[2] TAMS is a member of the National Consortium for Specialized Secondary Schools of Mathematics, Science and Technology.

TAMS was established on June 23, 1987 by the 70th Texas Legislature, in order to provide high school students an opportunity to take advanced coursework in math, science, and engineering.

[3][4] It was designed as a residential program at the University of North Texas for high school-aged students gifted in mathematics and science.

The establishment of this innovative program is from national concern among educators about anticipated shortages of students who would be sufficiently well prepared in mathematical and scientific problem solving.

Recognizing that American youth would need to compete in an increasingly technological society, several states including Texas opted to create alternative educational programs that would attract students to the fields of mathematics and science as well as offer bright, motivated young people an accelerated education in these areas of study.

[5] TAMS is required by "to identify exceptionally gifted and intelligent high school students at the junior and senior levels and offer them a challenging education to maximize their development".

Applications are typically accepted between July and mid-May of a student's sophomore year of high school, though some freshmen apply.

Multiple criteria are assessed, including middle and high school grades, the rigor of classes taken at school (particularly for mathematics classes), letters of recommendation from teachers and an academic counselor or principal, SAT scores from no later than the January of the applicant's sophomore year, and an essay.

In the 2013 Siemens Foundation Competition, 2 TAMS students were named regional finalists and 17 more were recognized as semifinalists.

[4] While at TAMS, they are considered to be concurrently enrolled in high school and college, and attain a college-like experience all while living among same-age peers.

[19] TAMS students are responsible for paying for room and board in McConnell Hall and a mandatory UNT meal plan every semester, as well as a yearly $2,500 program charge and approximately $5,500 tuition fees (after scholarship is applied).

Students at TAMS are encouraged to take the opportunity of conducting research under the guidance of a professor either on or off-campus during the school year as well as during the summer.

The other common room, Mac Café, aptly named because it once was home to a university cafeteria, hosts various student activities and serves as a gathering place for both academic and social interaction.

Volunteers collect donated computers and laptops from the community and some companies, and distributes them to schools and homes in need after repairing and renovating them.

It is known to be an online tutoring service in which TAMS students volunteer their time to schools in need of academic aid.

TAMS has a number of student activities and events, ranging from academic competitions to performance and cultural groups.

A selection of currently active clubs (as well as selected competitions entered by TAMS students), many of which offer volunteering opportunities, can be found below:[31] Many students participate in yearly or more frequent events such as proms, school dances, talent shows, coffee houses, and an annual homecoming dance.