He availed leave from Mar Athanasius College and proceeded to Madurai University to pursue research in mathematics.
He was awarded the Doctor of Philosophy degree in 1976 for his dissertation on "Studies in Compactifications and other Extensions" written under the supervision of Prof. T. Soundararajan.
In 1977 he moved over to the Department of Mathematics in Cochin University of Science and Technology where he held several positions until his retirement in 2003.
After retirement from Cochin University of Science and Technology, he joined St. Joseph's College, Irinjalakuda to help develop a research centre in mathematics.
[2] During the 79th Annual Conference of the Indian Mathematical Society held at Rajagiri School of Engineering & Technology, Kochi, during 28–31 December 2013, Thrivikraman, along with two other mathematicians from Kerala Prof. K. S. S. Nambooripad and Prof. R. Sivaramakrishnan, were honoured in a special event called Guruvandanam for their lifetime contributions to mathematics.