000 03127nam a2200361 a 4500
001 00011973
003 WSP
007 cr cnu|||unuuu
008 201206s2020 si ob 001 0 eng
040 _a WSPC
_b eng
_c WSPC
010 _z 2020044703
020 _a9789811225529
_q(ebook)
020 _z9789811227677
_q(hbk.)
020 _z9789811225512
_q(pbk.)
050 0 4 _aQA9.54
_b.R45 2020
072 7 _aMAT
_x030000
_2bisacsh
072 7 _aMAT
_x018000
_2bisacsh
072 7 _aMAT
_x022000
_2bisacsh
082 0 4 _a511.3/6
_223
100 1 _aReiser, Elana,
_d1979-
_921194
245 1 4 _aThe science of learning mathematical proofs
_h[electronic resource] :
_ban introductory course /
_cby Elana Reiser.
260 _aSingapore :
_bWorld Scientific,
_c2020.
300 _a1 online resource (xvi, 226 p.)
505 0 _aPreface to students -- Preface to professors -- Pedagogical notes for professors -- Brain growth -- Team building -- Setting goals -- Logic -- Problem solving -- Study techniques -- Pre-proofs -- Direct proofs (even, odd, & divides) -- Direct proofs (rational, prime, & composite) -- Direct proofs (square numbers & absolute value) -- Direct proofs (gcd & relatively prime) -- Proof by division into cases -- Proof by division into cases (quotient remainder theorem) -- Forward-backward proofs -- Proof by contraposition -- Proof by contradiction -- Proof by induction -- Proof by induction part II -- Calculus proofs -- Mixed review. Appendices. 100# task activity sheet. Answers for hiking activity. Escape room. Proof for exercise 17.11. Selected proofs from all chapters. Proof methods. Proof template. Homework log -- Bibliography -- Index.
504 _aIncludes bibliographical references and index.
520 _a"College students struggle with the switch from thinking of mathematics as a calculation based subject to a problem solving based subject. This book describes how the introduction to proofs course can be taught in a way that gently introduces students to this new way of thinking. This introduction utilizes recent research in neuroscience regarding how the brain learns best. Rather than jumping right into proofs, students are first taught how to change their mindset about learning, how to persevere through difficult problems, how to work successfully in a group, and how to reflect on their learning. With these tools in place, students then learn logic and problem solving as a further foundation. Next various proof techniques such as direct proofs, proof by contraposition, proof by contradiction, and mathematical induction are introduced. These proof techniques are introduced using the context of number theory. The last chapter uses Calculus as a way for students to apply the proof techniques they have learned"--Publisher's website.
538 _aMode of access: World Wide Web.
538 _aSystem requirements: Adobe Acrobat Reader.
650 0 _aProof theory.
_916154
655 0 _aElectronic books.
_93294
856 4 0 _uhttps://www.worldscientific.com/worldscibooks/10.1142/11973#t=toc
_zAccess to full text is restricted to subscribers.
942 _cEBK
999 _c72767
_d72767