LEADER 03685nam 22006255 450 001 9910983042303321 005 20251028160125.0 010 $a9783031734342 010 $a3031734343 024 7 $a10.1007/978-3-031-73434-2 035 $a(CKB)37627858700041 035 $a(MiAaPQ)EBC31913517 035 $a(Au-PeEL)EBL31913517 035 $a(DE-He213)978-3-031-73434-2 035 $a(OCoLC)1503843192 035 $a(EXLCZ)9937627858700041 100 $a20250218d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDiscrete Structures /$fby Andreas Klappenecker, Hyunyoung Lee 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (637 pages) 225 1 $aUndergraduate Texts in Mathematics,$x2197-5604 311 08$a9783031734335 311 08$a3031734335 327 $aPreface -- Notation -- I. Discrete Structures -- 1. Introduction.-2. Mathematical Arguments.-3. Sets -- 4. Proof by Induction -- 5. Equivalence Relations -- 6. Partial Orders and Lattices -- 7. Floor and Ceiling Functions -- 8. Number Theory -- II. Summation and Asymptotics -- 10. Asymptotic Analysis -- III. Combinatorics -- 11. Counting -- 12. Generating Functions -- 13. Recurrence Relations -- 14. Graphs -- 15. Probability -- Bibliography -- Index. 330 $aThe aim of this text is to introduce discrete mathematics to beginning students of mathematics or computer science. It does this by bringing some coherency into the seemingly incongruent subjects that compose discrete math, such as logic, set theory, algebra, and combinatorics. It emphasizes their theoretical foundations and illustrates proofs along the way. The book prepares readers for the analysis of algorithms by discussing asymptotic analysis and a discrete calculus for sums. The book also deduces combinatorial methods from the foundations that are laid out. Unlike other texts on this subject, there is a greater emphasis on foundational material that leads to a better understanding. To further assist the reader in grasping and practicing concepts, roughly 690 exercises are provided at various levels of difficulty. Readers are encouraged to study the examples in the text and solve as many of the exercises as possible. The text is intended for freshman or sophomore undergraduate students in mathematics, computer science, or similar majors. The assumed background is precalculus. The chapter dependency chart included is designed to help students, independent readers, and instructors follow a systematic path for learning and teaching the material, with the option to explore material in later chapters. 410 0$aUndergraduate Texts in Mathematics,$x2197-5604 606 $aDiscrete mathematics 606 $aComputer science$xMathematics 606 $aDiscrete Mathematics 606 $aMathematical Applications in Computer Science 606 $aMatemātica discreta$2thub 606 $aInformātica$2thub 608 $aLlibres electrōnics$2thub 615 0$aDiscrete mathematics. 615 0$aComputer science$xMathematics. 615 14$aDiscrete Mathematics. 615 24$aMathematical Applications in Computer Science. 615 7$aMatemātica discreta 615 7$aInformātica 676 $a511.1 700 $aKlappenecker$b Andreas$01785041 701 $aLee$b Hyunyoung$01785042 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910983042303321 996 $aDiscrete Structures$94316651 997 $aUNINA