheuristic optimisation, scalability in optimisation and large scale problems.



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