The cooperation with universities is extensive and diversified. Many members of the Institute take part in undergraduate and graduate teaching, in examination commissions, in seminars and in joint research grants. The representation in scientific councils is mutual. The Institute cooperates with universities in the organization of conferences, summer schools, workshops etc. Moreover, the Institute cooperates with universities on formulation of projects of mathematics education in elementary and secondary schools and with the Union of Czech Mathematicians and Physicists in the preparation and organization of the Mathematical Olympiad competitions. The Institute's library – the largest mathematical library in the country – collaborates with libraries of universities and research institutes in the Czech Republic and abroad.
As an abstract discipline, mathematics finds its role in the domain of applications in most cases indirectly, in cooperation with some branch of science, technical sciences etc. The Institute endeavours to collaborate in this field with other institutes of the Academy, universities as well as industrial companies. The topics comprise, e.g., transfer phenomena of convection or diffusion of pollutants, fluid dynamics, properties of thin layers of metals and isolants on semiconductor surfaces or metastatic activities of tumor cells.
Of cardinal importance are scientific contacts with foreign research institutions and universities comprising mutual research visits and invitations for lectures often underset with contracts on research exchange. The Institute makes a regular effort to generate resources for visiting scholars.
This is a joint department of the Institute of Mathematics and the Faculty of Mathematics and Physics of the Charles University in Prague, established on 18 March 2013 to continue the efforts of a joint project funded by the Ministry of Education, Youth and Sports in 2005–2011. Its general goal is to establish a significant scientific team in the field of mathematical properties of models in continuum mechanics and thermodynamics, developed by an intensive collaboration of important research teams at both institutions and their goal-directed collaboration with top experts from abroad.
Its role is at least two-fold: first, to act as a counseling centre in questions which approach to a given problem should be taken, and second, to be an acceptor of new stimulations to further development. Organization of lecture courses and the everyday interaction with Ph.D. students and undergraguate students aims at upbringing new generation of competent scientist and forming a basis for a strong and stable research team.
DIMATIA was established in September 1996 as a consortium of the Faculty of Mathematics and Physics of the Charles University in Prague, the Institute of Mathematics and the Institute of Chemical Technology in Prague with the aim to foster research in all fields of discrete mathematics and its modern applications and relationship to computer science, operations research and fields as diverse as biology, chemistry and social sciences. The centre organizes a continuing programme of workshops, conferences and research visits, postdoctoral positions announced and jointly supported by the partners and short-term visits of senior researches.
ITI was established as a consortium for joint project of the Faculty of Mathematics and Physics of the Charles University in Prague, the Institute of Mathematics, the Institute of Computer Science CAS in Prague, the Faculty of Applied Sciences of the University of West Bohemia in Pilsen and the Faculty of Informatics of the Masaryk University in Brno, funded by the Ministry of Education, Youth and Sports in 2005–2011. Its activity continues in frames of a joint project of a centre of excellence supported by the Czech Science Foundation in 2012–2018. Its main aim is to promote research in theoretical computer science and related fields with emphasis on the work of young researchers. ITI will also provide temporary positions for postdocs and distinguished senior researchers.