# Abdullahi Umar

**Abdullahi Umar**

Associate Professor of Mathematics

Mathematical Sciences

+971 (0)2 60 75134

aumar@pi.ac.ae

Dr. Abdullahi Umar earned his PhD in Mathematics from the University of St Andrews, Scotland in 1992, following on his first class Hons BSc in Mathematics from Ahmadu Bello University, Zaria, Nigeria (1983).

After holding several positions in universities in Nigeria, Dr. Umar joined the King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia in 1997 as an assistant professor. He was promoted to the rank of Associate Professor at KFUPM in 2005. In 2007, he moved to Sultan Qaboos University (SQU), Oman, where he remained until 2014 when he moved to the Petroleum Institute, (now part of Khalifa University of Science and Technology) as an associate professor. While at SQU, he won a substantial research grant (approx. US$150,000) from The Research Council TRC of Oman for “Studies in semigroups of contractions mappings of a finite chain”.

Dr. Umar is an expert on the theory of semigroups of transformations, especially on their algebraic, combinatorial and rank properties. He has published more than 45 peer reviewed research papers (approx. 400 citations; h-index = 13 – Google Scholar). In 2015-16, a German mathematician and his coauthors, Billhardt et al. recognized the importance of his constructions (in his paper of 1994), by exhibiting certain universal properties it possesses and named $E(F_A)$ and $F_A$ as Umar band and Umar semigroup, respectively in his honor. It is one of the greatest achievements to see a mathematical object named after someone, more so during their lifetime. He also has interests in recreational mathematics: magic squares and cubes, and calendars.

As a faculty member Dr. Umar has co-supervised two PhD students and three MSc students to graduation, and currently co-supervising two PhD students. He is a journal referee for several international journals and is reviewer for Mathematical Reviews (since 2008). He is also currently a member of the Nigerian Mathematical Society (NMS, since 1987), Edinburgh Mathematical Society (EMS, since 2008), American Mathematical Society (AMS, since 2016) and Combinatorial and Mathematical Society of Australasia (CMSA, since 2011, now a life member).

**Courses taught:**

- MATH161 Calculus II
- MATH212 Calculus III
- MATH261 Differential Equations
- MATH241 Probability and Statistics
- MATH461 Linear Algebra

- Studies in semigroups of contractions mappings of a finite chain
- Semigroups of transformations
- Algebraic semigroup theory

**JOURNAL PAPERS**

- Umar, A. On the semigroups of order-decreasing finite full transformations.
*Proc. Roy. Soc. Edinb. Sect. A***120**(1992), 129-142. - Umar, A. On the semigroups of partial one-to-one order-decreasing finite transformations.
*Proc. Roy. Soc. Edinb. Sect. A***123**(1993), 355-363. - Umar, A. A class of quasi-adequate transformation semigroups
*.**Portugaliae Mathematica*Vol.**51**Fasc. 4 (1994), 553-570. - Umar, A. On the ranks of certain finite semigroups of order-decreasing transformations.
*Portugaliae Mathematica*Vol.**53**Fasc. 1 (1996), 23-34. - Umar, A. Semigroups of order-decreasing transformations: the isomorphism theorem.
*Semigroup Forum*Vol.**53**(1996), 220-224. - Makanjuola, S. O. and Umar, A. On a certain subsemigroup of the bicyclic semigroup.
*Communications in Algebra***25**(2) (February, 1997), 509-519. - Umar, A. On certain infinite semigroups of order-decreasing transformations I.
*Communications in Algebra***25**(9) (September,1997), 2987-2999. - Umar, A. Some remarks about Fibonacci groups and semigroups.
*Communications in Algebra***25**(12) (December, 1997), 3973-3977. - Umar, A. Enumeration of certain finite semigroups of transformations.
*Discrete Math.***189**(1998), 291-297. - Umar, A. A class of (0)-idempotent-free transformation semigroups.
*Semigroup Forum***59**(1999), 74-78. - Umar A., On certain infinite semigroups of order-increasing transformations II.
*Arab J. Sci. Eng.**Sect. A.*Vol.**28**, (2003), 203-210. - Laradji, A. and Umar, A., Combinatorial results for semigroups of order-preserving partial transformations.
*Journal of Algebra***278**(2004), 342-359. - Laradji, A. and Umar, A., On certain finite semigroups of order-decreasing transformations I.
*Semigroup Forum***69**(2004), 184-200. - Laradji, A. and Umar, A., On the number of nilpotents in the partial symmetric semigroup.
*Communications in Algebra*,**32**(2004), 3017-3023. - Laradji, A. and Umar, A., Combinatorial results for semigroups of order-decreasing partial transformations.
*J. Integer Sequences***7**(2004), 04.3.8. - Laradji, A. and Umar, A., Asymptotic results for semigroups of order-preserving partial transformations.
*Communications in Algebra***34**(2006), 1071-1075. - Laradji, A. and Umar, A., Combinatorial results for semigroups of order-preserving full transformations.
*Semigroup Forum***72**(2006), 51-62. - Laradji, A. and Umar, A., Combinatorial results for the symmetric inverse semigroup.
*Semigroup Forum***75**(2007), 221-236. - Umar , B. Yushau and B. M. Ghandi, “Convolution of two series.”
*Australian**Senior Maths Journal***21**(2) (2007), 6-11. - Ali, Bashir and Umar, A., Some combinatorial properties of the alternating group.
*Southeast Asian Bulletin Math.***32**(2008), 823-830. - Junaidu, S. B., Laradji, A. and Umar, A., Powers of integers as sums of consecutive odd numbers.
*Math. Gazette***94**(529)(March, 2010), 117-119. - Umar, A., Some combinatorial problems in the theory of symmetric inverse semigroup.
*Algebra and Discrete Math.,***9**(2010), 115-126. - Laradji, A. and Umar, A., Some Combinatorial Properties of the Symmetric Monoid.
*International Journal of Algebra and Computations*,**21**(2011), 857-865. - Umar, A., Combinatorial Results for Semigroups of Orientation-Preserving Partial Transformations.
*Journal of Integer Sequences*,**14**(2011), 11.7.5 - Abdullahi Umar and Rajai Alassar. “A Classroom Note on: Bounds on Integer Solutions of xy= k(x+y) and xyz= k(xy+ xz+ yz).”
*Mathematics and Computer Education*45.2 (2011): 141-147. - Laradji, A. and Umar, A., On the number of subpermutations with a fixed orbit size,
*Ars Combinatoria*,**CIX**(2013), 447-460. - AlSharawi, Z., Burnstein, A., Deadman, M. and Umar A., A recursive sequence arising from a combinatorial problem in botanical epidemiology,
*J. Difference Equ. Appl.*,**19**(6) (2013), 981-993. - Ali, Bashir, and Umar, A. Dihedral groups as epimorphic images of Fibonacci groups.
*SQU Journal for Science*,**18**(2013), 54-59. - Al-Kharousi, F., Kehinde, R. and Umar, A., Combinatorial results for certain semigroups of partial isometries of a finite chain,
*Australas. J. Combin*.**58**(3) (2014), 365-375. - Umar, A., Some Combinatorial Problems in the Theory of Partial Transformation Semigroups.
*Algebra and Discrete Math.,***17**(2014), 110-134. - Laradji, A. and Umar, A., Combinatorial Results for Semigroups of Order-Preserving or Order-Reversing Subpermutations,
*J. Difference Equ. Appl.**,***21**(2015), 269-283. - Kudryavtseva, G., Maltcev, V. and Umar, A. Presentation for the Partial Dual Symmetric Semigroup.
*Communications in Algebra*,**43**(2015), 1621-1639. - Al-Kharousi, F., Cain, A. J., Maltcev, V. and Umar, A., A countable family of finitely presented infinite congruence-free monoids,
*Acta Sci Math. (Szeged)***81**(2015), 437 – 445. - Al-Kharousi, F., Kehinde, R. and Umar, A., On the semigroup of partial isometries of a finite chain.
*Communications in Algebra*,**44**(2)(2016), 639-647. - Laradji, A. and Umar, A., Lattice paths and partial order-preserving transformations,
*Utilitas Mathematica,***101**(2016), 23-36. - Adeshola, A. D. and Umar, A.,Combinatorial results for certain semigroups of order-preserving full contraction mappings of a finite chain,
*JCMCC*, (To appear). - Umar, A. Presentations for subsemigroups of PDn,
*Czechoslovak Math. Journal*, (To appear).

**OTHER PUBLICATIONS**

- Umar, A., “Construction of Even Order Magic Squares,” Technical Report No. 233, (July 1998) Department of Mathematical Sciences, KFUPM.
- Higgins, P. M. and Umar, A., “Semigroups of weak V-Stabilizer mappings,” Technical Report No. 238, (November 1998) Department of Mathematical Sciences, KFUPM.
- Higgins, P. M. and Umar, A., “Semigroups of Order-decreasing Transformations: Some Fundamental Congruences,” Technical Report No. 268, (September 2001) Department of Mathematical Sciences, KFUPM.
- Laradji, A. and Umar, A., “On some generalizations of the hat problem and transformation semigroups,” Technical Report No. 358, (October 2006) Department of Mathematical Sciences, KFUPM.
- R Kehinde, SO Makanjuola A Umar, “On the semigroup of order-decreasing partial isometries of a finite chain,” arXiv preprint arXiv:1101.2558.
- A Umar, “On the Construction of Even Order Magic Squares,” arXiv preprint arXiv:1202.0948.
- A Distler, V Maltcev, A Umar, “$ mathcal {J}^{ ast}= mathcal {D}^{ ast} $ need not hold in finite semigroups,” arXiv preprint arXiv:1302.0985.
- AM Ibrahim, HM Jibril, A Umar, “Constructing Even Order Magic Squares By Consecutive Numbering,” arXiv preprint arXiv:1303.4536.
- F Al-Kharousi, RK Kehinde and A Umar, “Combinatorial results for certain semigroups of order-decreasing partial isometries of a finite chain,” arXiv preprint arXiv:1702.04485.