The Department of Mathematics is one four Departments of the School of Science in the college of Science and technology (CST) MISSION AND VISION Vision: The vision of the Department is to become a high level centre for quality teaching and research in mathematics and statistics that has an international reputation, providing graduates with a strong and broad background in mathematics and statistics and the experience needed to work successfully in private and public sectors in Rwanda and in the region. Mission: Transmit mathematics knowledge and application from one generation to another, conduct scientific research, and make mathematics more marketable. Objectives (to include):
 Develop interdisciplinary, problembased academic programmes aligned with Rwanda's development needs.
DEPARTMENT STRUCTURE The Department of Mathematics has two undergraduate programs, MSc in Applied Mathematics and PhD program
Rationale According to the Government’s 2020 Vision, Rwanda would like to be a modern nation, able to generate and disseminate technological knowledge and innovations in its socioeconomic development. In order to achieve this goal, there is a need to build a critical mass of scientists and technicians both quantitatively and qualitatively to meet the needs of the nation. The UR School of Sciences has a mission to offer a comprehensive education in fundamental and applied sciences, to conduct applied research and provide services to the community. Today, there is an increasing demand in business, industry and the public sector for graduates with skills in quantitative analysis. One reason for this demand is the need for greater and deeper understanding of quantitative methods and management science in today's organizations, where information technology is providing everincreasing amounts of data to be processed, interpreted and exploited. The program in Applied Mathematics will offer courses for catering this demand and will enhance the career prospects of those who successfully complete it. All topics will emphasize the application rather than theory and most make extensive use of computer software. Furthermore, the laureates of this program will be able to pursue postgraduates studies (MSc) in Mathematics and Statistics
Educational Aims
The programme goals are: (i) To develop skills in Applied Mathematics in order to meet the demand by industry in Rwanda and other neighbourhood and abroad countries. (ii) To develop research skills for study anticipating a MSC in Mathematical Sciences or in Applied mathematics (iii) To contribute to the development of highly knowledgeable and skilled researchers in mathematics in Rwanda (iv) To produce independent researchers who are broadly educated in mathematics for productive research and who can apply their knowledge in modern industry. (v) To develop skills in entrepreneurship and leadership for the use of mathematical methods for problem solving in any area of the real life Topics in the programme will include problem structuring approaches, elements of applied mathematics, some statistic courses, applied multivariate calculus, numerical methods, prediction selected topics of operations research, some selected topics of actuarial mathematics and actuarial sciences. Students will get a working knowledge of software package like Mat lab, Mathematica, Stata and R as well as software used in applications outside academia. Students will exit the programme with, a Bachelor Degree with honours according to the UR framework and regulations for undergraduate degrees
Year 1: English for Specific purpose, ICT skills, Calculus 1, General Physics 1 ( Mechanics), Linear algebra 1, Analytical geometry 1, Calculus 2, Analytical geometry, linear algebra 2, analytical geometry 2, ordinary differential equations, general physics 2 ( Electricity and Magnetism), Complex analysis, special functions Year 2: General topology and its applications, probability and Statistics, Numerical analysis and Programming, measure theory and integration, functional analysis, Partial differential equations, inferential statistics, Operations research and optimization, mathematical modeling, stochastic Process and time series, Nonlinear analysis, Fluid dynamics, Multivariate analysis Year three: Optimal control, Differential geometry, Dynamical systems, mathematical biology, research methodology for mathematicians, Econometrics, Entrepreneurship development, Financial Mathematics, Internship, final year project
Rationale The UR School of Sciences has a mission to offer a comprehensive education in fundamental and applied sciences, to conduct applied research and provide services to the community. With the 2017 Rationalization, The Department of Mathematics has been requested to update its actual program and to include new more attractive programs. The present is the updated option of Statistics within the former applied mathematics program. Today’s operations systems provide big data that needed to be analyzed and exploited. For this, there is a high demand for qualified staff in this area. One reason for this demand is the need for greater and deeper understanding of quantitative methods and management science in today's organizations, where information technology is providing everincreasing amounts of data to be processed, analyzed, interpreted and exploited. The program of Mathematics Statistics will offer courses for catering this demand and will enhance the career prospects of those who successfully complete it. All topics will emphasize the application rather than theory and most make extensive use of computer software. Furthermore, the laureates of this program will be able to pursue postgraduates studies (MSc) in Statistical sciences Educational Aims The programme goals are:
Programme content: Topics in the programme will include problem structuring approaches, elements of applied mathematics, some statistic courses, applied multivariate calculus, numerical methods, prediction selected topics of operations research, some selected topics of actuarial mathematics and actuarial sciences. Students will get a working knowledge of software package like Mat lab, Mathematica, Stata and R as well as software used in applications outside academia. Students will exit the programme with, a Bachelor Degree with honors according to the UR framework and regulations for undergraduate degrees 1.2.2. Programme Structure: Year 1: English for Specific purpose, ICT skills, Calculus 1, Introduction to Statistics , Probability 1, Matrix algebra 1, Analytical geometry 1, Calculus 2, Introduction to Statistical Computing, Demographic statistics, Survey methodology, analytical geometry 2, ordinary differential equations, Statistical quality control, Complex analysis Year 2: English for Academic purpose, probability theory 2, Numerical analysis and Programming, Markov Chain and Queuing models, functional analysis, Partial differential equations, inferential statistics, Selected topics of Operations research , mathematical modeling, stochastic Process and time series, Stochastic Process, Regression Analysis, Time series analysis and Forecasting, Biostatistics, Design and Analysis of experiments Year three: Multivariate statistical Methods , Actuarial and Financial Mathematics, Research methodology, Econometrics, Production of national statistics, survival Analysis, Decision theory, Entrepreneurship Development, Industrial Attachment, Final year Project
1.2.3. LEARNING STRATEGY The competence based learning (CBL) approach is followed as a teaching strategy. This approach is oriented to problemsolving method. The student is the centre of learning process. For each module, lecturer will choose problems to be solved after a short introduction of the method to be used and then, by application students will discover the reality. The role of the lecturer here is “The guide”; the use of software package: MATLAB, Maple, Mathematica, and R will be used in applications
1.2.4. ASSESSMENT STRATEGY The taught modules are evaluated through assignments and examinations. Assignments consist of computer based exercises and continuous assessment test. Each course lecturer serves as an internal examiner. An external Examiner is appointed to moderate question papers, students’ scripts and reports. The Programme is completed with a final year project. The assessment of final year projects is based on UR regulations.
The programme goals are:
2.3.LEARNING AND TEACHING STRATEGYThe problemoriented part of the Common Core may vary in structure from course to course to include regular weekly class sessions, to include short intensive workshop weeks, or continuous "clinic" investigations. Whatever the structure, each student will, over a period of one year, be exposed to a range of relevant problems in Applied mathematics and scientific computing
The taught modules are evaluated through assignments and examinations. Assignments consist of computer based exercises and continuous assessment test. Each course lecturer serves as an internal examiner. An external Examiner is appointed to moderate question papers, students’ scripts and reports. The Programme is completed with a dissertation, lasting at least eight months, which is concerned with Statistics for decision making, policy formulation and complex data set by using statistical methods. An external Examiner is appointed to assess the dissertation according to the UR framework and regulations
The programme is designed to students who completed undergraduate studies with at least upper second class in all disciplines with background in mathematics. Admission into the Programme shall follow the existing UR framework and regulations
mathematics and Statistics
There are three active research groups in the following areas:
Research Grants:
Research group 1. Pure Mathematics Dr. Shumbusho Michel Dr. Kurujyibwami Celestin Dr. Nyagahakwa Venuste Dr. Rusagara Innocent Mr. Umutabazi Vincent Mr. Ruganzu Fidele Mr. Mugisho Jerome
Research group 2: Applied Mathematics:
Mathematical modeling, Biomathematics, Optimization, Inverse problems, differential equations and their Applications, Numerical Analysis, Stochastic processes and Applications

RESEARCH
There are three active research groups in the following areas:
 Pure Mathematics: Lie Groups and their Applications, Topology and Measure theory
 Applied Mathematics: Mathematical modeling, Inverse Problems, Optimization, Symmetry of Differential Equations and their Applications, Numerical Analysis, Biomathematics, Actuarial sciences
 Statistics: Linear Models ( Bilinear and trilinear models)
Research Grants:
 Mathematical modeling of cardio vascular and respiratory system for patients and sportsmen in Rwanda
 EAUMP agreement 20182020
REGIONAL AND INTERNATIONAL COLLABORATION:
 Eastern Africa Universities Mathematics Programme (EAUMP). Participating departments are:
Department of Mathematics of University of Rwanda, Makerere University, University of Dar es Salaam, University of Zambia and the School of Mathematics of the University of Nairobi. The overall purpose of this network is to strengthen pure mathematics in the region through postgraduate training and research.
Through this network, annual summer school is organized with the support of ISP and ICTP, international conferences are organized.
 Applied Mathematics and Statistics subprogram under Sida bilateral Program: The Department of Mathematics is collaborating with the Department of Mathematics of Linkoping University and Stockholm University in implementation of the subprogram of applied mathematics and Statistics. Through this program, 6 Staff have been trained in PhD programme and graduated on the Sandwich model. 5 staff are still under training in this mode.
With the support of this program the Masters Programme in Applied mathematics is operational since 2008. More than 47 students graduated from this Programme and a big number is serving the University of Rwanda and others public and private institutions in Rwanda
 East Africa centre for Mathematical Research (EACMaR). The Department of Mathematics at UR, MAK and UDSM in Collaboration with Swedish partners and IUCEA establish a regional centre for mathematical research. The purpose of this centre is to promote regional collaboration, mobility of students and staff, benchmarking and regional research groups.
 Others regional and International Collaboration:
CIMO/HEIICI, ISP, CIMPA, LMS, DAAD, EMS, AMS, AIMS, EAIFRICTP
RECENT PUBLICATIONS
 Ntaganda Jean Marie, PerturbationIteration Method for Solving Mathematical Model of Blood Partial Pressures in Human CardiovascularRespiratory System during Physical Activity, International Journal of Scientific and Innovative Mathematical Research (IJSIMR), Academics'Research center (ARC), PP 18, ISSN 2347307X (Print) & ISSN 23473142 (Online), 2017
 L. N. Nkamba, J. M. Ntaganda, H. Abboubakar, J. C. Kamgang, Lorenzo Castelli, Global Stability of a SVEIR Epidemic Model: Application to Poliomyelitis Transmission Dynamics, Open Journal of Modelling and Simulation, Scientific Research Publishing, pp 98112, ISSN Online: 23274026, ISSN Print: 23274018, 2017
 Innocent Ngaruye, Joseph Nzabanita, Dietrich von Rosen &Martin Singull, Small Area Estimation under a Multivariate Linear Model for Repeated measures Data, Communication in StatisticsTheory and Methods, Vol. 103 No.2, 2016
 Innocent Ngaruye, Dietrich von Rosen &Martin Singull, Crop yield estimation at district level for agricultural seasons 2014 in Rwanda, African Journal of Applied Statistics in Statistics, Vol 2, pp. 6990, 2016
 Joseph Nzabanita, Dietrich von Rosen, Martin Singull, Extended GMANOVA Model with a Linearly Structured Covariance Matrix, Mathematical Methods of Statistics, Vol 24 No. 4, 2015
 Joseph Nzabanita, Dietrich von Rosen, Martin Singull, Bilinear regression model with Kronecker and linear structures for the covariance matrix, Africa Statistika, Vol. 10 No. 2, 2015
 CassienHabyarimana, Martin Singull, Joseph Nzabanita, Extended GMANOVA Model with a Linearly Structured Covariance Matrix, Mathematical Methods of Statistics, Vol. 24 No.4, 2015
 Joseph Nzabanita, Dietrich von Rosen, Martin Singull, Estimation of Parameters in the Growth Curve Model with a Linearly Structured Covariance Matrix: A Simulation Study, International Journal of Scientific Engineering and Technology, Vol. 6 No.1, 2017
 Vitalij A. Chatyrko and VenusteNyagahakwa, Vitali selectors in topological groups and related semigroups of sets, Questions and answers in General Topology, Vol. 33, pp. 93102, 2015
 Berntsson, Fredrik, Munyeshyaka Jean Marie Vianney, Ndahayo, Fidele, and Nyalihama, Yves, Simulation of a Shieleded Thermocouple, Rwanda Journal, Vol. 27 Series C, pp. 311, 2012
 Ndanguza D. 2013 Numerical and Nonlinear Analysis: Applications to Real Life Problems, LAP LAMBERT Academic Publishing (May 31, 2013), ISBN10: 3659396648, ISBN13: 9783659396649
 Ndanguza D. Haario H. 2012. Analysis of SDEs applied to SEIR epidemic models, Conference paper, Bahir Dar Ethiopia. http://inverseproblems.org/presentation_bahir_dar.pdf
 Bonus Ntagengerwa, Felix Hagenimana, Denis Ndanguza, JojakMung’atu, Modeling Drivers of Fertility in Rwanda, International Journal of Mathematics and Physical Sciences Research, Vol. 5, No.1, pp. 3040, 2017
 J. Niyobuhungiro, Subdifferentiability of infimal convolution on Banach couples, Functiones et approximation, Vo. 52, pp. 311326, 2015
 Marie Emmanuel Ntigura, Ndahayo, Fidele, and Berntsson, Fredrik, Air Pollution Tracking Using PDEs, Rwanda Journal, Vol. 27, Series C, pp. 6369, 2012
 Herberthson, Magnus, Minani Froduald, Nzabanita Joseph, and Turesson, BengtOve, Static Equilibrium configurations of charged Metallic Bodies, Rwanda Journal, Vol 27, Series C, 2012
 Fredrik B, Vladimir Kozlov, MpinganzimaLydie, An accelerated alternating procedure for the Cauchy problem for the Helmholtz equation, Computers and Mathematics with Applications, Vol. 68 (12), pp. 4460, 2014
 Nzabanita Joseph, Estimation of parameters in the extended growth curve model with a linearly structured covariance matrix, Acta et CommentationnesUniversitatisTartuensis de Mathematica, Vol. 16, 120, 2012
 W. Banzi,Virunga Mountain Gorilla Population Dynamics: Age structured model, East Africa Journal of Science and Technology, Vol 3(1), pp. 265284, http://eajournal.unilak.ac.rw/index.php/publications/eajstvolume3issue1
 Banzi Wellars: Modeling the competition from Virunga Mountain Gorilla with Golden Monkey in the Volcanoe National Park. East Africa Journal of Science and Technology. Vol (5) Issue 2. PP 5066 ISSN:22271902 (online) http://eajournal.unilak.ac.rw/index.php/publications/eajstvolume5issue2
 Banzi Wellars. Human Population Dynamics in Great lakes Countries up to 2050. Kabarak International Conference proceedings.. Pp 151161, Nakuru 2011
 Banzi Wellars, Newton Kantorovich method to solve nonlinear reaction diffusion Systems. 3^{rd} EAUMP conference proceedings. Pp 7289. Kampala 2017
 Jean Marie NTAGANDA, Benjamin MAMPASSI, 2012 Modelling glucose and insulin in diabetic human during physical activity,ICM2012 Proceeding, Tome1331344,Fourth International Conference on Mathematical Sciences, ICM2012
 Jean Marie NTAGANDA, 2012, Modelling blood and pulmonary pressures for solving a performance optimal control problem for sportsmen, International Scholarly Research Network, ISRN Applied Mathematics, Volume 2012, 116 Article ID 470143, http://dx.doi.org/10.5402/2012/470143
 Jean Marie Ntaganda, Benjamin Mampassi, 2012 CARDIOGUI: An Interface Guide to Simulate Cardiovascular Respiratory System during Physical Activity, Applied Mathematics, Vol. 3,20002006, http://dx.doi.org/10.4236/am.2012.312275
 Jean Marie Ntaganda, Benjamin Mampassi, 2012 CARDIOGUI: An Interface Guide to Simulate Cardiovascular Respiratory System during Physical Activity, Applied Mathematics, Vol. 3,20002006, http://dx.doi.org/10.4236/am.2012.312275
 Jean Marie Ntaganda, Benjamin Mampassi March, 2013 An Optimal Control Problem for Hypoxemic Hypoxia TissueBlood Carbon Dioxide Exchange during Physical Activity,Open Journal of Applied Sciences Vol. 3. N°15661 http://dx.doi.org/10.4236/ojapps.2013.31009
 Jean Marie Ntaganda October, 2013 Matlab Design for Solving an Orthostatic Stress Optimal Control Problem of CardiovascularRespiratory System, International Journal of Scientific and Innovative Mathematical Research (IJSIMR)Volume 1, Issue 2 103116 ISSN 2347307X (Print) & ISSN 23473142 (Online) http://www.arcjournals.org/pdfs/ijsimr/v1i2/V1I26.pdf
 Jean Marie Ntaganda November, 2013 Fuzzy Logic Strategy for Solving an Optimal Control Problem of Glucose and Insulin in Diabetic Human, Open Journal of Applied Sciences Vol. 3 421429, http://dx.doi.org/10.4236/ojapps.2013.37052
 Jean Marie Ntaganda, December, 2013 MATLAB Design for Solving a Mathematical Model of Insulin Dynamic International Journal of Scientific and Innovative Mathematical Research (IJSIMR), Volume 1, Issue 3, 225233ISSN 2347307X (Print) & ISSN 23473142 (Online) http://www.arcjournals.org/pdfs/ijsimr/v1i3/ijsimrv1i37.pdf
 J. M. Ntaganda, Hopf Bifurcation of a Two Delay Mathematical Model of Glucose and Insulin during Physical Activity, OJAppS, Vol. 4 No 2, pp. 4355, 2014
 Marcel Gahamanyi, Jean Marie Ntaganda, MahamatSalehDaoussa, Gaggar, Purturbationiteration method for solving mathematical model of glucose and insulin in diabetic human during physical activity, Journal of Applied Sciences, Vol. 6 No 12, pp. 826838, 2016
 Gilbert MUGENZI, Dr. Joseph K. Mung’atu, Dr. Marcel Ndengo,Modeling the Determinants Influencing Labour Force Participation in Rwanda 2013/14, Using Logistic Regression Approach, International Journal of Mathematics and Physical Sciences Research ISSN 23485736 (Online)Vol. 5, Issue 1, pp: (4154), 2017
 Innocent Ngaruye, Joseph Nzabanita, Dietrich von Rosen &Martin Singull, Small Area Estimation under a Multivariate Linear Model for Repeated Measures Data, Communications in Statistics  Theory and Methods ,103(2):112, 2016
 Cassien Habyarimana, Martin Singull, Joseph Nzabanita, Estimation of Parameters in the Growth Curve Model with a Linearly Structured Covariance Matrix: A Simulation Study", International Journal of Scientific Engineering and Technology, 6(1): 4549, 2017
 Innocent Ngaruye, Dietrich von Rosen & Martin Singull, Crop yield estimation at district level for agricultural seasons 2014 in Rwanda, African Journal of Applied Statistics ,3(1): 6990, 2016
 Minani Froduald, Hausdorff contninuous viscosity solutions of HamiltonJacobi equations, Sprink link, Book series LNCS Vol. 5910, Large scale scientific computing, 2009, pp 231238
 C.Tuyizere, J.K Mung’atu, D.Ndanguza, (2017), Rainfall Forecasting in Gasabo District Using markov Chain Properties. International Journal of Scientific Engineering and Technology. Vol. 6 Issue 4 ISSN 22771581 pp 128131 SCI indexing
 Nsengiyumva Emmanuel, Josephk. Mung’atu, Denis Ndanguza (2017), Queuing models, Application to Kibagabaga hospital services. International Journal of Mathematics and Physical Research. Vol. 5 Issue 2. Research Publis Journal. ISSN 23485736 pp 3139 CiteSeer, citeulike,Academia.edu, Google
 Ndanguza Denis, Mutarutinya Vedaste (2017), A model perception on independence of PhD students in promoting the research. Rwanda Journal of Education. Volume 4, Issue 1. Rwanda journal
 Ndanguza Denis, Isambi S, Mbalawata, Heikki Haario, Jean M. Tchuenche (2017) Analysis of bias in an ebola epidemic model by extended kalman filter approach. Mathematics and computers in simulation. Vol 142 Elsevier. Science Direct pp 113129
 Cyemezo H, Mung’atu J, Ndanguza Denis (2017), System Delivery Service: A case study of Banque Populaire du Rwanda Kimironko Branch. International Journal Of Scientific Engineering and Technology. Vol 6 issue 10 pp 331334
 Muhirwa Jean Pierre, Ndanuza Denis (2017), Effect of Random Noise, Quasi random Noise and systematic Random noise on Unknown Continuous Stirred Tank reactor. Applied Mathematical Sciences. Vol 11 Issue 62 HIKARI Ltd pp 30513071
 Bonus Ntagengerwa, Felix Hagenimana, Denis Ndanguza, Joseph K Mung’atu, (2017), Modelling Drivers of fertility in Rwanda. International Journal of Mathematics and Physical Sciences Research Vol 5 Issue 1. Research Publishing journals 3040 ISSN 23485736