## Research

**Research Area:** Geometry & Topology, Mathematics Education

**Research Profile:** *Differential Geometry, Applications, and Mathematics Education*

My research dealt with some aspects of the curvature of a Riemannian manifold, in particular the way various curvature assumptions influence the topological properties (pinching theorems). I had also employed the tools of Riemannian geometry (especially foliations on Riemannian manifolds) in order to study the properties of orbits of vector fields coming from various control theory problems. In collaboration with Ernst Ruh and Maung Min-Oo, I obtained new parametrization of the space of multivariate normal distributions (and a new distance formula).

My new research directions consist of applying math to problems in medicine and biology (in collaboration with colleagues and grad students from Health Sciences), and also mathematics education. Besides investigating my own teaching practice, I have been studying transition from secondary to tertiary mathematics, as well as the ways mathematics textbooks promote learning of mathematics.

## Publications

Marc Colangelo, Miroslav Lovric, Johathan R. Stone. A Mathematical and Computational Model for Simulating Complex Dynamic Cancer Growth and Metastasis. I. J. Comput. Appl. 19(3):145-153 (2012).

Marc Colangelo, Miroslav Lovric, et. Al. Modelling of House Dust Mite-Induced Chronic Airway Eosinophiliaā€¯ to appear in Biology Direct.

Miroslav Lovric. Learning Mathematics In An Interdisciplinary Science Program. Proceedings of the 12^{th} International Congress on Mathematical Education, COEX, Seoul, Korea, 2012, pp 1331-1340.

Miroslav Lovric. Collaboration Between Research in Mathematics Education and Teaching Mathematics: Case Study of Teaching Infinity in Calculus. Proceedings of the CMESG (= Canadian Mathematics Education Study Group) Meeting, Quebec City, 2012.

Ann Kajander, Miroslav Lovric. Mathematics Textbooks And Their Potential Role In Supporting Misconceptions. The Best Writing on Mathematics 2010, Princeton University Press, 2010.

Megan Clark, Miroslav Lovric. Suggestion for a Theoretical Model for the Secondary-Tertiary Transition in Mathematics, Mathematics Education Research Journal, Vol. 20, No. 2, 2008, pp 25-37.

Laura Fenwick-Sehl, Marcella Fioroni, Miroslav Lovric. Recruitment and retention of mathematics students in Canadian universities. International Journal of Mathematical Education in Science and Technology, Volume 40, Issue 1, 2009, pages 27-41.

Textbooks:

Calculus for Life Sciences: Modeling the Dynamics of Life, (with F. Adler), Nelson 2011 (676 pages); new edition coming out in 2014.

Probability and Statistics for the Life Sciences, Nelson 2011 (195 pages).

Functions of Several Variables for the Life Sciences, Nelson 2011 (144 pages).

Linear Algebra for the Life Sciences Nelson, 2011 (138 pages).

Vector Calculus, John Wiley and Sons, 2007 (623 pages).

## Graduate Students

Current Supervising:

Myles Marin (MSc Math)