Ömür Uğur was born in İstanbul, Turkey, on 8th March, 1971. After completing his elementary and secondary education he was accepted to Uluğbey (Private) High School with scholarship from İstanbul Eğitim ve Kültür (İSTEK) Vakfı.

He started his undergraduate studies at the Department of Mathematics, Middle East Technical University (METU) in 1991 and took his B.S. degree in 1995. At the same time he completed courses in Physics Minor Programme. He became a research assistant at the Department of Mathematics, METU, in the same year, and started his graduate studies. He received his M.Sc. degree in Mathematics in 1998, with a thesis entitled "Hypervirial Analysis of Enclosed Quantum Mechanical Systems", and published his first international article "An Eigenfunction Expansion for the Schrödinger Equation with Arbitrary Non-Central Potentials" in the Journal of Mathematical Chemistry, Vol. 32, No. 4, 2002.

He received his Ph.D. degree in Mathematics, with a thesis entitled "Boundary Value Problems for Higher Order Linear Impulsive Differential Equations", in 2003. After working as a part-time instructor at the Department of Mathematics, METU, for half a year, he received a post-doc position at the Institute of Applied Mathematics (IAM), METU. His first international book "An Introduction to Computational Finance" was published by the Imperial College Press in December 2008.

Presently, he is a member of the faculty at IAM, METU.