The Mathematics Study Program of UIN Sunan Kalijaga Yogyakarta once again organized an Analysis Colloquium on May 12, 2026. The event featured two Mathematics students who presented the progress of their undergraduate thesis research while also sharing their experiences in the process of completing their final projects in the field of analysis. The colloquium was conducted in an academic and interactive atmosphere and was attended by lecturers as well as students from the 2022, 2023, and 2024 cohorts.

The first presenter, Tri Mauliana Ningsih, delivered a presentation entitled “Common Fixed Points on Contractive-(θ, τ) and Contractive-(ψ, τ) Mappings in Complete Metric Spaces.” In her presentation, she explained the concept of common fixed point theory as an extension of Banach’s contraction principle in complete metric spaces. The research discusses the existence and uniqueness of common fixed points on contractive-(θ, τ) and contractive-(ψ, τ) mappings, along with their applications in mathematical problems such as dynamic programming. In addition to presenting her research findings, she also shared strategies for independent learning, stages of thesis preparation, and the importance of understanding theorems and mathematical proofs step by step.

The second presenter, Mauliya Azizatun Ni’mah, presented her research entitled “Analysis of the Existence Theorem of Periodic-3 Trajectories on Elliptical Billiard Tables.” This research examines the existence of periodic trajectories in billiard problems using geometrical and analytical approaches. During her presentation, she explained the relationship between periodic trajectories, inscribed triangles, and conic sections such as ellipses through Marden’s Theorem and several recent research results. She also shared her experiences in studying research papers, constructing theorem proofs, and utilizing GeoGebra software to visualize geometrical concepts.

Through this colloquium, students gained broader insights into research topics in analysis as well as a clearer understanding of the process of writing a mathematics thesis, ranging from literature review and theoretical understanding to systematic mathematical proof construction. The activity is expected to motivate students and strengthen their readiness in conducting undergraduate research.