The word "advanced" is relative to the intended audience and it's obvious how he meant that word to be applied. The author wrote: ", chances are if you are co

The word "advanced" is relative to the intended audience and it's obvious how he meant that word to be applied. The author wrote: ", chances are if you are considering studying advanced mathematics you will already have formal qualifications in the basics, particularly the mathematics learnt in junior and senior highschool (GCSE and A-Level for those of us in the UK!). " The author is not a Fields Medalist writing to other PhD mathematics graduate students. In such a case, the adjective "advanced" would have a different meaning.