Month: March 2024

Different Career Routes : Air Traffic Controller

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This month’s theme of our career event organized by the DEU Faculty of Science Department of Mathematics in cooperation with the DEU Career Planning Center is “Different Career Routes”. Everyone who is interested is invited to the conversation on “Air Traffic Controller”, which we will hold with “Tuğçe SERTOĞLU”, 2009 graduate of the Department of Mathematics, who works as an air traffic controller in state airports. (Participants other than Mathematics Department students are requested to contact the moderator to participate the event.)

Speaker: Tuğçe SERTOĞLU (DEU Mathematics 2009 Graduate / DHMI Air Traffic Controller)
Moderator: Asst. Prof. Dr. Celal Cem SARIOĞLU
Date and Time: 29.03.2024, 21:00
Location: online.deu.edu.tr
Channel:  DEUMatematikKARİYER

Matematiksel Bilginin Doğası

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Prof. Dr. Beno KURYEL, İzmir Ekonomi Üniversitesi (Ege Üniv. Kimya Mühendisliği, Emekli) Tarih: Daha sonra ilan edilecek. Zaman: Daha sonra ilan edilecek. Yer: Deü Fen Fakültesi B255 nolu derslik

Özet: Matematik, tarih boyunca felsefi düşüncenin ve araştırmalarının zengin kaynaklarından birisi olmuştur. Karşılıklı bir etkileşim bütünlüğünde felsefe de matematiksel bilginin üretimine, kavramsal zenginlik kazanmasına, yöntemsel tasarımların oluşmasına kaynaklık etmiştir. Ancak son yıllarda teknolojinin belirleyici kültür şemsiyesinde matematik, teknik ve pragmatik bir araçsallığa indirgenmiştir. Bu durum hem matematik öğrenimini hem de matematiksel teori ve pratiği dar bir kalıp içine hapsetmektedir. Matematiksel bilginin doğasını incelemek ve öğretim süreçleri ile bütünleştirmek bu araçsallığın eleştirisi için atılacak önemli adımlardan birisidir. Bu çalışma, konunun farklı boyutlar içinde bilgikuramsal bir çözümlemesini ve yeni felsefi açılımların geliştirilmesini hedeflemektedir.

A Countable Prime Avoidance Theorem and Its Generalization to Prime Submodules

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M. R. Pournaki, Sharif University of Technology. Date: 29th of March, 2024, Friday, Time: 13.00 – 14.00. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B255.

Abstract: One of the fundamental cornerstones of commutative ring theory is the prime avoidance theorem, which states that, if \frak{p_1},\ldots,\frak{p_n} are prime ideals of R and \frak{a} is an ideal of R such that \frak{a}\subseteq {\bigcup_{i=1}^n} \frak{p_i}, then \frak{a}\subseteq \frak{p_i} for some 1\leq i\leq n. In this talk, we give a proof for the countable version of this theorem due to Sharp and Vamos. The proof uses the celebrated Baire’s category theorem in metric spaces. We then discuss its generalization to the prime submodules.

A Glimpse to the Stanley Depth: A Geometric Invariant for Modules

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M. R. Pournaki, Sharif University of Technology. Date: 22nd of March, 2024, Friday, Time: 13.00 – 14.00. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B255.

Abstract: Stanley depth is a geometric invariant of a module which has some common properties with the homological depth invariant. In this talk, we first review briefly the basic concepts of Stanley depth and then discuss some of the recent developments in the theory.

 

 

 

A Glimpse to Unit Graphs: The Graphs Arising From Rings

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M. R. Pournaki, Sharif University of Technology. Date: 15th of March, 2024, Friday, Time: 13.00 – 14.00. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B255.

Abstract: The ring \mathbb{Z}_2\times\mathbb{Z}_2, having only one unit, cannot be generated by its units. It turns out, in the general theory of rings, that this is essentially the only example. In this talk, we give an elementary proof of “A finite commutative ring with nonzero identity is generated by its units if and only if it cannot have \mathbb{Z}_2\times\mathbb{Z}_2 as a quotient.” The proof uses graph theory and pointed out to the story of how unit graphs have been arisen. At the end, we discuss some of the recent developments in the theory.

When Three Subjects of Mathematics Meet Each Other

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M. R. Pournaki, Sharif University of Technology. Date: 8th of March, 2024, Friday, Time: 13.00 – 14.00. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Class B255.

Abstract: Fermat’s little theorem states that if p is a prime number, then a^p \equiv a (mod p) holds true for any integer a. One may ask what happens when p is not a prime. The answer to this question seems little known to mathematicians, even to number theorists (as Dickson said in his “History of the Theory of Numbers”). In this talk, we discuss the missing result which is essentially due to Gauss and its generalizations.