Genel

Using Artificial Neural Networks in Solving Differential Equations

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The theme of our career event this month is “Generative Artificial Intelligence and Our Profession” and within the scope of the theme, a seminar titled “Using Artificial Neural Networks in Solving Differential Equations” will be given by Dr. Cem ÇELİK in our department. The seminar is open to everyone who is interested.

Speaker: Dr. Cem ÇELİK (DEU, Department of Mathematics)
Title: Using Artificial Neural Networks in Solving Differential Equations
Date and Time: 19.03.2025 (Wednesday),  12:00
Place: B256 (DEU Faculty of Science Department of Mathematics Block B 2nd floor)

Abstract: The intersection of scientific computing and machine learning has given rise to a paradigm known as Scientific Machine Learning (SciML). This talk will explore the principles of SciML, with a particular focus on Physics-Informed Neural Networks (PINNs), a novel approach that integrates the principles of physics with machine learning techniques to solve complex scientific and engineering problems. By embedding physical laws directly into the neural network architecture, PINNs enable the modeling of systems governed by partial differential equations (PDEs) while leveraging the strengths of data-driven methods. This presentation will cover the foundational concepts of PINNs through practical examples, and participants will gain insights into the potential of PINNs to revolutionize problem-solving.

Actuarial Career for Mathematics Students

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The theme of our career event this month is “Actuarial” and a talk will be held with our 2023 graduate Mustafa EROL on the subject of “Actuarial Career for Mathematics Students”. The event is open to all mathematics students and anyone interested.

Speaker: Mustafa Erol (AXA Insurance Actuarial Assistant Specialist)
Subject: Actuarial Career for Mathematics Students
Date and Time: 13.01.2025, 12:00
Place: B256 (Faculty of Science, Department of Mathematics)
Moderator: Asst.Prof.Dr. Celal Cem SARIOĞLU

Fundamental Theorem of Symmetric Polynomials, Newton’s Identities and Discriminants

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Mustafa Eren Taşlı, Dokuz Eylül University. Date: 26th of December, 2024, Wednesday, Time: 15.00 – 16.00. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B255.

Abstract: We will define symmetric polynomials and the elementary symmetric polynomials in n indeterminates over a field F. The elementary symmetric polynomials in the indeterminates x_1, x_2, \ldots, x_n are as follows:

    \begin{align*} \sigma_1=&x_1+x_2+\ldots+x_n \\ \sigma_2=&\sum_{1 \le i < j \le n} x_ix_j \\ \vdots\\ \sigma_n =&x_1 x_2 \ldots x_n \end{align*}

The Fundamental Theorem of Symmetric Polynomials states that any symmetric polynomial can be expressed as a polynomial in the elementary symmetric polynomials, that is:

Theorem. Let f(x_1, x_2, \ldots, x_n) be a symmetric polynomial in the n indeterminates x_1, x_2, \ldots, x_n over a field F. Then, there exists a polynomial g(y_1, y_2, \ldots, y_n) in the n indeterminates y_1, y_2, \ldots, y_n such that

    \[f(x_1, x_2, \ldots, x_n) = g(\sigma_1, \sigma_2, \ldots, \sigma_n),\]

where \sigma_1, \sigma_2, \ldots, \sigma_n are the above elementary symmetric polynomials of the n indeterminates x_1, x_2, \ldots, x_n. Moreover, the polynomial g(y_1, y_2, \ldots, y_n) is uniquely determined.

We will prove this theorem using the graded lexicographic order for multivariable polynomials.

Using the recurrence relation from the Newton Identities, we will learn how to express the sum of powers of the indeterminates, that is, the polyomials

    \[s_k = x_1^k + x_2^k + \ldots + x_n^k\]

for a positive integer k, as polynomials in terms of the elementary symmetric polynomials. We will reinforce this understanding with examples.

The discriminant in the indeterminates x_1, x_2, \ldots, x_n over the field F is given by:

    \[\Delta = \prod_{1 \leq i < j \leq n} (x_i - x_j)^2 \in F[x_1, \dots, x_n].\]

The discriminant is a symmetric polynomial, and we will express it in terms of the elementary symmetric polynomials using determinants.

This seminar, as part of my graduation project titled Symmetric Polynomials, Newton’s Identities, Discriminants, and Resultants, serves as an introduction to a method for calculating the discriminant (\Delta) of an n-th degree polynomial without finding its roots.

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Cryptography and Mathematics

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This month’s career event theme is “Cryptography and Mathematics”. We are pleased to host a talk on this subject with Beste AKDOĞAN KÖSEMEN, a 2016 graduate of our department and currently pursuing her Ph.D. in Cryptography at METU Institute of Applied Mathematics. The event is open to all mathematics department students and anyone interested. (Non-mathematics department participants are kindly requested to contact the moderator for attendance.)

Speaker: Res. Asst. Beste AKDOĞAN KÖSEMEN (Ankara Yıldırım Beyazıt University, Mathematics Department & METU Institute of Applied Mathematics)
Topic: Mathematics and Cryptography
Date & Time: December 23, 2024, 12:00 PM
Venue: online.deu.edu.tr
Channel: DEUMatematikKARİYER
Moderator: Asst.Prof.Dr. Celal Cem SARIOĞLU

 

From Mathematics to Codes: Shaping the Future with Artificial Intelligence

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The theme of our career event this month, organized by DEU Faculty of Science, Department of Mathematics in collaboration with DEU Career Planning Center, is “Career Tips from Young Graduates”. Everyone interested in the talk titled “From Mathematics to Codes: Shaping the Future with Artificial Intelligence”, which we will hold with our 2024 graduate of the Department of Mathematics “Şule YALIM”, who works as an expert software developer at Morfoz AI, is invited. (Participants other than students of the Department of Mathematics are kindly requested to contact the moderator for event participation.)

Speaker: Şule YALIM (DEU Mathematics 2024 Graduate / Morfoz AI, Expert Software Developer)
Moderator: Asst. Prof. Dr.  Celal Cem SARIOĞLU
Date and Time: 30.11.2024, 19:00
Place: online.deu.edu.tr
Chanel: DEUMatematikKARİYER

How to Write a TUBITAK 2209 A/B Project? What Should be Considered?

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The theme of our career event this month is “+1 Step in Career: I am Writing a TÜBİTAK 2209 Project”. In our event, information will be given about TÜBİTAK 2209 University Student Research Projects and a conversation will be held on the points to be considered when writing a project. The event is open to all mathematics department students and those who are interested.

Speaker: Dr. Öğr. Üyesi Celal Cem SARIOĞLU
Date and Time: 25.10.2024, 12:15
Place: B256 (DEU Faculty of Science, Department of Mathematics)

 

Dreams That Touch the Sky

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Salih AKIN, Second Pilot at THY (graduated from DEU, Faculty of Science, Department of Mathematics)

Saadet SARICA, THY Cargo Marketing Directorate, Fare Specialist at the Fare Department (graduated from DEU, Faculty of Science, Department of Mathematics)

Date: Thursday, May 23, 2024

Time: 13:30

Location: DEÜ, Faculty of Science, B block, Prof. Dr. Ömer Köse Conference Hall

Summary: In this event, we will share my business processes and career experiences in the aviation industry.

 

Hydroelastic waves propagating in ice-covered channel

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Prof. Dr. Tatyana Khabakhpasheva, School of Mathematics, University of East Anglia, Norwich/United Kingdom

Date: May 24, 2024, Friday

Time: 14:00 am

Place: B255, Faculty of Science, Dokuz Eylül University

Abstract: Characteristics of linear hydroelastic waves propagating in an ice channel are investigated. The channel is of rectangular cross section with finite depth and of infinite extent. Liquid in the channel is inviscid and incompressible. The liquid flow caused by the ice deflection is potential. The ice is modeled by a thin elastic plate. The coupled hydroelastic problem is reduced to the problem of the wave profiles across the channel. The wave profiles are sought as series of normal dry modes of the plate, coefficients of which are to be determined. Dispersion relations of these hydroelastic waves, their critical speeds, and corresponding strain and stress distributions in the plate are determined. Several special cases in which boundary conditions, ice thickness distributions across the channel width, and ice plate compression were changed were investigated and compared with each other.

Coupled/decoupled linear/nonlinear responses of ice cover to external loads

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Prof. Dr. Alexander Korobkin, School of Mathematics, University of East Anglia, Norwich/United Kingdom

Date: May 24, 2024, Friday

Time: 13:00 am

Place: B255, Faculty of Science, Dokuz Eylül University

Abstract: Modelling response of an elastic floating plate to a body moving under the plate is discussed. The original problem is nonlinear and coupled with the plate deflection being dependent on the hydrodynamic pressure, which in turn depends on the plate deflection. It is shown that the problem can be treated as decoupled for some conditions of the body motion, which significantly simplifies the analysis. Within the decoupled model, the body motion and the hydrodynamic pressure along the plate/water interface are calculated without account for the plate deflection. Then this pressure is applied to the equations of the plate dynamics without account for the fluid response to the plate deflection. It is known that only rather small strains are allowed in ice plates, which limits the deflections of the ice and importance of the nonlinear effects. It is shown that nonlinear effects in problems of hydroelastic response of floating ice sheets can be approximately neglected in many practical situations.