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This is a textbook for advanced undergraduate students and
beginning graduate students in applied mathematics. It presents the
basic mathematical foundations of stochastic analysis (probability
theory and stochastic processes) as well as some important
practical tools and applications (e.g., the connection with
differential equations, numerical methods, path integrals, random
fields, statistical physics, chemical kinetics, and rare events).
The book strikes a nice balance between mathematical formalism and
intuitive arguments, a style that is most suited for applied
mathematicians. Readers can learn both the rigorous treatment of
stochastic analysis as well as practical applications in modeling
and simulation. Numerous exercises nicely supplement the main
exposition.
The book systematically introduces the basic contents of data
science, including data preprocessing and basic methods of data
analysis, handling special problems (e.g. text analysis), deep
learning, and distributed systems.In addition to systematically
introducing the basic content of data science from a theoretical
point of view, the book also provides a large number of data
analysis practice cases.
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