The Department’s research agenda is set with the emphasis placed on the interface between mathematical problems and real-world problems. Natural phenomena like waves, earthquakes, economic predictions, robotics, recognitions, simulations, and even in biology, cancer, and heart problems are simulated and modelled by mathematical problems. This vision fosters a unique academic environment where pure and applied mathematics are both conducted in harmony. We seek for inventing new tools and solving open problems in pure mathematics. Then, when it is appropriate, we use these tools to the real-world problems.
Our perception is that all mathematics can be pure and applied alike. Several topics in mathematics started as pure then they found realizations and were applied in significant ways. Good examples here could be number theory and the theory of finite fields, these are beautiful pieces of pure mathematics that are applied heavily in cryptography. The opposite can also be true, pure mathematics can be invented for application reasons. The logical definition of limits was invented by Cauchy to justify the work of Newton in the study of motions and the effect of infinitesimal changes.
The pure mathematics in our department is quite vibrant, with active collaboration with scholars from Europe and the Middle East. The research in this field is mainly concerned with objects that are equipped with a structure. It is true that we might be fascinated with the beauty of some specific mathematical structure, but we are still wondering what the structure can tell about itself. What are the concepts that can be defined? How can they be defined? Our contribution to pure mathematics is recognized through high quality papers published in prestigious international journals.
The applied mathematics constitutes the link between science and the real-world problems. The point is, the logic needs modelling, the modelling needs information, the information needs relations and, the relations need mathematical and logical models, the models are evaluated by the results and, finally all are called applied mathematics. In our applied mathematical group, we have several internationally recognized experts in this field who attribute to the scientific society with many books and novel articles published in the most respected publishing houses. In addition, our department is at the forefront with various projects carried out by our academicians. Our most up-to-date project, which we can exemplify on popular topics, titled "Pruning the Layers of Deep Neural Networks with Sparse Second-Order Conic Programming", was funded by TÜBİTAK in August 2019 and led by our Department Chair Assoc. Prof. Dr. Sureyya AKYÜZ.
Research Areas:
• Mathematical Analysis and PDEs.
• Complex Analysis and Applications.
• Applied and Numerical Analysis.
• Machine Learning.
• Statistics and Financial Mathematics.
• Algebra and Number Theory.
• Universal Algebra and Algebraic Logic.
• Mathematics in Philosophy and Cognitive Science.
• Mathematics in Medicine.
• Biological Mathematics
• Mathematical Physics
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