LEADER 04071nam 2200589 a 450 001 9910957926803321 005 20250715211939.0 010 $a0-88385-983-1 035 $a(CKB)2560000000081410 035 $a(OCoLC)681148788 035 $a(CaPaEBR)ebrary10733066 035 $a(SSID)ssj0000577715 035 $a(PQKBManifestationID)11347938 035 $a(PQKBTitleCode)TC0000577715 035 $a(PQKBWorkID)10561668 035 $a(PQKB)11410534 035 $a(MiAaPQ)EBC3330423 035 $a(Au-PeEL)EBL3330423 035 $a(CaPaEBR)ebr10733066 035 $a(OCoLC)929120363 035 $a(RPAM)15023025 035 $a(EXLCZ)992560000000081410 100 $a20070926d2007 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNumber theory through inquiry /$fDavid C. Marshall, Edward Odell, Michael Starbird 205 $a1st ed. 210 $aWashington, D.C. $cMathematical Association of America$d2007 215 $a1 online resource (151 p.) 225 0 $aAMS/MAA Textbooks,$x2577-1213 ;$vv. 9 225 0$aMAA textbooks 300 $aIncludes index. 311 08$a0-88385-751-0 327 $aIntroduction -- Divide and conquer -- Prime time -- A modular world -- Fermat's Little Theorem and Euler's Theorem -- Public key cryptography -- Polynomial congruences and primitive roots -- The golden rule : quadratic reciprocity -- Pythagorean triples, sums of squares, and Fermat's Last Theorem -- Rationals close to irrationals and the Pell equation -- The search for primes -- Mathematical induction : the domino effect. 330 $aNumber Theory Through Inquiry is an innovative textbook that leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. One goal is to help students develop mathematical thinking skills, particularly, theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for an independent study experience, or for a course designed as an introduction to abstract mathematics. Math or related majors, future teachers, and students or adults interested in exploring mathematical ideas on their own will enjoy Number Theory Through Inquiry.Number theory is the perfect topic for an introduction-to-proofs course. Every college student is familiar with basic properties of numbers, and yet the exploration of those familiar numbers leads us to a rich landscape of ideas. Number Theory Through Inquiry contains a carefully arranged sequence of challenges that lead students to discover ideas about numbers and to discover methods of proof on their own. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors' materials explain the instructional method. This style of instruction gives students a totally different experience compared to a standard lecture course. Here is the effect of this experience: Students learn to think independently: they learn to depend on their own reasoning to determine right from wrong; and they develop the central, important ideas of introductory number theory on their own. From that experience, they learn that they can personally create important ideas, and they develop an attitude of personal reliance and a sense that they can think effectively 330 8 $aabout difficult problems. These goals are fundamental to the educational enterprise within and beyond mathematics. 606 $aNumber theory$vTextbooks 615 0$aNumber theory 676 $a512.7 700 $aMarshall$b David C$01831348 701 $aOdell$b E$g(Edward)$01831349 701 $aStarbird$b Michael$0737667 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910957926803321 996 $aNumber theory through inquiry$94403575 997 $aUNINA