Biography

I obtained a PhD in Operator theory from the Cardiff School of Mathematics- Cardiff University, UK in 2012 under the supervision of Marco Marletta.

  • Mar. 2022-present: Assistance Professor, Department of Mathematics, College of Science, University of Salahaddin.
  • Sept. 2012 PhD: Lecturer, Department of Mathematics, College of Science, University of Salahaddin.
  • Oct. 2008- Apr. 2012:: PhD student, Cardiff School of Mathematics- Cardiff  University, UK.
  • Oct.2005- Sept. 2008 Master: Lecturer, Department of Mathematics, College of Science, University of Salahaddin.
  • ·Sept. 2003- Sept. 2005 Master: Assistant Lecturer, Department of Mathematics, College of Science, University of Salahaddin.
  • Sept.2001- Aug.2003 Master student, Department of Mathematics, College of Science, University of Salahaddin.

Education 

  • April 2012 Doctor of Philosophy, PhD in Mathematics. Cardiff  School of Mathematic- Cardiff  University, UK  Thesis title: Approximation of Quadratic Numerical Range of Block Operator Matrices.
  • August 2004 Master of Science (M.Sc.) in Mathematics.  Department of Mathematic- College of Science, Salahaddin University-  Erbil, Iraq  Thesis title: Some generalizations of Numerical Range of operators on a complex  Hilbert spaces.

Administrative duties

  • Jan.2024- Jul.. 2024: Member of final examination committee of M.Sc and PhD. students of the college of Science, University of Salahaddin,
  • Sept.2023-Oct.2024 : Member of the Scientific and Higher study committee of the Department of Mathematics. -College of Science, University of Salahaddin,
  • Sept. 2014: Member of the  final examination committee of B.Sc of the college of Science, University of Salahaddin,
  • Sept. 2015 :Member of the  final examination committee of B.Sc of the College of Science, University of Salahaddin,
  • Oct.2003- Jun.2008 : Deputy Head of Department of Mathematics, College of Science, University of Salahaddin,
  • Oct.2003- Jun.2007: Member of the Scientific and Higher study committee of the Department of Mathematics.
  • Jun.2008:  Member of final examination committee of M.Sc and PhD. students of the College of Science, University of Salahaddin,
  • Oct.2003- Jun.2008: Member in most committee in the Salahaddin University, especially in the College of Science.  

Editorial Board

  • Jul. 2023- present:  Section Editor, for the Zanko Journal of Pure and Applied Science.

Research interests

My research interests are in functional analysis, operator theory and spectral theory.  In particular I am interested in: 

  • Spectral approximation for linear operators  ( spectral pollution ).
  • Numerical range of differential operators and operator pencils, and involve both analysis and computational mathematics.
  • Differential operators, e.g. Schrödinger operators, Advection-diffusion operators,Hain-Lust operators and Stokes operators .
  • Applications in mathematical physics, e.g. in magnetohydrodynamics

One of the main achievements of my research to date has been the absence of quadratic numerical range-pollution, which is new result in operator theory because in general, discretization of differential operators may result in spectral pollution. I have shown that  this does not happen for finite difference discretizations of the Hain-Lüst operator is a little more tricky than proving that every point of the quadratic numerical range can be approximated. 

Publications

Textbook

  • Ahmed Muhammad and Hardi Nabe,  Advanced Calculus, Salahaddin University Press, Salahaddin 2023.  ISBN: 978-9922-21-430-6

Journal Article

  • A. Muhammad and W. Hammad, Computing  c-numerical range of differential operators,  Journal of Filomat 38:77(2024), 2243-2225.
  • Amer M. Salman, Mohd Hafiz, and Ahmed Muhammad, A Novel Approach to investigate the Stability Analysis and the Dynamics of  Reaction-Diffusion SVIR Epidemic Model. Communications in Nonlinear Science and Numerical Simulation 126 (2023) 107517.
  • A. Muhammad, B. Azeez, and F. Taheri, Computing the S-numerical range of differential operators, Journal of Operator and Matrices 17 (2023), 583-598.
  • A. Muhammad, Approximation of numerical range of polynomial operators. Journal of Operator and Matrices 15 (2021), 1073-1087.
  • A. Muhammad and F. Shareef, Computing the $q$-numerical range of differential operators, Journal of Applied Mathematics Volume 2020, Article ID 6584805, 12 pages, (2020).
  • A. Muhammad and F. Shareef, A numerical investigation of $q$-numerical range of operator matrices.   Far east Journal of mathematical science 125 (2020), 1-33.
  • W. Jalal and A. Muhammad, Elliptic numerical range of matrices. International mathematical Forum 15 (2020), 293-315.
  • B. Azeez and A. Muhammad, Some results on S-numerical range of operator matrices. Zanko Journal of pure and Applied science 32 (2020), 57-63.
  • A. Muhammad and W. Jalal, A numerical investigation of the $c$-numerical range of differential operator. Bulletin of Iranian mathematical society 45 (2019), 1755-1775.
  • A. Muhammad and M. Marletta, A numerical investigation of the quadratic numerical range of  Hain-L\\\"{u}st operator. International Journal of Computer Mathematics 90 (2013), 2431-2451.
  • A. Muhammad and M. Marletta, Approximation of quadratic numerical range of  block operator matrices. Integral Equation and Operator Theory  74 (2012), 151-162.
  • A. Muhammad and M. Marletta, Computation of boundary of quadratic numerical range (Approved to be published).
  • A. Muhammad, Joint Numerical Range of matrix polynomials. Al-Rafiden Journal of Computer Science and Mathematics, Vol.6  No.2  (2009), p.129-136.
  • A. Muhammad, The Numerical range of 6 by 6 Irreducible matrix, Al-Rafiden Journal of Computer Science and Mathematics, Vol.4  No.2  (2007), p.89-98.
  • A. Muhammad, The line segment on the boundary of Numerical range, Zanco, The Scientific journal of Salahaddin University-Erbil, Vol.17  No.1  (2005), p.105-111.
  • A. Muhammad, Elliptical Range of an n-tuple operators on a complex Hilbert space, Zanco, The Scientific journal of Salahaddin University-Erbil, Vol.17  No.1  (2005), p. 113-117

Teaching

I have taught a variety of undergraduate courses in calculus, multivariable calculus, vector calculus, foundation of mathematics, fundamental of mathematics, linear algebra, differential equations, topology on real line, linear programming, non-linear programming, abstract algebra, mathematical analysis, functional analysis and complex analysis.

  • 2024- 2025:  Assistance professor, Department of Mathematics- College of Science, University  of  Salahaddin, Erbil-Iraq.
  • Teaching Courses: Complex Analysis, Functional Analysis.
  • 2023- 2024:  Assistance professor, Department of Mathematics- College of Science, University  of  Salahaddin, Erbil-Iraq.
  • Teaching Courses: Complex analysis, Functional Analysis.
  • 2023- 2024:  Visiting Lecturer, Department of Mathematics- College of Science, Koya  University .
  • Teaching Courses: Mathematical analysis,
  • 2022- 2023: Assistance professor, Department of Mathematics- College of Science, University  of Salahaddin, Erbil-Iraq.
  • Teaching Courses: Multivariable  Calculus,  Vector Calculus,Functional Analysis.
  • 2021- 2022: Lecturer, Department of Mathematics- College of Science, University of  Salahaddin,,Erbil-Iraq.
  • Teaching Courses: Multivariable  Calculus, Vector Calculus, Mathematical Analysis.
  • 2020- 2021: Lecturer, Department of Mathematics- College of Science, University of  Salahaddin,,Erbil-Iraq.
  • Teaching Courses: Multivariable Calculus,Vector Calculus, Mathematical Analysis.
  • 2019- 2020: Lecturer, Department of Mathematics- College of Science, University of  Salahaddin,,Erbil-Iraq.
  • Teaching Courses: Mathematical Analysis Analysis.
  • 2018- 2019: Lecturer, Department of Mathematics- College of  Science, University of  Salahaddin,, Erbil-Iraq.
  • Teaching Courses: Advanced calculus, Functional Analysis.
  • 2018- 2019 Visiting Lecturer, Department of Mathematics- College of Science, Koya University.
  • Teaching Courses:  Mathematical Analysis.
  • Teaching Courses: Foundation of Mathematics.
  • 2017- 2018: Lecturer, Department of Mathematics- College of Science, University of  Salahaddin,,Erbil-Iraq.
  • Teaching Courses:  Advanced  Calculus, Functional Analysis.
  • 2016—2017: Lecturer, Department of Mathematics- College of Science, University of  Salahaddin,, Erbil-Iraq.
  • 2015- 2016: Lecturer, Department of Mathematics- College of Science, University of  Salahaddin,, Erbil-Iraq.  T
  • Teaching Courses : Foundation of Mathematics.
  • 2014--2015 : Lecturer, Department of Mathematics- College of Salahaddin,, Erbil-Iraq.
  • Teaching Courses: Fundamental of Mathematics, Advanced  Calculus.
  • 2013- 2014: Lecturer, Department of Mathematics- College of  Salahaddin,, Erbil-Iraq.
  • Teaching Courses: Fundamental of Mathematics, functional analysis.
  • 2012 - 2013: Lecturer, Department of Mathematics- College of Science, University of  Salahaddin,, Erbil-Iraq.
  • Teaching Courses: Linear algebra, abstract algebra..
  • Oct. 2008-- Sept. 2012 : PhD student at Cardiff school of Mathematics-Cardiff University, UK.
  • 2007- 2008: Lecturer, Department of Mathematics- College of Science, University of  Salahaddin,,Erbil-Iraq.
  • Teaching Courses: Foundation of Mathematics, Mathematical analysis, Complex analysis.
  • ·2006--2007 : Lecturer, Department of Mathematics- College of Science, University of   Salahaddin,, Erbil-Iraq.
  • Teaching Courses: Foundation of Mathematics, Advanced Calculus, Mathematical analysis.
  • 2005-2006: Lecturer, Department of Mathematics- College of Science, University of  Salahaddin,,Erbil-Iraq.
  • Teaching Courses: Foundation of Mathematics, (first and second semesters), Mathematical   Analysis, (first and second semesters), Complex Analysis, (first and second  semesters)
  • 2004 - 2005: Assistant Lecturer, Department of Mathematics- College of Science, University of  Salahaddin,, Erbil-Iraq.
  • Teaching Courses: Foundation of Mathematics, (first and second semesters), Mathematical   Analysis, (first and second semesters).
  • 2003--2004 : Assistant Lecturer, Department of Mathematics- College of Science, University of  Salahaddin,, Erbil-Iraq.
  • Teaching Courses: Functional analysis, (first and second semesters), Linear Algebra, Abstract  Algebra (second semester).
  • 2002 - 2003 : Assistant Lecturer, Department of Mathematics- College of Science, University of  Salahaddin,, Erbil-Iraq.
  • Teaching Courses: Functional analysis, (first and second semesters), Abstract Algebra, (first  and  second semesters), Ordinary differential equation, (first semester),  Linear programming (second semester).

On the other hand  I have taught a variety of postgraduate courses in spectral theory, operator theory and functional analysis.

  • 2023- 2024:  Assistance professor, Department of Mathematics- College of Science, University  of  Salahaddin, Erbil-Iraq.
  • Teaching Courses: Functional Analysis( first semester- Master)
  • 2023- 2024:  Assistance professor, Department of Mathematics- College of Science, University  of  Salahaddin, Erbil-Iraq.
  • Teaching Courses: Spectral theory ( second  semester - Master)
  • 2023- 2024:  Visiting Lecturer, Department of Mathematics- College of Science, Koya  University .
  • Teaching Courses: , Functional Analysis II (first semester PhD)
  • 2023- 2024:  Visiting Lecturer, Department of Mathematics- College of Science, Koya  University .
  • Teaching Courses: , Linear analysis ( second semester – Master ).
  • 2023- 2024:  Visiting Lecturer, Department of Mathematics- College of Science, Soran  University .
  • Teaching Courses: Operator theory. ( first semester –PhD ).
  • 2020—2021: Lecturer, Department of Mathematics- College of Science, University of  Salahaddin,,Erbil-Iraq.
  • Teaching Courses: Operator theory (Master students- second semester).
  • 2020--2021  Visiting Lecturer, Department of Mathematics- College of Science, University of  Sulaimani
  • Teaching Courses: Spectral theory ( master students- second semester).
  • 2020- -2021: Visiting Lecturer, Department of Mathematics- College of Science, Koya  University.
  • Teaching Courses: Functional Analysis II (PhD students)
  • 2017- 2018 : Visiting Lecturer, Department of Mathematics- College of Science, Koya University.
  • Teaching Courses: Functional Analysis (Master students-first semester).
  • 2015--2016 : Visiting Lecturer, Department of Mathematics- College of Science, Soran University.
  • Teaching  Courses: Functional Analysis (Master students-first semester).
  • 2014 - 2015: Lecturer, Department of Mathematics- College of Science, University of  Salahaddin,, Erbil-Iraq.
  • Teaching Courses: Functional analysis II (Master students).

Supervision of PhD Thesis at University Sains Malaysia  

  • 2021-present Amer Muhammad Salman, Ph.D, School of Mathematical Sciences Universiti Sains  Malaysia.(co-advised with Mohd Ha z Mohd)  Thesis titled: On Stability analysis.

Supervision of Master Theses at Salahaddin University

  • 2024-present Rawaz Hassan Maoulod, M.Sc. Thesis titled: Computing numerical range for unbounded operator linear pencil.
  • December  2022  Darawan Zrar Muhammad, M.Sc.  Thesis titled: S-numerical range of polynomial operator matrices.
  • October 2015  Fiza Abdullah Shareef, M.Sc.  Thesis titled: Approximation of q-numerical range of operator matrices with applications.

Supervision of PhD Thesis and Master Theses at Soran University

  • 2024-present Walat Jalal Hamad, Ph.D  Thesis titled: Computing quadratic numerical range and block numerical range of polynomail di erential  operators.
  • April 2017 Walat Jalal Hamad, M.Sc.  Thesis titled: Approximation of generalized numerical range of operator matrices with applications.

Supervision of Master Thesis at Koya University 

  • March 2019 Berivan Faris Aziz, M.Sc.  Thesis titled: On the approximation of Krein space numerical range of operator matrices with applications.

Undergraduate research supervised at Salahaddin University

Every academic year, I propose and supervise a selection of projects on various topics. If you are currently studying Mathematics at Salahaddin University and consider doing a project on a topic related to the Mathematics  of Operator theory and spectral theory, please feel free to contact me.

  • July 2014 Darawan Zrar Muhammad, B.Sc.  Research titled: Numerical range of matrix polynomial..
  • July 2015 Sheren Abdulstar and Sheren Omer, B.Sc.  Research titled: A Review on the Lebesgue Spaces.
  • July 2017 Chenar Abdulla Hassan and Redar Nadr Taha, B.Sc.  Research titled: Geometry of Numerical Range and S-Numerical Range of Operator Matrices.
  • July 2017 Hozan Burhan and Hangaw Shakir, B.Sc. Research titled: : Characterization of numerical range of matrix operator
  • July 2018 Amer Mohammad Salman, B.Sc. Research titled: Geometry of Numerical Range and Quadratic Numerical Range of Block Operator Matrices.
  • July 2018 Sharmen Ghazi, B.Sc.  Research titled: Computing spectrum of  nite dimensional operators.
  • July 2019 Shayan Zeravan, B.Sc.  Research titled: Geometry of q-Numerical Range of Operator Matrices.
  • July 2019 Bawan Rebwar, B.Sc.  Research titled: Some results on k-numerical range operators.
  • July 2020 Abdulqadr Yasin Abdulla, B.Sc.  Research titled: Gershgorin discs versus numerical range.
  • July 2021 Mustafa Fuad, B.Sc.  Research titled: Computing numericval range for 2 by 2 matrix polynomials.
  • July 2021 Bahasht Mouhammad, B.Sc.  Research titled: A Note On Metric Equivalence Of Some Operator.
  • July 2022 Hazar Adel and Ali Lalid, B.Sc.  Research titled: Application on Banach  xed point theorem.
  • July 2023 Najeb Zuher, B.Sc.  Research titled: Computing numerical raduis of operator matrices.
  • July 2023 Huda Khalid, B.Sc.  Research titled: A study on Caputo fractional operator.
  • July 2024 Ismail Syamand, B.Sc.  Research titled: Some properties and applications of fractional operators.
  • July 2025 Juan Sarteb, B.Sc.  Research titled: Double sequence and double series

 

 

 

Research Interest

 

Publications

 

Teaching