Analytical Methods in Number Theory

Concentrate on the problem of determining an estimation of the exponential sums for multi-variable polynomials, estimation of the multiple exponential sums for two-variable polynomials of higher degree and also to find the p-adic sizes of factorial functions which involve Bernoulli functions, left Kurepa’s factorial functions and other functions.

 Mathematical Cryptography

Among the related research are primarily testing, factoring large integers, lattice-based cryptography, sieve methods, elliptic curve cryptography and discrete log problems. Eventual aims are the development, improvement and implementation of cryptographic protocols that are mathematically based that can become standards for communications security.

 Structural Theory of Algebras

The research concerns the classification problem of finite dimensional complex none Lie filiform Leibniz algebras. The approach that we use for classification is invariant. It is algebraic and the conditions will be given in terms of invariant functions.

 Chromaticity of Graphs

This field of research encompasses the following topics: Planar graph colouring, Colouring of graphs on higher surfaces, Colouring number, Critical Graphs, Conjectures of Hadwiger and Hajos, Sparse graphs, Perfect graphs, Edge colourings, List colouring, Orientation and flows, Chromatic polynomials, Matching Polynomials and Domination Polynomials.

Wave Propagation

Applications in telecommunications, sensors, dielectric models and singular aspects of crack problems

Fluid Dynamics

Stability of fluid flow, surface tension gradient phenomena, computational plasma physics and granular or traffic flow.

 Computational and Mathematical Biology

Spatio-temporal aspects of disease spread, computational modeling of large molecular systems and mathematical models in agriculture.

 Quantum Information Science

Research on information-theoretic aspects of quantum systems and related matters with particular emphasis on foundations of quantum theory, quantum computing and quantum information. Topics of current interest are geometric and topological aspects of quantization and quantum information, spintronics.

 High Performance Computing and Distributed and Applications

Traffic engineering such as external and internal routing protocols, optimization of network design and placement of servers, mobile and wireless networks, network security and managements such as SSH protocol, secure parallel TCP protocol, management of PCs and HPC clusters and grid computing, various aspects of small-worlds and random networks.

 Scientific Computing and Applications

Development of new efficient parallel algorithms for scientific problems, architecture of high speed computing which includes interconnection of processors, cache architecture and related protocols, developing programs in GridMathematica and real-world implementation of grid computing..

 Network  Theory and Applications

Computer algebra, (parallel) numerical algorithms, simulation and visualization for applications like waveguides, optical fibre cables, wave propagation in antenna design, fluid dynamic phenomena.

 Computer-Aided Instructions and Knowledge Management

Authoring multimedia content in advanced learning and development of web-based modules using resources like webMathematica.

 Computational Mathematics

This field of research consists of the following six areas: Numerical Analysis, Mathematical Programming, Approximation, Optimization, Quality Control, and Operations Research.

 Statistical Modeling and Forecasting

This field encompasses of Time Series Analysis, Forecasting, Spatial Modelling, Regression Analysis and Design and Analysis of Experiments.

 Computational Statistics and Inference

This research consists of Robust Statistics, Influence Diagnostic, Bootstrapping, Bayesian Statistics, Markov Chain Monte Carlo (MCMC) and Statistical Data Mining.

 Reliability Analysis

This field consists of five areas of research which are survival analysis, medical statistics, biostatistics, extreme value theory and environmetrics.

 Philosophy of Mathematics and Etnomathematics

Philosophy of mathematics - studies into views and conception from various schools of thoughts about the nature of mathematics as well as the development of philosophy of mathematics.

Ethnomathematics - studies of the relationship between mathematics and culture and various perspectives on history of mathematics.

 Pedagogy in Mathematics Education

Theories and practices in mathematics education for the enhancement of mathematical understanding - constructivism, mastery, collaborative, contextual learning problem-based learning, cognitively-guided instruction, zone of proximal development, expert-novice paradigm, postmodern pedagogy, critical pedagogy. Other areas include development of mathematical thinking, mathematical values and beliefs, policy issues and current issues related to pedagogy of mathematics.

 Instructional Design and Technology in Mathematics

Technological tools related to teaching and learning mathematics and its development. Also focus on technology operations and concepts, designing mathematical learning environment, assessment in mathematics instructions, social, ethical and human issues related to use of technology in mathematics instruction.

Psychology of Teaching and Learning Mathematics

Theoretical work and research in the psychology of learning and teaching mathematics related to behavioral psychology, cognitive psychology, situated learning, constructivism, meta-cognitive, and psychometrics of mathematics learning.