Mathematics was always part of the instruction at Newark later Delaware, College. The first mathematics professor at Newark College was Nelson Z. Graves, who joined the faculty in 1834 shortly into the first academic term. He had previously taught Mathematics at the Academy of Newark. Nelson also led the Academical Department (which was the preparatory course equivalent to the Academy.) In 1837, the Newark College catalog noted that Nelson was Professor of the Academical Department and Adjunct Professor of Mathematics. Revered William Pendleton then held the title Professor of Mathematics and Natural Philosophy.
Only after the 1890s was Delaware College large enough to organize faculty into departments. There is no specific date for the establishment of Mathematics, however, your department was known as the Department of Mathematics prior to 1933, when it was officially renamed the Department of Mathematics and Astronomy. The unit was renamed Department of Mathematics in 1963 and Department of Mathematical Sciences in 1978.