Özdebir Denemesinden...

Sanırım 2008 yılına ait, cevaplarıyla beraber, Özdebir'in denemesinden matematik sorularına buradan ulaşabilirsiniz...Genelde kaliteli soruları oluyor bu sınavların, incelemekte fayda var diye düşünüyorum...

Üçgende Açı

İlköğretim ve lise geometri derslerinin ilk konularından olan üçgende açı ile ilgili çözümlü sorular ve testlerden oluşan bir dökümana buradan ulaşabilirsiniz...

2008 ÖSYS Matematik Soru ve Çözümleri

2008 yılına ait matematik soru ve çözümlerini resim dosyaları olarak hazırlamıştım zamanında...

Buradan indirebilirsiniz...

Rehberlik Dosyası

Güncel olduğunu söyleyemem ama meslekler ve üniversitelerle ilgili yararlı olabilecek bir kaynak elime geçti...Aşağıdaki linkten indirebilirsiniz...


http://www.megafileupload.com/en/file/132200/REHBER-zip.html

Matematik Dünyası

Ülkemizdeki en kaliteli matematik kaynaklarından biri (belki de birincisi) olan Matematik Dünyası dergisinin 2009 I ve II sayıları tek cilt olarak matematikseverlere sunuldu...Kapak konusu ise Topoloji...Derginin içeriği şöyle:


S:1
Başyazı
Giriş Yazısı
Ali Nesin
S:3-5
Haber
Kısa Kısa
Kısa Kısa...
Şafak Alpay
S:6-7
Okurlardan
Okurlardan
S:8-17
Haber
Basın
Basında Matematik
S:18
Haber
Basın
Ya Siz, Ya Kimse!
S:19-23
Topoloji
Gerçel sayılar
Bir Noktada Süreklilik ve Komşuluk
S:24-28
Topoloji
Gerçel sayılar
Süreklilik ve Açık Kümeler
S:29-33
Topoloji
Topolojik Uzay
S:34-37
Topoloji
Topolojik Uzayda Diziler ve Limitleri
S:38-39
Topoloji
Topolojik Uzaylarda Sürekli Fonksiyonlar
S:40-45
Topoloji
Topoloji Üretmek
S:46-49
Topoloji
İndirgenmiş Topoloji
S:50-54
Topoloji
Çarpım Topolojisi
S:55-57
Topoloji
Topolojik Eşleşlmeler (Homeomorfizmalar)
S:58-62
Topoloji
Kapalı Kümeler ve Kapanış
S:63-68
Topoloji
Bağlantılılık
S:69
Topoloji
Ortaya Karışık Topoloji Alıştırmaları
S:70-84
Tarih
Hepimizin Ustası Leonhard Euler
Ali Törün
S:85-90
Tarih
Osmanlı Dönemi Bilim Tarihinden Bir Kesit Hüseyin Tevfik Paşa
Fikri Akdeniz
S:91-94
Eğitim
Eğitim Anlayışı ve Üniversite
Cahit Arf
S:91-94
Tarih
Cahit Arf
Eğitim Anlayışı ve Üniversite
Cahit Arf
S:95-102
Geometri
Öklid Geometrisi
Simedyan Noktası
Mustafa Yağcı
S:103-109
Sonlu matematik
Güvercin Yuvası İlkesi
Haluk Oral, Can Hıraş
S:103-109
Sayma
Güvercin Yuvası İlkesi
Haluk Oral, Can Hıraş
S:110-112
Sayılar Kuramı
Mükemmel Sayılar
Halime Yanar
S:110-112
Aritmetik
Mükemmel Sayılar
Halime Yanar
S:113-115
Sonlu Matematik
Sayma
Parçalanış Sayısı
Behçet Pekünlü
S:113-115
Sonlu matematik
Kombinatorik
Parçalanış Sayısı
Behçet Pekünlü
S:116-120
Sonlu matematik
Şifreleme
Kriptoloji ve Güvenli Fonksiyonel Hesaplamalar
Mehmet Sabır Kiraz
S:121-126
Sonlu matematik
Çizge Kuramı
Adlandırılmış Ağaç Sayısı
Sayar Bayar
S:121-126
Sonlu matematik
Çizge Kuramı
Adlandırılmış Ağaç Sayısı
Sayar Bayar
S:127-138
Cebir
Cebir
Tensör Cebiri
Ali Nesin
S:139-142
Problemler, sorular
Alizade Köşesi
Problemler ve Çözümleri
Refail Alizade
S:143-144
Problemler, sorular
Olimpiyat Soruları
Olimpiyat Soruları Köşesi
Korkmaz Sönmez
S:145
Problemler, sorular
Olimpiyat Soruları
Olimpiyat Kampı Soruları
Ali Nesin, Andrei Ratiu, Selçuk Demir
S:146-149
Problemler, sorular
Olimpiyat Soruları
ABD Matematik Olimpiyatlarında Polinom Soruları
S:150
Problemler, sorular
Cahit Arf Matematik Günleri
Cahit Arf Matematik Günleri VIII-2009 Birinci Gün Sınavının Soruları
S:151-157
Problemler, sorular
Cahit Arf Matematik Günleri
Cahit Arf Matematik Günleri VII-2008 İkinci Gün Sınavının Yanıtları
S:158-159
Problemler, sorular
Doğuş Üniversitesi Matematik Yarışması
Doğuş Üniversitesi Matematik Kulübü Fen Liseleri Takım Yarışması 2007 Sorular
S:160-161
Problemler, sorular
Bilkent Soruları
Bilkent 2008 Soruları
Azer Kerimov
S:162-165
Problemler, sorular
Sabancı Üniversitesi Matematik Yarışması
Sabancı Üniversitesi Matematik Kulübü 2009 Liseler Arası Matematik Yarışması Birinci Aşama Soruları
S:166-167
Problemler, sorular
Bilmece
Beyincik
Haydar Göral
S:168-169
Problemler, sorular
Bilmece
Eureka
Haydar Göral
S:170-171
Kitap Tanıtım
Yayın Dünyası
Canan Okur
S:172-175
Satranç Köşesi
Satranç Köşesi: Şu Garip Piyonlar
Kıvanç Çefle
S:176
Mizah
Ergun Akleman Köşesi
Ergun Akleman

Ayrıntılı bilgiye matematikdunyasi.org adresinden ulaşabilirsiniz...

When art and math collide

An exhibit of mathematical art reveals the aesthetic side of math

By Julie Rehmeyer

Mathematics is beautiful: intellectually elegant, exquisitely austere and pretty. Yes, pretty. Like, pretty to look at.

That aesthetic beauty was easy to see at the 2009 Joint Mathematics Meetings in Washington, D.C., January 5–8, which showcased mathematics research and also invited artists and mathematicians to come together to create a display of mathematical art.

PENROSE TILESUNDERNEATH This shows the pattern of the Penrose tiles at the center of Stacy’s artwork. Artist Paul Stacy made the joints between the tiles invisible when he painted it.

Paul Stacy, an Australian landscape architect, got seduced by the beauty of math when a friend brought him some ceramic Penrose tiles. The tiles don’t seem like much at first glance: they can be one of two diamond shapes, either fat or skinny. But these tiles hold a secret. Put together according to certain rules, they form patterns that never, ever repeat, no matter how far you extend them. Even more surprisingly, they have five-fold rotational symmetry, so you can turn the whole pattern 72 degrees and it will look exactly the same.

Stacy started playing with the tiles to make shapes of his own. He put together nine of the skinny tiles to form a yellow cross on a blue background, and then he did the same with nine of the fat tiles. These larger, nine-tile groups were each the same shape as the individual diamond-shaped tiles that made them up, so Stacy used each nine-tile group as a Penrose tile, following the construction rules of Penrose tiles to create a never-repeating pattern.

RHOMBIC DODECAHEDRON I:Vladimir Bulatov took inspiration for this sculpture from an unusual polyhedron.Vladimir Bulatov

What emerged was a swarm of groups of blue tiles against a yellow background that seemed to swirl and buzz like a swarm of bees. Stacy discovered that the rules of Penrose tile construction meant there were precisely seven shapes the groups of blue tiles could form. Only long after he finished his piece did he find out that this “discovery” had in fact long been known by mathematicians.

Artist and physicist Vladimir Bulatov builds his artwork like a mathematical proof. He began his Rhombic Dodecahedron I by pondering a funny, irregular looking polyhedron built out of 12 diamond shapes called rhombuses. Bulatov imagined replacing each rhombic face with a sort of four-armed starfish. Instead of connecting the arms directly to those of the closest starfish, he used the symmetries of the polyhedron to interlace the arms, forming an intricate knot.

THREE-FOLD SYMMETRYThe arms of each "starfish" polyhedron connect at symmetry points. A rhombic dodecahedron has the same symmetries as a cube, and this spot corresponds to the corner of a cube.Vladimir Bulatov

The symmetries of a rhombic dodecahedron, it turns out, are the same as a cube, even though the two are different shapes. Imagine, for example, holding the cube by putting one finger in the middle of a face and the other in the middle of the face directly opposite; you could then keep your fingers still, spin the cube by 90 degrees and have it line up exactly as it was. Your fingers were on either side of an axis of four-fold symmetry. You could do the same with the rhombic dodecahedron.

Because a cube has three pairs of faces, the cube has three axes of four-fold symmetry — and so does the rhombic dodecahedron. In addition, the cube and the rhombic dodecahedron have four axes of three-fold symmetry (if your fingers are on corners of the cube that are diagonally opposite) and six axes of two-fold symmetry (if your fingers are on edges of the cube that are diagonally opposite).

MONGE’S THEOREMSuman Vaze took inspiration from a theorem in geometry for this painting. Suman Vaze

Mathematically, Bulatov realized, it was possible to twist the faces 90 degrees and weave their arms to meet inside the figure at each of these symmetry points. The question then was: What would it look like?

“I’m a visual person, but I can only rarely imagine my pieces before I make them,” Bulatov says. “I build them like mathematical relationships. For the first time, when I see them on the computer screen, it’s a surprise. I just have to see, does it have aesthetic value?” In this case, the mathematical relationships resulted in an almost magical, twisting, interweaving knot.

TREFOIL KNOTSThese three knots are different configurations of an overhand knot, called a trefoil. The usual, simplest configuration is on the left. Friedman used the one in the middle as the basis for his sculpture.Nat Friedman

Suman Vaze, a high school math teacher in Hong Kong, takes her inspiration directly from mathematical proofs. In Monge’s Theorem, she illustrates one of the more surprising results in geometry. Take three circles on a plane, any three you like as long as they’re different sizes and none is completely inside another. Connect each pair of circles with two lines that both just touch each edge of the two of the circles. Now consider the three points where each of these pairs of lines intersect one another. It turns out that the points will lie on a single straight line.

Vaze found she couldn’t get this theorem out of her head. “It was like a bee in my bonnet,” she says. “I couldn’t shake it off, so I started doodling.” Her doodles reminded her of the Symphony of Lights, the enormous nightly laser show in Hong Kong, which includes lights from 44 buildings on both sides of Victoria Harbor and is orchestrated to symphonic music “It’s out of this world,” she says. She knew this was a theorem she had to capture in a painting.

TREFOIL KNOT MINIMAL SURFACEThis is the shape a soap film forms over the simplest knot there is, a trefoil.Nat Friedman

She also loved the simple proof of the theorem: Imagine each circle with its pair of tangent lines as a slice of a cone. There will be two planes that just touch the three cones, and their intersection will form a straight line. The points where the original lines intersect will also lie in the intersection of the planes, and hence along that same straight line.

Nat Friedman, a retired mathematician at the University at Albany in New York, finds intriguing shapes for his sculptures through mathematics. Some of the most profound questions in math concern the most humdrum, everyday objects, like knots and soap bubbles. Friedman combined these by twisting wire to form the simplest knot there is — an overhand knot mathematicians call a trefoil — and then dipping it into soapy water. A film formed across the wire, and he then carved this shape out of limestone. Viewed from some angles, it looks a bit like a yin-yang symbol.

Mathematical art started for Friedman as a side amusement from his mathematical work, but it has come to be a central part of his life. Art, he believes, should be far more central in education. “Learning to see is fundamental to both art and mathematics,” he says. “Whole new worlds open up when you can see better.”

www.sciencenews.org

Mathematician answers Supreme Court plea

New, fair method for dividing states into congressional districts could reduce political squabbles.

In 2003, Republicans in the Texas state legislature proposed a bill that would redistrict the state to increase the likelihood of Republican victories. The Democratic representatives, lacking the votes to defeat the measure, fled the state to deny a quorum. After two standoffs (one lasting 45 days), a Democrat broke down and returned to work, and Republicans pushed the measure through. In the next election, Texas Republicans gained six seats in the U.S. House of Representatives, for a total of 21 seats out of 32.

Democrats sued. The Republicans argued that the new districting was only redressing past wrongs, as Republicans had held fewer than half of the Texas congressional seats, even though they had 57 percent of the vote. In 2006, the case reached the Supreme Court.

“Because there are yet no agreed upon substantive principles of fairness in districting, we have no basis on which to define clear, manageable, and politically neutral standards,” Justice Anthony Kennedy had written two years earlier in a similar case in which the judges upheld the redistricting of Pennsylvania. “If workable standards do emerge … courts should be prepared to order relief.”

In the intervening two years, no such standards had presented themselves. The Texas redistricting was upheld.

The next time a redistricting case goes before the Supreme Court, a mathematician says he can provide a method that may satisfy the court. The solution, says Zeph Landau of the University of California, Berkeley lies in cutting cake.

Politicians figured out the power of redrawing district boundaries back in 1812, when Governor Elbridge Gerry lumped most of the Massachusetts Federalists into a single district, allowing his own part to take control of all the other districts in the state. Newspapers mocked the strange, salamander shaped districts, saying he had “gerrymandered” the state. Oddly shaped congressional districts are now common across the country.

By arranging the boundaries to lose big in a few districts and win the rest by small but safe margins, a party can as much as double its percentage of seats. So if, for example, 40 percent of people in the state voted Democratic, redistricting could in theory make 80 percent of the congressional seats Democratic. If, on the other hand, the Republicans drew the boundaries when they had 60 percent of the vote, they might be able to almost double their percentage and get every last seat, although these theoretical maximums often can’t be realized because of geographical constraints.

So what’s fair?

An entire field of mathematics is devoted to answering just this kind of question. For example, take the classic “I cut, you choose” method of dividing cake: If I cut a cake into two pieces I’d be equally happy with, and you pick which of the two you like better, then neither of us will prefer the other person’s piece to the one we have. The division will be fair in that sense even if our priorities are different. For example, I might really want the rose made of frosting, while you might care only about the size of your piece.

Landau and his collaborators, students Ilona Yershov and Oneil Reid of the City College of New York, realized that the mathematics of fair division could be used to solve the redistricting problem. They used a variation on another cake-cutting method: A third party wields the knife, moving left to right across the cake until one of us calls out, “Stop!” when it seems that both sides are equally good. Then the person who called out gets the left piece and the other gets the right one.

The researchers proposed that a variation of this method be used to divide the state into two regions such that neither political party preferred the other’s region. From there, each party would divide up its own region however it liked.

At first blush, this plan doesn’t seem to solve the problem at all. After all, if one party has only 40 percent of the vote, why should it get a full half of the control of the process of dividing the state into districts?

But the mathematicians showed that equally shared control will lead to about the right outcome even if the parties get very different proportions of the votes. If Democrats get only 40 percent of the vote, they can divide up their half of the state to get at most 80 percent of the seats in that region. If the Republicans get all the seats in their half, that means the Democrats would get about 40 percent of the total seats, which corresponds to their percentage of the total vote anyway.

“The idea is to set up the rules of the game so that cheating isn’t really possible,” Landau says.

Landau points out that any restrictions ordinarily applied to the entire state would continue to be applied to the two half-states. So, for example, districts would continue to be required to have approximately equal populations, and the Voting Rights Act would continue to require that for both half-states, the majority of the population in some districts be ethnic minorities.

This fair division method offers the alluring possibility that each party may feel it got the better deal. The reason goes back to the cake: If I care most about the rose made of frosting and you care most about the size of your piece, we each may think our piece superior to the other’s. Similarly, Landau points out, one political party might particularly want to be able to win the district with a stadium in it, while the other party cared more about a district with an important donor.

The team presented its findings in January at the Joint Mathematics Meetings in Washington, D.C., and the research will appear in an upcoming issue of Social Choice and Welfare.

Political scientist David Epstein of Columbia University praised the approach as innovative, but said it’s unlikely to be politically feasible. “The idea that any subset of people is going to have 100 percent dictatorial control of any portion of any state is totally incompatible with the democratic process,” he says. Still, he believes the idea could be useful in other settings, such as perhaps for sharing power within a corporation.

Landau points out that in the current scheme, the ruling party has nearly dictatorial control already, and his scheme assures that that control can’t be used unfairly. “The problem is that the underpinnings of its fairness aren’t quite transparent,” he says. “It requires a paper to explain it.”

What is clear in any case is that a solution is urgently needed. In the 2004 Pennsylvania case, Justice David Souter remarked, “The increasing efficiency of partisan redistricting has damaged the democratic process to a degree that our predecessors only began to imagine.”

www.sciencenews.org

2010 – ÖSYS Öğrenci Seçme ve Yerleştirme Sistemi

Birinci Aşama : Yüseköğretime Geçiş Sınavı (YGS)

Sınav Tarihi : Nisan ayının ilk yarısında

Testler ve Soru Sayıları

l Türkçe testi : 40 soru

l Temel Matematik Testi : 40 Soru

l Sosyal Bilimler Testi : 40 Soru

l Fen Bilimleri Testi : 40 Soru

TOPLAM : 160 Soru

Sınav Süresi : 160 dakika

Testlerin Niteliği : Ortak müfredata dayalı testler

2009-ÖSS’deki ilk 4 test ile aynı niteliklere sahip

Soru Kitapçığı : Tek Soru Kitapçığı

Cevap Kağıdı : Tek Cevap Kağıdı

Birinci Aşama (YGS) Puan Türleri

Testlerin Ağırlıkları (% olarak)

Puan Türü Türkçe Tem. Mat. Sos. Bil. Fen Bil.

YGS-1 20 40 10 30

YGS-2 20 30 10 40

YGS-3 40 20 30 10

YGS-4 30 20 40 10

YGS-5 37 33 20 10

YGS-6 33 37 10 20

YGS Puanları Değer Aralıkları: Her puan türündeki puanlar, en küçüğü 100

en büyüğü 500 olan puanlar olarak hesaplanacaktır.

Birinci Aşama (YGS) Taban Puanları ve Sağlayacağı Haklar:

1) Taban puan-1^*

Önlisans programları ile açıköğretim programlarını tercih etme hakkı.

2) Taban Puan-2^*

İkinci aşama sınavlara katılma hakkı.

3) Taban Puan-3^*

Birinci aşama puanlarıyla da öğrenci alan lisans programlarını tercih etme

hakkı (2009-ÖSYS’de SAY-1, SÖZ-1 veya EA-1 puanlarıyla girilen programlar)

*) YÖK Genel Kurulunda Taban Puanların daha sonra belirlenmesi kararı alınmıştır.

Taban puanlar en geç 2010 ÖSYS Kılavuzunda açıklanacaktır.

İkinci Aşama : Lisans Yerleştirme Sınavları (LYS)

Sınav Tarihi : Haziran ayının ikinci yarısında

(bir ya da iki hafta sonunda)

Sınavlar, Testler ve Soru Sayıları

1. Matematik Sınavı

l Matematik testi : 50 Soru, 75 dakika

l Geometri testi : 30 Soru, 45 dakika

TOPLAM : 80 Soru, 120 dakika

Notlar:

1) Matematik ve Geometri testleri için ayrı Soru Kitapçıkları kullanılacaktır.

2) Cevap Kağıdı iki test için ortak olacaktır.

3) Geometri testindeki sorularının 8 tanesi Analitik Geometri sorusu olacaktır.

2. Fen Bilimleri Sınavı

l Fizik testi : 30 Soru, 45 dakika

l Kimya testi : 30 Soru, 45 dakika

l Biyoloji testi : 30 Soru, 4 dakika

TOPLAM : 90 Soru, 135 dakika

Notlar:

1) Fizik, Kimya ve Biyoloji testleri için ayrı Soru Kitapçıkları kullanılacaktır.

2) Cevap Kağıdı üç test için ortak olacaktır.

3. Edebiyat, Coğrafya Sınavı

l Türk Dili ve Edebiyatı testi : 56 Soru, 85 dakika

l Coğrafya-1 testi : 24 Soru, 35 dakika

TOPLAM : 80 Soru, 120 dakika

Notlar:

1) Türk Dili ve Edebiyatı testi ile Coğrafa-1 testi için ayrı Soru Kitapçıkları

kullanılacaktır.

2) Cevap Kağıdı iki test için ortak olacaktır.

4. Sosyal Bilimler Sınavı

l Tarih testi testi : 44 Soru, 65 dakika

l Coğrafya-2 testi : 16 Soru, 25 dakika

l Felsefe Grubu testi : 30 Soru, 45 dakika

TOPLAM : 90 Soru, 135 dakika

Notlar:

1) Tarih, Coğrafya-2 ve Felsefe Grubu testleri için ayrı Soru Kitapçıkları

kullanılacaktır.

2) Cevap Kağıdı üç test için ortak olacaktır.

3) Felsefe Grubu testinde 10 Psikoloji, 10 Sosyoloji, 10 da Mantık sorusu yer

alacaktır.

5. Yabancı Dil Sınavı

l Yabancı Dil testi : 80 Soru, 120 dakika

Notlar:

1) Yabancı Dil testi İngilizce, Almanca ve Fransızca dillerinde hazırlanacaktır.

2) Yabancı Dil testi için tek Soru Kitapçığı ve tek Cevap Kağıdı kullanılacaktır.

İkinci Aşama (LYS) Puan Türleri

1. MF Grubu Puan Türleri (SAY-2 yerine kullanılacak)

Testlerin Ağırlıkları (% olarak)

P. Türü Türkçe Tem.Mat. Sos.Bil. Fen Bil. Mat. Geo. Fiz. Kim. Biyo.

MF-1 11 16 5 8 26 13 10 6 5

MF-2 11 11 5 13 16 7 13 12 12

MF-3 11 11 7 11 13 5 13 14 15

MF-4 11 14 6 9 22 11 13 9 5

MF-1 puan türü Matematik Ağırlıklı Temel Bilim Programları için,

MF-2 puan türü Fen Ağırlıkı Temel Bilim programları için,

MF-3 puan türü Sağlık Bilimleri programları için,

MF-4 puan türü ise Mühendislik ve Teknik Programlar için öngörülmüştür.

2. TM Grubu Puan Türleri (EA-2 yerine kullanılacak )

Testlerin Ağırlıkları (% olarak)

P. Türü Türkçe Tem.Mat. Sos.Bil. Fen Bil. Mat. Geo. TD ve Edb. Coğ-1

TM-1 14 16 5 5 25 10 18 7

TM-2 14 14 7 5 22 8 22 8

TM-3 15 10 10 5 18 7 25 10

TM-1 puan türü az da olsa Matematik ağırlıklıdır.

TM-3 puan türü az da olsa Türkçe-Edebiyat ağırlıklıdır.

TM-2 puan türünde Matematik ile Türkçe-Edebiyat eşit ağırlıklıdır.

3. TS Grubu Puan Türleri (SÖZ-2 yerine kullanılacak )

Testlerin Ağırlıkları (% olarak)

P. Türü Türkçe Tem.Mat. Sos.Bil. Fen Bil. TD ve Edb. Coğ-1 Tar. Coğ-2 Fel.Gr

TS-1 13 10 12 5 15 8 15 7 15

TS-2 18 6 11 5 25 5 15 5 10

TS-1 puan türü sosyal programlar için,

TS-2 puan türü dil (Türkçe, edebiyat) ve tarih programları için öngörülmüştür.

4. Yabancı Dil Grubu Puan Türleri

Testlerin Ağırlıkları (% olarak)

P. Türü Türkçe Tem.Mat. Sos.Bil. Fen Bil. Yab. Dil

DİL-1 15 6 9 5 65

DİL-2 25 7 13 5 50

DİL-1 puan türü İngilizce, Almanca ve Fransızca Yabancı Dil Programları için,

DİL-2 puan türü diğer Dil Programları için öngörülmüştür.

2009-ÖSYS Puan Türlerinin 2010 ÖSYS’deki karşılıkları

1. Önlisans ve Açıköğretim Programları

2009-ÖSYS 2010-ÖSYS

SAY-1 YGS-1 veya YGS-2

SÖZ-1 YGS-3 veya YGS-4

EA-1 YGS-5 veya YGS-6

2. Lisans Programları (Meslek Lisesi çıkışlı adayların ek puanla girdikleri hariç)

2009-ÖSYS 2010-ÖSYS

SAY-2 MF-1, MF-2, MF-3 veya MF-4

SÖZ-2 TS-1 veya TS-2

EA-2 TM-1, TM-2 veya TM-3

DİL DİL-2 veya DİL-2

3. Lisans Programları (Meslek Lisesi çıkışlı adayların ek puanla girdikleri)

2009-ÖSYS 2010-ÖSYS

SAY-1 Birinci Puan Türü : MF-1, MF-2, MF-3 veya MF-4

İkinci Puan Türü : YGS-1 veya YGS-2

SÖZ-1 Birinci Puan Türü : TS-1 veya TS-2

İkinci Puan Türü : YGS-3 veya YGS-4

EA-1 Birinci Puan Türü : TM-1, TM-2 veya TM-3

İkinci Puan Türü : YGS-5 veya YGS-6

İki puan türü bulunan programlara yerleştirmede, iki puandan büyük olanı

kullanılacaktır.

Ortaöğretim Başarı Puanı (OBP) ve

Ağırlıklı Ortaöğretim Başarı Puanı (AOBP) Değer Aralıkları

OBP ve AOBP mevcut hesaplama yöntemine göre hesaplanacak,

ancak değer aralığı 50 – 100 yerine 100 – 500 olacaktır.

Yerleştirme Puanlarının Hesaplanması

1) Yerleştirme puanları hesaplanırken, Ağırlıklı Ortaöğretim Başarı Puanı (AOBP)

0,15 ile çarpılarak sınav puanlarına (YGS ve LYS puanları) eklenecektir.

Y-YGS = YGS + (0,15 x AOBP)

Y-LYS-MF = LYS-MF + (0,15 x AOBP)

Y-LYS-TM = LYS-MF + (0,15 x AOBP)

Y-LYS-TS = LYS-TS + (0,15 x AOBP)

Y-LYS-DİL = LYS-DİL + (0,15 x AOBP)

LYS, YGS ve AOBP puanları en büyük değeri 500 olduğu için, yerleştirme

puanının en büyük değeri:

500 + (0,15 x 500) = 575 olacaktır

2) Meslek lisesi ve öğretmen lisesi çıkışlı adaylar kendi alanlarındaki lisans

programlarına yerleştirilirken yerleştirme puanlarına eklenecek ek puan

(0,06 x AOBP) olarak hesaplanacaktır.

Ek puanın en büyük değeri 500 x 0,06 = 30 olacaktır.

3) Bir önceki yıl bir yükseköğretim programına merkezi sistemle yerleştirilen

veya ön kayıtla kaydolan adayların yerleştirme puanları hesaplanırken 0,15

ve 0,06 katsayılarının yarısı alınacaktır (0,15 yerine 0,075; 0,06 yerine de 0,03)

Twin Prime Proof Proffered

By Eric W. Weisstein

Author's note:
After this news story was written, a serious error was found in Arenstorf's proof. In particular, Lemma 8 was found to be incorrect. As a result, the paper has been retracted and the twin prime conjecture remains fully open.
June 9, 2004--A recent preprint by Vanderbilt University mathematician R. F. Arenstorf appears to come close to settling the long-standing question of the infinitude of twin primes. Twin primes are pairs of prime numbers such that the larger member of the pair is exactly 2 greater than the smaller, i.e., primes p and q such that q - p = 2. Explicitly, the first few twin primes are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), and (41, 43).

The properties and the distribution of twin primes (so named by P. Stäckel, 1892-1919) are active areas of mathematical research. While the distribution of twin primes has remained elusive, mathematician V. Brun proved in 1919 that the sum of the reciprocals of the members of each twin prime pair

converges to a definite number even if the sum contains an infinite number a terms, a result known as Brun's theorem. The number B, known as Brun's constant, is difficult to compute, but is known to be approximately equal to 1.902160583104. (Amusingly, it was T. Nicely's 1995 high-precision computation of Brun's constant that first revealed a serious hardware bug in Intel's Pentium microprocessor.) Since the sum of the reciprocals of all the primes diverges (which represents a strengthening of Euclid's second theorem on the infinitude of the primes that was first proved by Euler in 1737), Brun's theorem shows that the twin primes are sparsely distributed among the primes.

The twin prime conjecture states that there are an infinite number of twin primes. While Hardy and Wright (1979) note that "the evidence, when examined in detail, appears to justify the conjecture," and Shanks (1993) states even more strongly, "the evidence is overwhelming." Hardy and Wright also note that the proof or disproof of conjectures of this type "is at present beyond the resources of mathematics."

In fact, no proof of the twin primes conjecture had been constructed despite the efforts of dozens of mathematicians over almost a century. In contrast, a recent preprint has apparently succeeded in showing the existence of prime arithmetic progressions of any length k, a related and also long-outstanding problem (MathWorld headline news story, April 12, 2004).

In a May 26 preprint, however, R. F. Arenstorf published a proposed proof of the twin prime conjecture in a stronger form due to Hardy and Littlewood (1923). The proof uses methods from classical analytic number theory, including the properties of the Riemann zeta function, ideas from the proof of the prime number theorem, and a so-called Tauberian theorem by Wiener and Ikehara from 1931, the last of which leads almost immediately to Arenstorf's main result.

While Arenstorf's approach looks promising, an error in one particular step of the proof (specifically, Lemma 8 on page 35; a lemma is short theorem used in proving a larger theorem) has recently been pointed out by French mathematician G. Tenenbaum of the Institut Élie Cartan in Nancy (Tenenbaum 2004). While mathematicians remain hopeful that any holes in the proof can be corrected, Tenenbaum opines that this particular error may have serious consequences for the integrity of the overall proof. Additional analysis by other mathematicians over the coming weeks and months will establish whether, like the originally flawed proof of Fermat's last theorem, the twin prime result can also be corrected, thus finally settling this long-open problem, or if it requires additional insight and tools before it can finally be cracked.

References

Arenstorf, R. F. "There Are Infinitely Many Prime Twins." Preprint. 26 May 2004.
http://arXiv.org/abs/math.NT/0405509

Brun, V. "La serie 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/29 + 1/31 + 1/41 + 1/43 + 1/59 + 1/61 + ..., les dénominateurs sont nombres premiers jumeaux est convergente où finie." Bull. Sci. Math. 43, 124-128, 1919.

Guy, R. K. "Gaps between Primes. Twin Primes." §A8 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 19-23, 1994.

Hardy, G. H. and Littlewood, J. E. "Some Problems of 'Partitio Numerorum.' III. On the Expression of a Number as a Sum of Primes." Acta Math. 44, 1-70, 1923.

Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, p. 5, 1979.

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 30 and 219, 1993.

Tenenbaum, G. "Re: Arenstorf's paper on the Twin Prime Conjecture." NMBRTHRY@listserv.nodak.edu} mailing list. 8 Jun 2004.
http://listserv.nodak.edu/scripts/wa.exe?A2=ind0406&L=nmbrthry&F=&S=&P=1119

The Mathematics of Tsunamis

By Eric W. Weisstein and Michael Trott

January 14, 2005--The recent tragic events following the December 2004 magnitude 9.0 earthquake in the Indian Ocean have reminded us of the need for scientific understanding and modeling of complicated physical phenomena in order to prevent unnecessary loss of life from natural disasters (cf. Post and Vatta 2005).

While the full-scale physics and modeling of tsunamis are difficult problems requiring the use of supercomputers and complicated custom software, a number of approximations can be made that render the problem of tsunami propagation tractable for a computer of modest power running off-the-shelf software such as Wolfram Research's Mathematica.

The simplest theory of water waves that reasonably approximates the behavior of real ocean waves is the system of coupled partial differential equations known as the shallow water wave equations (Pelinovsky et al. 2001, Layton 2002), reproduced above. Here, u and v are the horizontal velocity components of the water surface, x and y are the spatial coordinates of the wave, t is elapsed time, g is the acceleration due to gravity, and h is the height of the wave above the ocean floor topography b.

Part of the physics of tsunamis encompasses the phenomenon of "breaking," or flipping over, as waves near a coastline. However, as the top interface of the water touches only the layer of air above it, it is essentially free. This means the differential equations must be solved in the context of a so-called free boundary value problem, which in general are notoriously difficult to handle and require complicated and difficult computations (Guyenne and Grilli 2003). In addition, as a tsunami propagates over long distances, so-called Coriolis acceleration terms must be included to account for the fact that the frame of reference with respect to which the wave is propagating (i.e., the Earth) is rotating.

Zahibo et al. (2003) have carried out such full-blown calculations. But because the shallow water wave equations are difficult to solve, these equations are sometimes simplified in a number of ways, including by linearizing them. The linearized version takes the velocity of water particles to be (u, v) = , i.e., the gradient of a scalar potential. Even this linearized version has highly nontrivial boundary conditions that are difficult to treat correctly. Taking various asymptotic limits of Euler's equations of inviscid motion results in a host of integrable and nearly integrable equations such as the Korteweg-de Vries equation, Camassa-Holm equation, nonlinear Schrödinger equation, and so on (Rahman 1995, Johnson 2003). Unfortunately, while these equations have exact (integrable) solutions, they also diverge from the true behavior described by the full equations for any but very short time scales (Johnson 2003). Full solution of the shallow water wave equations is therefore needed in order to gain any realistic picture of tsunami propagation.

Visualization of a tsunami computed by Mathematica by numerically solving the shallow water wave equations. Initial conditions are a Gaussian displacement, and the bottom geometry is taken to be flat in the deep ocean, approaching the shoreline like a cosine function, and radially symmetric.

To create the tsunami visualization shown above, we used Mathematica's NDSolve command to solve the shallow water wave equations for an initial Gaussian water displacement. The ocean floor is assumed to be deep and of constant depth in the middle, while smoothly sloping towards the shore like a cosine function. In the animation above, we can clearly see a number of real physical effects, including (1) local propagation of the tsunami, (2) a small offset of the ocean level inside the radial wavefront (an effect only present in even-dimensional systems; in this case, 2-dimensional), and (3) a steepening of the wavefront as it nears the shore. The animation is halted as the wave nears the shore because the shallow wave equations cease providing an accurate description of the wave's propagation as the depth becomes comparable to the wavelength.

Much more complicated simulations performed with custom software and actual coastlines can be seen on the website of the National Oceanic and Atmospheric Administration. Readers interested in the code used to generate this animation may download the corresponding Mathematica notebook. Solving the equations takes less than a minute on a moderately fast desktop computer.

References

Guyenne, P. and Grilli, S. T. "Computations of Three-Dimensional Overturning Waves in Shallow Water: Dynamics and Kinematics." Proc. 13th Int. Offshore and Polar Eng. Conf., Honolulu, Hawaii, USA, May 25-30, 2003. International Society of the Offshore and Polar Engineers, 2003.

Johnson, R. S. "The Classical Problem of Water Waves: A Reservoir of Integrable and Nearly-Integrable Equations." J. Nonl. Math. Phys. 10, Suppl. 1, 72-92, 2003. http://www2.math.uic.edu/~bona/papers/boussineq-paper.pdf

Layton, A. T. and van de Panne, M. "A Numerically Efficient and Stable Algorithm for Animating Water Waves." Visual Comput. 18, 41-53, 2002.

National Oceanic and Atmospheric Administration. "NOAA Home Page: Tsunamis." http://www.noaa.gov/tsunamis.html

National Oceanic and Atmospheric Administration. "Tsunami: Indonesia 12-2004." http://www.noaanews.noaa.gov/video/tsunami-indonesia12-2004.qt

Pelinovsky, E.; Talipova, T.; Kurkin, A.; and Kharif, C. "Nonlinear Mechanism of Tsunami Wave Generation by Atmospheric Disturbances." Natural Hazard and Earth Sci. 1, 243-250, 2001.

Post, D. E. and Votta, L. G. Physics Today 58, 35, January 2005. http://www.aip.org/pt/vol-58/iss-1/contents.html

Rahman, M. Water Waves: Relating Modern Theory to Advanced Engineering Practice. Oxford, Enlgand: Clarendon Press, p. 306, 1995.

Zahibo, N.; Pelinovsky, E.; Yalciner, A. C.; Kurkin, A.; Koselkov, A.; and Zaitsev, A. "The 1867 Virgin Island Tsunami." Natural Hazard and Earth Sci. 3, 367-376, 2003.

47th Known Mersenne Prime Apparently Discovered

By Eric W. Weisstein

June 7, 2009--Less than a year after the 45th and 46th known Mersenne primes were discovered, Great Internet Mersenne Prime Search (GIMPS) project organizer George Woltman is reporting in a June 7 email to the GIMPS mailing list that a new Mersenne number has been flagged as prime and reported to the project's server. If verified, this would be the 47th Mersenne prime discovered. A verification run on the number has been started, and more details will be made available when confirmation of the discovery has been completed. The prime was apparently discovered in April, but was not noticed due to a configuration problem with the server that prevented a notification email being sent to the search organizers.

[Postscript: The prime has now been officially verified and announced to be M_42643801, which has 12837064 decimal digits, making it the 46th known Mersenne prime ranked by size, and hence only the second largest. It was found by Norwegian GIMPS participant Odd Magnar Strindmo.]

Mersenne numbers are numbers of the form M_n = 2ⁿ - 1, giving the first few as 1, 3, 7, 15, 31, 63, 127, .... Interestingly, the definition of these numbers therefore means that the nth Mersenne number is simply a string of n 1s when represented in binary. For example, M₇ = 2⁷ - 1 = 127 = 1111111₂ is a Mersenne number. In fact, since 127 is also prime, 127 is also a Mersenne prime.

The study of such numbers has a long and interesting history, and the search for Mersenne numbers that are prime has been a computationally challenging exercise requiring the world's fastest computers. Mersenne primes are intimately connected with so-called perfect numbers, which were extensively studied by the ancient Greeks, including by Euclid. A complete list of indices n of the previously known Mersenne primes is given in the table below (as well as by sequence A000043 in Neil Sloane's On-Line Encyclopedia of Integer Sequences). The last of these has a whopping 12,978,189 decimal digits. However, note that the region between the 39th and 40th known Mersenne primes has not been completely searched, so it is not known if M_20,996,011 is actually the 40th Mersenne prime.

The following table summarizes all known Mersenne primes.

#		digits	year	discoverer (reference)	value
1	2	1	antiquity		3
2	3	1	antiquity		7
3	5	2	antiquity		31
4	7	3	antiquity		127
5	13	4	1461	Reguis (1536), Cataldi (1603)	8191
6	17	6	1588	Cataldi (1603)	131071
7	19	6	1588	Cataldi (1603)	524287
8	31	10	1750	Euler (1772)	2147483647
9	61	19	1883	Pervouchine (1883), Seelhoff (1886)	2305843009213693951
10	89	27	1911	Powers (1911)	618970019642690137449562111
11	107	33	1913	Powers (1914)	162259276829213363391578010288127
12	127	39	1876	Lucas (1876)	170141183460469231731687303715884105727
13	521	157	Jan. 30, 1952	Robinson (1954)	68647976601306097149...12574028291115057151
14	607	183	Jan. 30, 1952	Robinson (1954)	53113799281676709868...70835393219031728127
15	1279	386	Jun. 25, 1952	Robinson (1954)	10407932194664399081...20710555703168729087
16	2203	664	Oct. 7, 1952	Robinson (1954)	14759799152141802350...50419497686697771007
17	2281	687	Oct. 9, 1952	Robinson (1954)	44608755718375842957...64133172418132836351
18	3217	969	Sep. 8, 1957	Riesel	25911708601320262777...46160677362909315071
19	4253	1281	Nov. 3, 1961	Hurwitz	19079700752443907380...76034687815350484991
20	4423	1332	Nov. 3, 1961	Hurwitz	28554254222827961390...10231057902608580607
21	9689	2917	May 11, 1963	Gillies (1964)	47822027880546120295...18992696826225754111
22	9941	2993	May 16, 1963	Gillies (1964)	34608828249085121524...19426224883789463551
23	11213	3376	Jun. 2, 1963	Gillies (1964)	28141120136973731333...67391476087696392191
24	19937	6002	Mar. 4, 1971	Tuckerman (1971)	43154247973881626480...36741539030968041471
25	21701	6533	Oct. 30, 1978	Noll and Nickel (1980)	44867916611904333479...57410828353511882751
26	23209	6987	Feb. 9, 1979	Noll (Noll and Nickel 1980)	40287411577898877818...36743355523779264511
27	44497	13395	Apr. 8, 1979	Nelson and Slowinski	85450982430363380319...44867686961011228671
28	86243	25962	Sep. 25, 1982	Slowinski	53692799550275632152...99857021709433438207
29	110503	33265	Jan. 28, 1988	Colquitt and Welsh (1991)	52192831334175505976...69951621083465515007
30	132049	39751	Sep. 20, 1983	Slowinski	51274027626932072381...52138578455730061311
31	216091	65050	Sep. 6, 1985	Slowinski	74609310306466134368...91336204103815528447
32	756839	227832	Feb. 19, 1992	Slowinski and Gage	17413590682008709732...02603793328544677887
33	859433	258716	Jan. 10, 1994	Slowinski and Gage	12949812560420764966...02414267243500142591
34	1257787	378632	Sep. 3, 1996	Slowinski and Gage	41224577362142867472...31257188976089366527
35	1398269	420921	Nov. 12, 1996	Joel Armengaud/GIMPS	81471756441257307514...85532025868451315711
36	2976221	895832	Aug. 24, 1997	Gordon Spence/GIMPS	62334007624857864988...76506256743729201151
37	3021377	909526	Jan. 27, 1998	Roland Clarkson/GIMPS	12741168303009336743...25422631973024694271
38	6972593	2098960	Jun. 1, 1999	Nayan Hajratwala/GIMPS	43707574412708137883...35366526142924193791
39	13466917	4053946	Nov. 14, 2001	Michael Cameron/GIMPS	92494773800670132224...30073855470256259071
40	20996011	6320430	Nov. 17, 2003	Michael Shafer/GIMPS	12597689545033010502...94714065762855682047
41?	24036583	7235733	May 15, 2004	Josh Findley/GIMPS	29941042940415717208...67436921882733969407
42?	25964951	7816230	Feb. 18, 2005	Martin Nowak/GIMPS	12216463006127794810...98933257280577077247
43?	30402457	9152052	Dec. 15, 2005	Curtis Cooper and Steven Boone/GIMPS	31541647561884608093...11134297411652943871
44?	32582657	9808358	Sep. 4, 2006	Curtis Cooper and Steven Boone/GIMPS	12457502601536945540...11752880154053967871
45?	37156667	11185272	Sep. 6, 2008	Hans-Michael Elvenich/GIMPS	20225440689097733553...21340265022308220927
46?	42643801	12837064	Jun. 12, 2009	Odd Magnar Strindmo/GIMPS	16987351645274162247...84101954765562314751
47?	43112609	12978189	Aug. 23, 2008	Edson Smith/GIMPS	31647026933025592314...80022181166697152511

The 13 largest known Mersenne primes (including the latest candidate) have all been discovered by GIMPS, which is a distributed computing project being undertaken by an international collaboration of volunteers. Thus far, GIMPS participants have tested and double-checked all exponents n below 18,000,949, while all exponents below 26,181,803 have been tested at least once. The candidate prime has yet to be verified by independent software running on different hardware. If confirmed, GIMPS will make an official press release that will reveal the number and the name of the lucky discoverer.

References

Caldwell, C. K. "The Largest Known Primes."
http://www.utm.edu/research/primes/largest.html

GIMPS: The Great Internet Mersenne Prime Search. "47th Known Mersenne Prime Found!"
http://www.mersenne.org

GIMPS: The Great Internet Mersenne Prime Search Status.
http://www.mersenne.org/status.htm

Woltman, G. "New Mersenne Prime?" Message to The Great Internet Mersenne Prime Search List. Jun. 4, 2009.
http://www.mail-archive.com/prime@hogranch.com/msg02351.html

Woltman, G. "New Mersenne Prime?" Message to The Great Internet Mersenne Prime Search List. Jun. 7, 2009.
http://www.mail-archive.com/prime@hogranch.com/msg02362.html

Woltman, G. "It's Official - 47th Mersenne Prime Found" Message to The Great Internet Mersenne Prime Search List. Jun. 12, 2009.
http://www.mail-archive.com/prime@hogranch.com/msg02379.html