03090nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001600167072002300183072001500206100007600221245017400297250001800471264007900489300004200568336002600610337002600636338003600662347002400698490004300722505032100765520100601086650002202092650001902114650002202133650002302155650002502178650002002203650002502223650002202248650003202270650002502302710003402327773002602361776003602387776003602423776003602459830004302495856004602538978-3-031-51822-5DE-He21320251030112033.0cr nn 008mamaa240510s2024    sz |    s    |||| 0|eng d  a97830315182257 a10.1007/978-3-031-51822-52doi 4aQA184-205 7aPBF2bicssc 7aMAT0020502bisacsh 7aPBF2thema1 aAlpay, Daniel.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aExercises in Applied Mathematicsh[electronic resource] :bWith a View toward Information Theory, Machine Learning, Wavelets, and Statistical Physics /cby Daniel Alpay.  a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Birkhäuser,c2024.  aIX, 694 p. 5 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aChapman Mathematical Notes,x3005-15170 aPrologue -- 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.  aThis 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. 0aAlgebras, Linear. 0aProbabilities. 0aMachine learning. 0aHarmonic analysis. 0aStatistical Physics.14aLinear Algebra.24aApplied Probability.24aMachine Learning.24aAbstract Harmonic Analysis.24aStatistical Physics.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303151821808iPrinted edition:z978303151823208iPrinted edition:z9783031518249 0aChapman Mathematical Notes,x3005-151740uhttps://doi.org/10.1007/978-3-031-51822-5