Latin Honors (cum laude, magna cum laude, or summa cum laude) are phrases that many universities attach to an undergraduate degree for work that deserves special recognition. Latin Honors are awarded by the student's undergraduate division. They are part of the degree, not the major, and are printed on the diploma.
The College of Arts & Sciences requires a recommendation from the student's major department as part of the decision to award Latin Honors, and each department within Arts & Sciences sets its own requirements for making such a recommendation. Other divisions (such as Engineering or Business) have their own criteria for adding Latin Honors to their degrees and the Mathematics Department is not involved in that decision.
Arts & Sciences students should read the College's requirements, as stated in the Undergraduate Bulletin. In particular, notice that the College requires you to be admitted to Candidacy for Latin Honors by the Department, and the Mathematics Department does this at end of the junior year, at which time you must have an overall GPA of at least 3.65. To become a candidate, a student should submit a Proposal for Admission to Candidacy for Latin Honors to the Associate Director of Undergraduate Studies, Dr. Blake Thornton.
At the time of graduation, the Department will recommend that a candidate receive Latin Honors if she or he has completed the Department's requirements for High Distinction or Highest Distinction in Mathematics. (each of which requires an Honors Thesis). The College will then approve the recommendation if the student's final cumulative overall GPA is at least 3.65.
The Undegraduate Bulletin describes how the level of Latin Honors is determined by the College. Notice that the College allows the Department to put an "upper bound" on the level of Latin Honors, e.g., "no higher than magna cum laude" based on the Department's assessment of the student's honors thesis.