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Dr. Muhammad Ishaq
Assistant Professor
Department of Mathematics

SNS
National University of Sciences and Technology (NUST)
School of Natural Sciences,Sector H-12, Islamabad, Pakistan
Tel : +92 51 9085 5591

Specialization
Algebra

Education
PhD, ASSMS, GC, Lahore

Education:

    PhD (Mathematics) (2007-2012) Abdus Salam School of Mathematical Sciences, GC University, Lahore.

    MSc (Mathematics) (2004-2006) Peshawar University , Peshawar.

    BSc (Mathematics, Physics) (2002-2004) Peshawar University , Peshawar.

Academic Prizes and Honors

  • Received the first prize in “5th World Conference on 21st Century Mathematics” held in Abdus Salam School of Mathematical Sciences February 09–13, 2011, in the category of young speaker.
  • Awarded a certificate by Abdus Salam School of Mathematical Sciences for commendable performance during PhD research work in area of ALGEBRA (2010).

 

 

 

 

 

 

 

 

 

 

 


 

 

 

Research Interests:

My area of research is Commutative Algebra. More specifically I am working with Stanley decompositions and Stanley depth of  multigraded modules over polynomial algebra. I am interested to find values and good bound for the Stanley depth and depth of  different classes of multigraded modules. We compare the values and bounds of the Stanley depth with the depth of these modules. This can be helpful for establishing a relation between depth and Stanley depth as it is expected by R.P. Stanley known as Stanley's conjecture.

Research Project:

Minimal depth and trivial modifications. (In Progress)
No: PM-IPFP/HRD/HEC/2012/2778

Research Student:

MPhil

Nayab (2012-)

Sobia Ashraf (2011-2013) "Bounds for the Stanley depth of some square free monomial ideals".

Research ​Publications:
 
​S/No ​Reference
​1. M. Ishaq, Values and bounds of the Stanley depth, Carpathian Journal of Mathematics, 27(2) (2011), 217-224.
​2. M. Ishaq, Upper bounds for the Stanley depth, Communications in Algebra, 40(1) (2012), 87-97.
​3. ​M. Ishaq, M.I. Qureshi, Stanley depth of edge ideals, Studia Scientiarum Mathathematicarum Hungarica, 49(4) (2012), 501-508.
​4. ​M. Ishaq, M.I. Qureshi, Upper and lower bounds for the Stanley depth of certain classes of monomial ideals and their residue class rings, Communications in Algebra, 41(1) (2013), 1107-1116.
​5. Muhammad Ishaq, Monoial ideals of minimal depth, Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, Vol. 21, Issue 3, 2013, Pages 13, IF 0.221​
​6. M. Ishaq, Lexsegment ideals are sequentially Cohen-Macaulay, accepted for publication in Algebra Colloquium.

Courses Taught:

    Abstract Algebra (UG)

    Linear Algebra (UG)

    Algebra (PG)

    Basic Mathematics (UG)