Due to a successful commitment to developing an international education offer, the number of foreign students enrolled in studies at Riga Technical University (RTU) is increasing significantly every year. In this paper, the authors describe the reasons why engineering studies at Riga Technical University are becoming so attractive to foreign students. The motivation and aims of foreign students, their hopes and expectations, and their future plans are also mentioned. Since mathematical subjects are essential to engineering students, a major factor in making engineering studies appealing to foreign students can be met by delivering the best possible quality of mathematical teaching. RTU teaching personnel are developing the proficiency of their teaching, and face the challenge of ensuring that all teaching is on a par across the study curriculum and with other issues related to education at RTU. A preliminary course to prepare students for mathematical subjects at RTU, questions regarding refining teaching proficiency to meet the needs of foreign students and lessons in English are also considered in the paper. The conclusions are made on the basis of student surveys and the long teaching experience of the Professors of the Department of Engineering Mathematics of RTU.