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The 'factorization method', discovered by Professor Kirsch, is a relatively new method for solving certain types of inverse scattering problems and problems in tomography. The text introduces the reader to this promising approach and discusses the wide applicability of this method by choosing typical examples., The factorization method is a relatively new method for solving certain types of inverse scattering problems and problems in tomography. Aimed at students and researchers in Applied Mathematics, Physics and Engineering, this text introduces the reader to this promising approach for solving important classes of inverse problems. The wide applicability of this method is discussed by choosing typical examples, such as inverse scattering problems for the scalar Helmholtz equation, a scattering problem for Maxwell's equation, and a problem in impedance and optical tomography. The last section of the book compares the Factorization Method to established sampling methods (the Linear Sampling Method, the Singular Source Method, and the Probe Method)., Preface ; 1. The Simplest Cases: Dirichlet and Neumann Boundary Conditions ; 2. The Factorization Method for Other Types of Inverse Obstacle Scattering Problems ; 3. The Mixed Boundary Value Problem ; 4. The MUSIC Algorithm and Scattering by an Inhomogenous Medium ; 5. The Factorization method for Maxwell's Equations ; 6. The Factorization Method in Impedance Tomography ; 7. Alternative Sampling and Probe Methods ; Bibliography, "This is a nice collection of results on the factorization method for a variety of scattering applications. It provides beginning researchers with a good survey of the basic theoretical approach, and for more experienced researchers working with factorization techniques it is a good reference source. I await the second edition with great anticipation."--SIAM Review