Berfikir_Matematis

7/30/2019 Berfikir_Matematis

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Berfikir MatematisDr. Rizky Rosjanuardi, M.Si.


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Matematika?


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Matematika: apa yangdipelajari?


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Bilangan
http://en.wikipedia.org/wiki/File:Arabic_numerals-en.svg


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Bilangan0 / * rei /

1 ichi /

2 ni, ji / ,

3 san /

4 shi /

5 go /

6 roku /

7 shichi /8 hachi /

9ky, ku /

,

10 j /

20 ni-j /
http://en.wikipedia.org/wiki/0_(number)http://en.wikipedia.org/wiki/1_(number)http://en.wikipedia.org/wiki/2_(number)http://en.wikipedia.org/wiki/3_(number)http://en.wikipedia.org/wiki/4_(number)http://en.wikipedia.org/wiki/5_(number)http://en.wikipedia.org/wiki/6_(number)http://en.wikipedia.org/wiki/7_(number)http://en.wikipedia.org/wiki/8_(number)http://en.wikipedia.org/wiki/9_(number)http://en.wikipedia.org/wiki/10_(number)http://en.wikipedia.org/wiki/20_(number)http://en.wikipedia.org/wiki/20_(number)http://ja.wikipedia.org/wiki/%E5%8D%81http://en.wikipedia.org/wiki/10_(number)http://ja.wikipedia.org/wiki/%E4%B9%9Dhttp://en.wikipedia.org/wiki/9_(number)http://ja.wikipedia.org/wiki/%E5%85%ABhttp://en.wikipedia.org/wiki/8_(number)http://ja.wikipedia.org/wiki/%E4%B8%83http://en.wikipedia.org/wiki/7_(number)http://ja.wikipedia.org/wiki/%E5%85%ADhttp://en.wikipedia.org/wiki/6_(number)http://ja.wikipedia.org/wiki/%E4%BA%94http://en.wikipedia.org/wiki/5_(number)http://ja.wikipedia.org/wiki/%E5%9B%9Bhttp://en.wikipedia.org/wiki/4_(number)http://ja.wikipedia.org/wiki/%E4%B8%89http://en.wikipedia.org/wiki/3_(number)http://ja.wikipedia.org/wiki/%E4%BA%8Chttp://en.wikipedia.org/wiki/2_(number)http://ja.wikipedia.org/wiki/%E4%B8%80http://en.wikipedia.org/wiki/1_(number)http://ja.wikipedia.org/wiki/0http://en.wikipedia.org/wiki/0_(number)


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Bilangan
http://en.wikipedia.org/wiki/File:Maya.svg


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Bentuk
http://simple.wikipedia.org/wiki/File:CircleArea.gifhttp://simple.wikipedia.org/wiki/File:Pyramids_of_Egypt1.jpghttp://simple.wikipedia.org/wiki/File:Sphere.jpghttp://simple.wikipedia.org/wiki/File:Cube.svg


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Bentuk
http://upload.wikimedia.org/wikipedia/commons/5/5d/Koch_curve.svghttp://upload.wikimedia.org/wikipedia/commons/8/80/Torus.jpg


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Kajian yang terkait:


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Struktur
http://simple.wikipedia.org/wiki/File:6n-graf.svghttp://simple.wikipedia.org/wiki/File:Lattice_of_the_divisibility_of_60.svghttp://simple.wikipedia.org/wiki/File:Group_diagdram_D6.svghttp://simple.wikipedia.org/wiki/File:Elliptic_curve_simple.svg


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Kajian yang terkait: Struktur aljabar.

Aljabar linier.

Teori bilangan.

Teori urutan.

Teori graf.


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Perubahan


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Apa yang seharusnyadilakukan olehmatematikawan?

Mencari pola.

Merumuskan konjektur baru.

Membuktikan kebenaran secara deduktifberdasarkan aksioma-aksioma dan

definisi.


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Deduksi Seorang matematikawan akan menyelesaikan

masalah dengan menggunakan logika dan

deduksi. Deduksi adalah sebuah cara sebuah

khusus dalam berfikir dalam memperoleh dan

membuktikan kebenaran yang baru dengan

menggunakan kebenaran yang sebelumnya.

Cara berfikir deduktif membedakan berfikirmatematis dengan yang lainnya.


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Pada pintu terpampang:Go away!!!

Im looking for thetruth, and the truth

is now going away!


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Apa sajakahpersamaannya?an Huef, A., Kaliszewski, S. &Raeburn, I. F. (2008). Covariant representations of Heckealgebras and imprimitivity for crossed products by homogeneous spaces.Journal of Pure and

pplied Algebra, 212 (10), 2344-2357.View Abstract

Kaliszewski, S., Quigg, J. &Raeburn, I. F. (2008). Proper actions, fixed-point algebras, and

naturality in nonabelian duality.Journal of Functional Analysis, 254 (12), 2949-2968.View Abstract

Crocker, D., Raeburn, I. F. &Williams, D. P. (2007). Equivariant Brauer and Picard groups anda Chase-Harrison-Rosenberg exact sequence.Journal of Algebra, 307(1), 397-408.

Adji, S., Raeburn, I. F. & Rosjanuardi, R. (2007). Group Extensions and the Primitive Ideal

Spaces of Toeplitz Algebras. Glasgow Mathematical Journal, 49 (1), 81-92.

an Huef, A., Raeburn, I. F. &Williams, D. P. (2007). Properties preserved under Morita

equivalence of C*-algebras. Proceedings of the American Mathematical Society, 135(5),1495-1503.


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Larsen, N. S. &Raeburn, I. (2007). Projective multi-resolution analyses arising from directlimits of Hilbert modules. Mathematica Scandinavica, 100 (2), 317-360.

an Huef, A., Kaliszewski, S. & Raeburn, I. (2007). Extension problems and non-abelian dualityfor C*-algebras. Bulletin of the Australian Mathematical Society, 75(2), 229-238.

an Huef, A., Kaliszewski, S., Raeburn, I. F. &Williams, D. P. (2007). Induction in stages for

crossed products of C*-algebras by maximal coactions.Journal of Functional Analysis, 252 (1),

356-398.View Abstract

Brownlowe, N. D. &Raeburn, I. F. (2006). Exel's crossed product and relative Cuntz-Pimsneralgebras. Mathematical Proceedings of the Cambridge Philosophical Society, 141 (3), 497-508.

Pask, D. A., Raeburn, I. F., Rordam, M. &Sims, A. D. (2006). Rank-2 graphs whose C*-

algebras are direct limits of circle algebras.Journal of Functional Analysis, 239 (1), 137-178.View Abstract

Apa sajakahpersamaannya?


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Spesialisasi


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Bergantung padalingkungan
http://en.wikipedia.org/wiki/File:Sterna_fuscata_flight.JPGhttp://en.wikipedia.org/wiki/File:House_sparrow04.jpg


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Di manakah masalahmatematika muncul?
http://c/From%20C/My%20Files%20and%20USB/My%20Removable%20USB/INDRAMAYU-PENATARAN/penataran%20Indramayu.ppt


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Berfikir matematis (kajiandi sekolah) Diambil dari tulisannya Kaye Stacey


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Teaching students to thinkmathematically. I will discuss a mathematical problem

which can be used to teach students to

think mathematically and to solvemathematical problems that areunfamiliar and new to them. Theprocesses of looking at special cases,

generalising, conjecturing and convincingwill be highlighted through theseexamples, These are key processes inthinking mathematically.


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Principles Mathematical thinking is an important goal of

schooling

Mathematical thinking is important as a way of

learning mathematics

Mathematical thinking is important for teachingmathematics

Mathematical thinking proceeds by specialising and generalising

conjecturing and convincing


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Andrew Wiles: Doing mathematics is like ajourney through a dark unexplored mansion.One enters the first room of the mansion and its dark. One

stumbles around bumping into furniture, but gradually youlearn where each piece of furniture is. Finally, after sixmonths of so, you find the light switch, you turn it on, andsuddenly its all illuminated. You can see exactly whereyou were. Then you move into the next room and spendanother six months in the dark. So each of thesebreakthroughs, while sometimes theyre momentary,sometimes over a period of a day or two, they are the

culmination of, and couldnt exist without, the manymonths of stumbling around in the dark that precedethem.

Andrew Wiles proved Fermats Last Theorem in 1994.

First stated by Pierre de Fermat, 1637.

Unsolved for 357 years.Quoted by Simon Singh (1997)


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Berfikir_Matematis

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