03320nam 22006615 450 991085779480332120250807135728.03-031-51822-510.1007/978-3-031-51822-5(MiAaPQ)EBC31337740(Au-PeEL)EBL31337740(CKB)31995366000041(DE-He213)978-3-031-51822-5(EXLCZ)993199536600004120240510d2024 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierExercises in Applied Mathematics With a View toward Information Theory, Machine Learning, Wavelets, and Statistical Physics /by Daniel Alpay1st ed. 2024.Cham :Springer International Publishing :Imprint: Birkhäuser,2024.1 online resource (0 pages)Chapman Mathematical Notes,3005-15173-031-51821-7 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.Chapman Mathematical Notes,3005-1517Algebras, LinearProbabilitiesMachine learningHarmonic analysisStatistical physicsLinear AlgebraApplied ProbabilityMachine LearningAbstract Harmonic AnalysisStatistical PhysicsAlgebras, Linear.Probabilities.Machine learning.Harmonic analysis.Statistical physics.Linear Algebra.Applied Probability.Machine Learning.Abstract Harmonic Analysis.Statistical Physics.515.076Alpay Daniel54298MiAaPQMiAaPQMiAaPQBOOK9910857794803321Exercises in Applied Mathematics4161301UNINA