Here is a list of books and on-line resources that cover many of the topics in CS 6959.

Please report broken links or new resources to teach-cs6959@list.eng.utah.edu.

- Discrete Inverse Problems: Insight and Algorithms, P.C. Hansen, SIAM Press, 2010. The main book for the course.
- Computational Inverse Problems, C. Vogel, SIAM Press, 2002. (This is an excellent book on inverse problems from a more mathematical point of view.).
- An Introduction to Inverse Problems with Applications, F.D.M. Neto and A. J. Neto, Springer, 2013. (A nice introduction to inverse theory from a mathematical point of view.).
- Rank-Deficient and Discrete Ill-Posed Problems, P.C. Hansen, SIAM Press, 1998. (This is an excellent book on discrete linear inverse problems).
- Linear and Nonlinear Inverse Problems with Practical Applications, Jennifer L. Müller and, Samuli Siltanen, SIAM Press, 2012. (This is very nice introductory book with several good applications).
- Parameter Estimation and Inverse Problems, Second Edition, Richard C. Aster, Brian Borchers, and Clifford H. Thurber, Academic Press, 2012. (This is very nice introduction to inverse problems with a geophysics bent).
- Inverse Problem Theory and Methods for Model Parameter Estimation Albert Tarantola, Siam Press, 2004. (This is a classic text on probabilistic inverse theory).
- Geophysical Inverse Theory and Regularization Problems, Michael S. Zhdanov, Elsevier, 2002. (This is a tour de force on geophysical inverse problems written by a Utah Geophysics Professor).
- Large-scale Inverse Problems and Quantification of Uncertainty, L Biegler, G. Biros, O. Ghattas et al. editors, Wiley, 2011. (This is a nice collection of papers on Bayesian techniques with a few large-scale applications.).
- Optimization and Regularization for Computational Inverse Problems and Applications, Y. Wang, A.G. Yagola, and C. Yang, editors, Springer, 2010. (A collection of papers that treat inverse problems as optimization problems).
- Inverse Problems in the Mathematical Sciences, C.W. Groetsch, Vieweg Mathematics for Scientists and Engineers, 1993. (This is a really nice introduction to inverse problems and has an excellent annotated bibliography).
- Statistical and Computational Inverse Problems, J. Kaipio and E. Somersalo, Springer, 2005. (A nice introduction to statistical inverse theory).
- Geophysical Data Analysis: Discrete Inverse Theory, W. Menke, Academic Press, 3rd edition, 2012 (A nice introduction to inverse theory within the context of geophysical problems).
- Computational Inverse Problems in Electrocardiography, Peter R. Johnston, WIT Press, 2001. (A nice collection of articles in inverse cardiology).
- Mathematically Modeling the Electrical Activity of the Heart: From Cell to Body Surface and Back Andrew J. Pullan, World Scientific Publishing Company, 2005. (A nice book on computational forward and inverse problems in cardiology).
- Handbook of Neural Activity Measurement, R. Brette and A. Destexhe, editors, Cambridge University Press, 2012. (Chapter 6 of this book is on MEG and EEG source estimation).
- Numerical Methods for the Solution of Ill-Posed Problems, A.N. Tikhonov, A.V. Goncharsky, V.V. Stepanov, and A.G. Yagola, Kluwer Academic Publishers, 1995 (a reprint of a 1990 Russian version). (This is a classic by one of the founders, Tikhonov, of regularization theory. It contains lots of Fortran code. Note that it is very expensive).
- An Introduction to the Mathematical Theory of Inverse Problems, A. Kirsch, Springer, 1996. (A nice overview of the mathematical analysis of classical inverse problems).
- Ill-Posed Problems: Theory and Applications, A. Bakushinsky and A. Goncharsky, Kluwer Academic Press, 1994 (a reprint of a 1989 Russian version). (A collection of chapters that use the concept of the ``regularizing algorithm'').
- Inverse and Ill-Posed Problems, Heinz Engl and C.W. Groetsch, editors, Academic Press, 1987. (An edited collection of papers on several aspects of inverse problems including theory and applications. Thisis an often cited collection).
- Conjugate Gradient Type Methods for Ill-Posed Problems, Martin Hanke, Pitman Research Notes in Mathematics Series 327, Longman Scientific and Technical, 1995. (This is a short monograph that contains recent efforts in iterative Krylov subspace type methods for inverse problems).
- Ill-Posed Problems in the Natural Sciences, A.N. Tikhonov and A.V. Goncharsky, editors, MIR Publishers, 1987. (This is a nice collection of inverse application papers).
- Regularization Methods for Ill-Posed Problems, V.A. Morozov, CRC Press, 1993. (This book is a mathematical treatise on regularization).
- Inverse Problems in Partial Differential Equations, D. Colton, R. Ewing, and W. Rundell, editors, 1990. (A collection of application papers and applied mathematics papers on inverse problems in various pdes).
- Plato's Cave and Inverse Problems, www.mlahanas.de/Greeks/PlatosCave.htm

- Regularization Toolkit for Matlab
- Numerical Computing with Matlab This book is a very nice overview of numerical analysis with several examples using Matlab. The book is available for free on-line. The Matlab codes used in the book are also available on-line.
- MATLAB Guide by Desmond J. Higham and Nicholas J. Higham, SIAM Press, 2005.
- Mastering MATLAB by Duane C. Hanselman and Bruce L. Littlefield, Prentice Hall, 2011.
- Octave - an open source, freely available alternative to Matlab
- Look at the Plot Catalog in MATLAB to view the various types
of plots, or see the online documentation here:

http://www.mathworks.com/access/helpdesk/help/techdoc/creating_plots/f9-53405.html - Tutorials from MathWorks (developer of MATLAB), with links to
other tutorials:

http://www.mathworks.com/academia/student_center/tutorials/launchpad.html - Users Guide (command, language, and object reference):

http://www.mathworks.com/access/helpdesk/help/techdoc/matlab_product_page.html - Good tutorial on the basics of matrix and vector operations
and programming (very little on plotting):

http://amath.colorado.edu/computing/Matlab/Tutorial/ - Tutorial focused on plotting basics:

http://www.engin.umich.edu/group/ctm/extras/plot.html

- SCIRun Software System: A scientific problem solving environment for modeling, simulation and visualization developed by the Scientific Computing and Imaging Institute at the University of Utah.
- SCIRun Forward/Inverse ECG Toolkit: This toolkit is a col- lection of modules and networks within the SCIRun system, which can be used to solve forward and inverse electrocardiography problems.

- Python Scripting for Computational Science by Hans Petter Langtangen, Springer, 2004.
- Python Essential Reference (3rd Edition) by David M. Beazley, Sams, 2006.
- Enthought Python Distribution (EPD), which includes the NumPy,
SciPy, matplotlib, mlab, Mayavi2, and other libraries, plus useful
tools such as the IPython interpreter shell (with features such
as code completion). Free for academic use.

http://www.enthought.com/products/epd.php - SciPy tutorial:

http://www.scipy.org/SciPy_Tutorial - NumPy tutorial:

http://www.scipy.org/Tentative_NumPy_Tutorial - matplotlib tutorial (2D plots):

http://matplotlib.sourceforge.net/users/pyplot_tutorial.html - mlab documentation (3D plots):

http://code.enthought.com/projects/mayavi/docs/development/html/mayavi/mlab.html - Python documentation:

http://www.python.org/doc/

- Scientific Computing: An Introductory Survey, Second Edition by Michael T. Heath, published by McGraw-Hill, New York, 2002.
- Scientific Computing with MATLAB by Alfio Quarteroni and Fausto Saleri, Springer, 2003.
- Online numerical analysis text
covering a variety of topics:

https://ece.uwaterloo.ca/~dwharder/NumericalAnalysis/Contents/ - Another set of numerical analysis notes with a wealth of other
resources:

http://numericalmethods.eng.usf.edu/ - Extensive collection of applets for scientific computing concepts
and methods:

http://www.cse.illinois.edu/iem/

- Data Analysis: A Bayesian Tutorial, Devinderjit Sivia and John Skilling, Oxford University Press, 2006. (This is a nice introduction to Bayesian data analysis).
- Demo of computing π by a Monte Carlo approximation:

http://polymer.bu.edu/java/java/montepi/ - Links to more examples of finding π by using Monte Carlo approximations:

http://math.fullerton.edu/mathews/n2003/montecarlopi/MonteCarloPiBib/Links/MonteCarloPiBib_lnk_1.html - Another set of overview slides for Monte Carlo integration,
with sample code in C (skip to page 5 for the relevant part):

http://www.sph.umich.edu/csg/abecasis/class/2006/615.22.pdf - Notes on both the theoretical basis and practical issues of
Monte Carlo integration, by a student here at the UofU SoC:

http://www.cs.utah.edu/~edwards/research/mcIntegration.pdf - Brief overview, with a ﬁnance example:

http://www.brighton-webs.co.uk/montecarlo/concept.asp - Detailed treatment of the mathematical background, but from
a scientiﬁc computing perspective:

http://www.cs.nyu.edu/courses/fall06/G22.2112-001/MonteCarlo.pdf