03489nam a22005895i 4500 978-3-031-51822-5 DE-He213 20251030112033.0 cr nn 008mamaa 240510s2024 sz | s |||| 0|eng d 9783031518225 978-3-031-51822-5 10.1007/978-3-031-51822-5 doi QA184-205 PBF bicssc MAT002050 bisacsh PBF thema Alpay, Daniel. author. aut http://id.loc.gov/vocabulary/relators/aut 76556 Exercises in Applied Mathematics [electronic resource] : With a View toward Information Theory, Machine Learning, Wavelets, and Statistical Physics / by Daniel Alpay. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Birkhäuser, 2024. IX, 694 p. 5 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Chapman Mathematical Notes, 3005-1517 Prologue -- Part I: Algebra -- Linear Algebra -- Positive Matrices -- Algebra and Error Correcting Codes -- Part II: Analysis -- Complements in Real and Complex Analysis -- Complements in Functional Analysis -- Part III: Probability and Applications -- Probability Theory -- Entropy: Discrete Case -- Thermodynamics. This text presents a collection of mathematical exercises with the aim of guiding readers to study topics in statistical physics, equilibrium thermodynamics, information theory, and their various connections. It explores essential tools from linear algebra, elementary functional analysis, and probability theory in detail and demonstrates their applications in topics such as entropy, machine learning, error-correcting codes, and quantum channels. The theory of communication and signal theory are also in the background, and many exercises have been chosen from the theory of wavelets and machine learning. Exercises are selected from a number of different domains, both theoretical and more applied. Notes and other remarks provide motivation for the exercises, and hints and full solutions are given for many. For senior undergraduate and beginning graduate students majoring in mathematics, physics, or engineering, this text will serve as a valuable guide as they move on to more advanced work. Algebras, Linear. 71217 Probabilities. 65724 Machine learning. 55059 Harmonic analysis. 72301 Statistical Physics. 70323 Linear Algebra. 71220 Applied Probability. 65727 Machine Learning. 55059 Abstract Harmonic Analysis. 72305 Statistical Physics. 70323 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031518218 Printed edition: 9783031518232 Printed edition: 9783031518249 Chapman Mathematical Notes, 3005-1517 76557 https://doi.org/10.1007/978-3-031-51822-5 ZDB-2-SMA ZDB-2-SXMS 59728 59728