Formal Education:

     Ph.D in Mathematics  (November, 2014)

Department of Mathematical Sciences,

Norwegian University of Science and Technology (NTNU), Trondheim Norway                       

Thesis: Higher order integrators for Hamilton´s equations: Modified Symplectic Algorithms

In this Ph.D thesis some new algorithms for numerical solutions for Hamiltonian equations have been proposed and tested. These methods preserve the symplectic structure exactly (to the accuracy of the numerical precision), and is of higher order in the time-step. Explicit general formulas with local accuracy till 8th order  has been presented, as well as a Python program of automatic implementation of numerical code for the solution of specific models.

    M.Phil - Applied Mathematics    (September, 2008)

Department of Mathematics, Government College University (GCU), Lahore Pakistan

Thesis: Some finite difference methods for two-dimensional elliptic equations.

In this thesis finite difference difference methods are introduced and used to approximate the solutions of elliptic partial differential equations. MATLAB programming is used for simulations.Earned the degree with very good CGPA from one of the distinguish institution of Pakistan.

Following courses were the mandotary part of the M.Phil studies besides thesis work.

Courses: Algebra, Functional Analysis, Numerical Analysis, Theory of Differential Equations, Advanced Group Theory, Module Theory and Group Representations, and Foundation of Mathematics.

   M. Sc.- Mathematics               (December, 2000)

Department of Mathematics, University of the Punjab, Lahore Pakistan

This University, established in 1882 at Lahore,  is the largest and the oldest seat of higher learning in Pakistan. It was the first to be established in the sub-continent in Muslim majority area. The fact that two Nobel laureate, Dr. Abdus Salam and Har Gobind Khorana, are from this University speaks volumes for its academic and research excellence.

Got master´s degree with first division from this prestigious university of the Pakistan. Studies following course in connection with the completion of this degree.

Courses: Real Analysis, Advanced analysis, Methods of Mathematical Physics, Complex Analysis, Computer Applications (Programming in FORTRAN), Functional Analysis and Topology, Numerical Analysis, Electromagnetic Theory, Mechanics and Differential Geometry, Algebra, Vectors and Tensors, Mathematical Statistics, Group Theory.

   B. Sc.- Mathematics and Statistics           (1998)

         Government Islamia College Civil Lines, Lahore Pakistan

Courses: Mathematics A Course : Calculus and Analytic Geometry , Linear Algebra and Differential Equation Mathematics and B Course : Vector Analysis and Mechanics, Mathematical Methods, Group Theory , Metric Spaces, Statistics, English Compulsory, Pakistan studies and Islamic Studies

   Intermediate (Mathematics & Statistics)     (1996)

Government Islamia College Civil Lines, Lahore Pakistan

Courses: English(I+II), Urdu(I+II), Islamic studies, Pakistan studies, Economics(I+II) , Mathematics(I+II), Statistics(I+II)

   Matric  (Science Subjects)                            (1994)

Government High School Shahdra, Lahore Pakistan.

Courses: English, Urdu, Islamic studies, Pakistan studies, Physics, Mathematics, Chemistry, Biology

 Professional Education:

   University Level Teaching Mathematics Course                          Nov 2015—Jun 2016

MatRIC: Centre for Research, Innovation and Coordination of Mathematics

It is the certificate course for recently appointed university/university college mathematics teachers and learners arranged by MatRIC/University of Adgar in collaboration with the NTNU Norway. It is designed to address many of the challenges for mathematics teachers (learner) and this can be used in partial fulfillment of the requirements of many universities and university colleges for teaching staff to undertake professional development in university pedagogy.

   Professional Teacher Education  (B.Ed; Bachelor of Education)      2001—2002

University of the Punjab, Lahore Pakistan

Bachelors of Education (1-year) in Elementary Education program is designed to help prospective teachers to develop the required pedagogical knowledge and skills to teach different subjects in elementary grades in public and private sector school. This program has emphasis on practical knowledge of teaching and prospective teachers develop a strong understanding of education after learning about foundations of education, learning theories and classroom management techniques.