[Turkmath:8772] yuksek lisans ders tanitimi: math590 selected topics in math modelling: graph theory modeling

[Turker Biyikoglu]

Merhabalar

Izmirde bulunan Yuksek lisans programlarinin (matematik, bilgisayar, bioinf
vb) geneline hitap edebilecegini dusundugum bir dersi duyurmak istiyorum.
Izmir Yuksek Teknoloji Enstitusunde actigimiz Math 590 Selected topics in
applied mathematics dersi.

Ders iceriginin esnekligini kullanarak cizge kuramini (graph theory) bir
matematiksel modelleme lisani olarak gorecegiz.
Ilk bes-alti haftada her hangi bir on bilgi gerektirmiyen modelleme icin
gerekli olan temel cizge kurami tanim ve ozelliklerinden sonra cizge kurami
ile modelleme, cizge modellerinin birbirinden farki, onemli cizge kuram
sabitleri, hangi problemlerin kazik oldugu (np-complete) kazik problemlere
nasil yaklasimlar getirilebildigi, derece dizi ve dagilimlari, cizgelerin
benzetimleri (simulation) gibi temel konular isledikten sonra bir birinden
farkli guncel arastirma alanlarinda onemli cizge modellemelerinden
bahsedecegiz. Bunlardan belli baslilari: Big data science and graph thoery,
social networks, chemical graph theory, dynamical systems, graph theory in
bioinformatics, eigenvectors from search engines to pattern recognition...

ogrenciler guncel bir arastirma alanindan secicekleri bir donem projesi
yapicaklar (arzu ederlerse modeleme icin problem getirebilirler) kritik bir
grup baska bir konudaki cizge kurami modelleme ve uygulamalarini gormek
isterse oda mumkun.

ilgilenebilecegini dusundugunuz izmirde bulunan yuksek lisans ve doktora
ogrencilerine (merakli lisans ogrencileride katilabiliri)
duyurabilirseniz sevinirim.

Cizge kurami ve uygulamalarina merakli herkez davetlidir.

asagida daha bir detayli ders tanitimi var.

iyi bir akademik bahar donemi dileklerimle

Turker


Math 590 Selected Topics in Applied Mathematics (3-0) 3 W:9-12
Instructor: Doc. Dr. Turker Biyikoglu, Math Dept
Contact: MD-202, phone 7764, e-mail: turkerbiyikoglu at iyte.edu.tr

Graph theory plays an important role in modeling problems not only in
Mathematics but also in areas such as Computer Engineering Bioinformatics,
Electronics and so forth. The goal of this course is to introduce graph
theory as a mathematical modeling language to all students.

Week 1: Recall mathematical modeling, basic graph theory terminology
Week 2: Graph modeling and Graph representations
Week 3: Important Graph Invariants and Properties
Week 4: Random graphs are strange
Week 5: NP-complete problems and their approximations
Week 6: Social and asocial networks
Week 7: Chemical graph theory
Week 8: Dynamical systems
Week 9: Graph theory in bioinformatics
Week10: Graph Eigenvectors from search engines to pattern recognition
Week11: Graph theory in economics
Week12: Big Data Science and the role of the graph theory
Week13: What can we do with hyper graps in neuroscience?
Week14: Student Presentations

The order or topics of Weeks 5-13 can be changed.

References:
D. West, Introduction to Graph Theory, Pearson.
Recent survey articles, research articles (e.g. from Nature, Science, PNAS)

Grading: Homeworks %40, Term project %40, Final %20.

Assoc. Prof. Turker Biyikoglu
Izmir Institute of Technology
Department of Mathematics
Gulbahce Urla 35430, Izmir, Turkey
Office: MD 202
Phone: +90 232 750 7764
e-mail: turkerbiyikoglu at iyte.edu.tr
URL: http://web.iyte.edu.tr/~turkerbiyikoglu
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