To be admitted to a degree, in formal University language, means to be awarded the degree, in this case to become a Bachelor of Science. This is from the traditional way of thinking of a degree, such as a Bachelor or a Master as being an academic rank, rather than just a qualification. When I graduated from an old Scottish university, the Chancellor said (in Latin) to the first alphabetically in the class "I promote you to the degree of Bachelor of Science, as a symbol of whicj I place this cap upon you" and to other students "and upon you"