Does this provide added security compared to a standard substitution cipher? Why or why not?

Consider a substitution cipher where 52 symbols were used instead of 26. In particular, each symbol in the cipher text is for either a lowercase English letter, or an uppercase English letter. (For example, let E be the encryption function then we could have E(‘S’) = ‘p’ and E(‘s’)=’m’.) Such a modification augments the key space to 52! Does this provide added security compared to a standard substitution cipher? Why or why not?

This does not add much security to the system at all. Capital letters usually appear only at the beginning of words at the beginning of sentences. Thus, the frequencies of capital letters are quite small in English text. You could simply consider this while using frequency analysis. Simply put, disregard all the characters of very small frequencies and concentrate on solving for the characters with the highest frequencies which will still be the same lowercase letters. Once these are solved for, there will be enough recovered plaintext to deduce most if not all of the capital letters in the message.