LEADER 02958nam 22005175 450 001 9911064736703321 005 20260206120408.0 010 $a3-032-08634-5 024 7 $a10.1007/978-3-032-08634-1 035 $a(CKB)45246667800041 035 $a(MiAaPQ)EBC32538417 035 $a(Au-PeEL)EBL32538417 035 $a(DE-He213)978-3-032-08634-1 035 $a(EXLCZ)9945246667800041 100 $a20260206d2026 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aComputational Homological Algebra /$fby Michael Robinson 205 $a1st ed. 2026. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2026. 215 $a1 online resource (567 pages) 225 1 $aMathematical Engineering,$x2192-4740 311 08$a3-032-08633-7 327 $aQuotients of vector spaces -- Sequences and chain complexes -- Chain maps -- Abstract simplicial complexes -- Simplicial homology and homotopy -- Sequences and chain complexes of sequences. 330 $aThis book is an attempt to reduce the barrier to entry for the key tools of homological algebra and develops the basic notions of homological algebra by emphasizing concrete, elementary, and computational examples in finite dimensional vector spaces. Linear algebra is the study of linear maps between vector spaces. The broad success of linear algebra in applications is due to the dimension theorem and the algorithms that exploit it, like Gaussian elimination and QR factorizations. Homological algebra is the study of what happens when linear maps are chained together, one after the next. Unlike linear algebra, homological algebra is little known outside of mathematics, but is poised to become useful in engineering and data science. The material covered in this book can be used for a one semester elementary course in computational homological algebra, but could also comfortably occupy a two-semester sequence. This book is written for mid-division undergraduate students who have a solid background in linear algebra, but no background in abstract algebra, topology, or category theory. Instead readers build insight by computation. By working the examples and exercises, the requisite background material is covered as needed, and the powerful tools of homological algebra are unlocked. 410 0$aMathematical Engineering,$x2192-4740 606 $aEngineering mathematics 606 $aAlgebra 606 $aEngineering Mathematics 606 $aAlgebra 615 0$aEngineering mathematics. 615 0$aAlgebra. 615 14$aEngineering Mathematics. 615 24$aAlgebra. 676 $a620.00151 700 $aRobinson$b Michael$037662 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911064736703321 996 $aComputational Homological Algebra$94545408 997 $aUNINA