Scientific solver admits he is perplexed by abbreviation of name on computer (7,5)
'scientific solver' is the definition.
(method of scientifically solving things)
'admits he is perplexed by abbreviation of name on computer' is the wordplay.
'is perplexed' is an anagram indicator.
'by' means one lot of letters go next to another.
'abbreviation of' means to remove the last letter (to abbreviate is to shorten or partly cut).
'name on computer' becomes 'apple' (Apple is a computer company).
'apple' with its final letter taken off is 'appl'.
'admitshe' is an anagram of 'iedmaths'.
'iedmaths' after 'appl' is 'APPLIED MATHS'.