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<p class="MsoNormal" style="text-align: left;" align="left">Matematik
Koyu'nde Kurban
Bayrami'nda matematige merakli lise ogrencilerine, ogretmenlerine
ve matematik
bolumu lisans ogrencilerine yonelik bir programimiz var. <br>
Cebir, olasilik ve cizgeler kuraminin ortak alanlarinda
dolasacagiz. <br>
Programin ayrintilari asagida ve <a
href="http://matematikkoyu.org/kurban_lise_lisans_2011">http://matematikkoyu.org/kurban_lise_lisans_2011</a>
sayfasinda. <br>
Kontenjanimiz oldukca kisitlidir. Katilmak isteyenler hemen
basvursunlar
lutfen. <br>
Onceden uyarayim: Cok kolay bir program degildir. <br>
Ali Nesin <br>
<br>
<br>
Ali Nesin, Cizgeler Kurami ve Cebir <br>
Genel Hatlar: Cizgeler kuraminda kullanilan bazi cebirsel
yontemler aciklanacaktir.
Bunu yaparken grup teorisinin ve grup etkimesinin temel
kavramlarini uygulamali
olarak gorecegiz. <br>
Onbilgi: Herhangi bir soyut cebir bilgisine gerek yoktur. <br>
Izlenecek Kitap: Chris Godsil ve Gordon Royle, Algebraic Graph
Theory,
Springer, Graduate Texts 207, 2001. <br>
Ayrintili Izlence <br>
5 Kasim (2 saat): Cizgeler, otomorfizma gruplari ve ornekler <br>
6 Kasim (2 saat): <b>Permutasyon gruplari ve asimetrik cizge
yogunlugu</b> <br>
7 Kasim (2 saat): <b>Orbitler, primitiflik, baglantililik</b> <br>
8 Kasim (2 saat): Gecisli cizgeler, kenar baglantililigi <br>
9 Kasim (2 saat): Kose baglantililigi. Esleme (matching). <br>
10 Kasim (4 saat): Hamilton yollari ve donguler; Hamilton
donguleri olmayan yonlendirilmis
Cayley cizgeleri <br>
11 Kasim (4 saat): <b>Buzulmeler. Simetrik grubunun uretecleri
uzerine</b> <br>
12 Kasim (4 saat): Yay-gecisli cizgeler. Petersen cizgesi.
Mesafe-gecisli cizgeler.
Coxeter cizgeleri. Tutte 8-cizgesi. <br>
13 Kasim (4 saat): Genellestirilmis dortgenler, izdusum
geometrisi, genellestirilmis
cokgenler. Feit-Higman teoremi. <br>
<span style=""> </span><br>
Ozlem Beyarslan, Rastgele Cizgeler Kurami <br>
Genel Hatlar: Rastgele cizgeler kuramina giris niteliginde bir
ders olacaktir. <br>
Izlenecek Kitap: J. Spencer, Strange Logic of Random Graphs. <br>
Ayrintili Izlence <br>
5 Kasim (2 saat): <b>Olasilik teorisinin temel ilkeleri</b> <br>
6 Kasim (2 saat): Cizgeler I <br>
7 Kasim (2 saat): Cizgeler II <br>
8 Kasim (2 saat): Rastgele cizge<br>
9 Kasim (2 saat): Biraz mantik <br>
10 Kasim (2 saat): Sifir-bir yasasi <span style=""> </span><br>
11 Kasim (2 saat): Erenfeucht-Mostowski Oyunlari ve kazanma
stratejileri <br>
12 Kasim (2 saat): Ornekler <br>
13 Kasim (2 saat): Rastgele yontemler nasil ise yarayabilir? <br>
<br>
Selcuk Demir, Olasilik Kurami <br>
Genel Hatlar: <b>Sonlu olasiliklar, olasilik kuraminin temelleri</b>
<br>
Izlenecek Kitap: Y.A. Rozanov,Probablity Theory: A Concise Course
<br>
Ayrintili Izlence <br>
5 Kasim (2 saat): Olaylar, temel olasilik. <br>
6 Kasim (2 saat): Kombinatorik analizin temelleri <br>
7 Kasim (2 saat): Elemanter olaylar, ornekleme uzayi <br>
8 Kasim (2 saat): Olasiliklarin toplanma kurali, ornekler <br>
9 Kasim (2 saat): Istatistiksel bagimsizlik <br>
10 Kasim (2 saat): Ayrik ve surekli rastsal degiskenler,
dagilimlar <br>
11 Kasim (2 saat): Beklenti, Chebyshev esitsizligi <br>
12 Kasim (2 saat): Bazi onemli olasilik dagilimlari <br>
13 Kasim (2 saat): Ornekler <br>
<br>
Sonat Suer, Periyodik Kenar Suslerinin Siniflandirilmasi <br>
Genel Hatlar: Dersin amaci temel grup teorisine somut bir ornek
uzerinden giris
yapmaktir. <span style=""> </span><br>
Onbilgi: Ogrencilerin cebir bilmesine gerek yoktur. <br>
Izlenecek Kitap: Algebra and Geometry, Alan F. Beardon, Cambridge
University
Press. <br>
Ayrintili Izlence <br>
5 Kasim (2 saat): Simetrinin tanimi, duzlemin simetrileri. <br>
6 Kasim (2 saat): Kenar susleri ve kenar susu gruplari. <br>
7 Kasim (2 saat): Altgruplar ve bolum gruplari. <br>
8 Kasim (2 saat): Siniflandirma teoremi, 1. kisim. <br>
9 Kasim (2 saat): Siniflandirma teoremi, 2. kisim.</p>
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