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Modern life is increasingly relying on digital technology, which in
turn runs on mathematics. However, this underlying math is hidden
from us. That is mostly a good thing since we do not want to be
solving equations and calculating fractions just to get things done
in our everyday business. But the mathematical details do matter
for anyone who wants to understand how stuff works, or wishes to
create something new in the jungle of apps and algorithms. This
book takes a look at the mathematical models behind weather
forecasting, climate change prediction, artificial intelligence,
medical imaging and computer graphics. The reader is expected to
have only a curious mind; technical math skills are not needed for
enjoying this text.
Modern life is increasingly relying on digital technology, which in
turn runs on mathematics. However, this underlying math is hidden
from us. That is mostly a good thing since we do not want to be
solving equations and calculating fractions just to get things done
in our everyday business. But the mathematical details do matter
for anyone who wants to understand how stuff works, or wishes to
create something new in the jungle of apps and algorithms. This
book takes a look at the mathematical models behind weather
forecasting, climate change prediction, artificial intelligence,
medical imaging and computer graphics. The reader is expected to
have only a curious mind; technical math skills are not needed for
enjoying this text.
Inverse problems arise in practical applications whenever there is
a need to interpret indirect measurements. This book explains how
to identify ill-posed inverse problems arising in practice and how
to design computational solution methods for them; explains
computational approaches in a hands-on fashion, with related codes
available on a website; and serves as a convenient entry point to
practical inversion. The guiding linear inversion examples are the
problem of image deblurring, x-ray tomography, and backward
parabolic problems, including heat transfer, and electrical
impedance tomography is used as the guiding nonlinear inversion
example. The book's nonlinear material combines the
analytic-geometric research tradition and the regularization-based
school of thought in a fruitful manner, paving the way to new
theorems and algorithms for nonlinear inverse problems.
Furthermore, it is the only mathematical textbook with a thorough
treatment of electrical impedance tomography, and these sections
are suitable for beginning and experienced researchers in
mathematics and engineering.
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