Dr. Abdullahi Umar
Dr. Abdullahi Umar Professor
Technical Areas
Research Interests

Professor, Department of Mathematics

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 50 peer reviewed research papers (approx. 500 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 four PhD students and three MSc students to graduation, and currently co-supervising a PhD student. 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).

Advisor to the following students & staffs: 8 undergraduate students and a mentor to Dr. Mo’tassem Al Arydah.

  • PhD, Mathematics, University of St. Andrews, Scotland, UK (1992)
  • MSc, Mathematics, Ahmadu Bello University, Zaria, Nigeria (1987)
  • BSc (Hons.), Mathematics, Ahmadu Bello University, Zaria, Nigeria (1983)
Technical Areas

King Fahd University of Petroleum & Minerals serving over 5,000 students per semester, I have had the chance to teach 9 different courses. These are:

  • Algebra and Trigonometry II (Math 002)
  • Calculus I (Math 101)
  • Calculus II (Math 102)
  • Finite Mathematics (Math 131)
  • Applied Calculus (Math 132)
  • Calculus III (Math 201)
  • Differential Equations (Math 202)
  • Introduction to sets and structures (Math 232)
  • Introduction to Linear algebra (Math 280).

During this time, I have served as a coordinator for the courses

  • Math 131 (four times)
  • Math 132 and Math 202.

At Sultan Qaboos University, I have had the opportunity to teach courses like

  • Pre-Calculus (MATH1106) Foundation of mathematics (MATH 2350/MATH3350/MATH357)
  • Calculus II (MATH2108)
  • Discrete mathematics for ECCE (MATH 3330)
  • Combinatorics (MATH 6204), Abstract Algebra I (MATH 4453).


At PI/KU, I have taught

  • Calculus II (MATH161/112)
  • Calculus III (MATH212/231)
  • Differential Equations (MATH261/206)
  • MATH241 (Probabilty and Statistics)
  • Modern Algebra (MATH 411)
  •  Linear Algebra (MATH 461/204).
Research Interests

Research Cluster:

  • Semigroups and Applications

Research Topics:

  • Semigroups of mappings/transformations.
  • Recreational mathematics: calendars, magic squares and cubes.

Research Projects:

  • Studies in semigroups of finite contraction mappings of a finite chain.