Adamance is firmness and determination. Your adamance about taking a popular class might be enough to convince the professor to let you join even though it's full.
When someone refuses to be swayed or influenced, but instead holds fast to her own opinion or decision, the person acts with adamance. Your adamance will come in handy if you're participating in a protest or advocating for something you need. The word comes from the adjective adamant, "insistent," from the Latin adamantem, "hardest iron" or "steel," which has a Greek root, adamas, "unbreakable or inflexible."