LEADER 03698nam 22005415 450 001 9910300098803321 005 20200706114300.0 010 $a3-319-90321-7 024 7 $a10.1007/978-3-319-90321-7 035 $a(CKB)4100000004243955 035 $a(DE-He213)978-3-319-90321-7 035 $a(MiAaPQ)EBC6311370 035 $a(PPN)227403681 035 $a(EXLCZ)994100000004243955 100 $a20180521d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aExploring Mathematics $eProblem-Solving and Proof /$fby Daniel Grieser 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XXI, 298 p. 77 illus., 15 illus. in color.) 225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085 311 $a3-319-90319-5 327 $aIntroduction -- 1 First explorations -- 2 Recursion ? a fundamental idea -- 3 Mathematical induction -- 4 Graphs -- 5 Counting -- 6 General problem solving strategies -- 7 Logic and proofs -- 8 Elementary number theory -- 9 The pigeonhole principle -- 10 The extremal principle -- 11 The invariance principle -- A A survey of problem-solving strategies -- B Basics on sets and maps -- List of symbols -- Glossary -- Lists of problems, theorems and methods -- Hints for selected exercises -- References. 330 $aHave you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics. Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book. Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is required, including an understanding of numbers and elementary geometry, but no calculus. Including numerous exercises, with hints provided, this textbook is suitable for self-study and use alongside lecture courses. 410 0$aSpringer Undergraduate Mathematics Series,$x1615-2085 606 $aMathematics 606 $aMathematics?Study and teaching  606 $aMathematics, general$3https://scigraph.springernature.com/ontologies/product-market-codes/M00009 606 $aMathematics Education$3https://scigraph.springernature.com/ontologies/product-market-codes/O25000 606 $aPopular Science in Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/Q26000 615 0$aMathematics. 615 0$aMathematics?Study and teaching . 615 14$aMathematics, general. 615 24$aMathematics Education. 615 24$aPopular Science in Mathematics. 676 $a510 700 $aGrieser$b Daniel$4aut$4http://id.loc.gov/vocabulary/relators/aut$065750 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300098803321 996 $aExploring Mathematics$92102299 997 $aUNINA