A 350-page introduction to the key mathematical ideas underlying uncertainty quantification, designed as a course text or self-study for finalist undergraduates, master\'s students, or beginning doctoral students.
T. J. Sullivan. Introduction to Uncertainty Quantification, volume 63 of Texts in Applied Mathematics. Springer, 2015. ISBN 978-3-319-23394-9 (hardcover) 978-3-319-23395-6 (e-book) doi:10.1007/978-3-319-23395-6
Update, 11 March 2016. A list of errata can now be found here.