The Department of Applied Mathematics and Complex Systems Modeling (AM&CSM) was established on September 1, 2016, by combining the departments of Applied and Computational Mathematics (A&CM) and Complex Systems Modeling (CSM). The department is headed by Igor V. Koplyk, Associate Professor, Candidate of Physical and Mathematical Sciences. Today 4 doctors of science and 8 candidates of science work at the department of AM&CSM.

The Chair of A&CM was established in September 1995 by Professor Leonid A. Fylshtynskyi as the Chair of Mathematical Physics. In 2002, in connection with the emergence of new scientific fields, the name was changed to the Department of Applied Mathematics and Mechanics. In the same year she became a graduate for the specialty "Applied Mathematics". In 2009, the name was changed to the Department of Applied and Computational Mathematics. All the years from 1995 to 2016, the department was headed by Doctor of Physics and Mathematics, Professor, L. A. Fylshtynskyi. He is the founder of the Sumy school of specialists in the field of mechanics of a deformable solid and electrodynamics of a continuous medium. Under the leadership of L. A. Fylshtynskyi 3 doctoral and more than 30 master's theses were prepared and successfully defended.

The CSM Department was established in May 2000 on the basis of the section of the Department of General and Experimental Physics and the Department of Economic and Mathematical Methods. From the beginning of the creation of the CSM department until 2001 it was headed by Doctor of Physical and Mathematical Sciences, Professor, S. P. Roshchupkin. From 2001 to 2015, the head of the department was Candidate of Physical and Mathematical Sciences, Associate Professor, Vasiliy D. Karpusha. From March 2015, Alexander Lysenko, Doctor of Physical and Mathematical Sciences, Professor, work as the Head of the Department of CSM.