The scientific research conducted at the Department of Descriptive Geometry focuses on three main areas: computer-aided geometric design (CAGD), tool geometry, and computer-aided design (CAD) systems. Within computer-aided geometric design, significant results have been achieved in the modeling of curves and surfaces, as well as in their constraint-based shape modification. Research in tool geometry mainly focuses on the geometric aspects of worm design. Regarding CAD systems, a specialized module has been developed to address specific user problems within the system.

Departmental research topics include functional equations, measure theory, mathematical statistics, theory of numbers, numerical methods, probability theory, optimisation, and special subjects of applied mathematics and informatics.

90% of the teachers of the department hold PhD degrees.

Research students have always played a crucial role in the research of the Department of Applied Mathematics, working on demanding research problems under the supervision of leading mathematical scientists and, in many cases, moving on to become research leaders themselves. The current aim of Department of Applied Mathematics is to continue this tradition by broadening the range of subject areas studied and using new mathematical and computational techniques.

The journal Miskolc Mathematical Notes was founded by the departments of Analysis and Applied Mathematics. This is the only periodical of the University of Miskolc possessing a Thomson-Reuters impact factor.

Some department members work in algebra and number theory: rings with polynomial identities, endomorphism rings of modules and matrix algebras centralisers in associative algebras, partially ordered sets and algebraic structures, lattices, universal algebras and compatible tolerances zeros of the shifted Hermite, Euler and Bernoulli polynomials, and effective Diophantine results related to Appel sequences.

Other research topics are in mathematical analysis: development of numerical-analytic methods for the investigation of various types of non-linear boundary value problems for ordinary differential equations, boundary and eigenvalue problems of ordinary and partial differential equations, exactly solvable differential equations of mathematical physics and application of differential equations in fluid mechanics and vibration, as well as functional equations and inequalities. A further research topic is the theory of Lie nilpotent manifolds and loops.

Numerous international conferences and workshops have been organised on differential equations. The department was the local organiser of the ECM satellite conference on ring theory.