How to demonstrate mastery of courses not taken during undergraduation In this answer, Anonymous Mathematician says, "You need to demonstrate that you have mastered the undergraduate material that is less relevant for computer science. For example, mathematical analysis along the lines of Rudin's Principles of Mathematical Analysis" 

How can I demonstrate I have mastered materials from Rudin's Principles of Mathematical Analysis or Artin's Algebra for admission in grad school?
I find this a hard question because I regularly have to deal with applicants claiming they have certain skills and because these cases are difficult to deal with. For example, recently an applicant got a bad grade for one module and wrote they really were much better. I decided the applicant's examiners are in a much better position than I to judge the applicant's capabilities.

In your case you want to prove you have knowledge you didn't formally study in your undergraduate school. If so it's impossible to prove your skills unless (1) somebody from your undergraduate school is willing to write a letter of recommendation, or (2) the grad school are willing to ``examine'' you.

In the case of (1) this may work. Unfortunately, (2) means the graduate school have to do more work and I think this is unlikely.

Finally, if the graduate school require the skills, it seems to me they think it is reasonable. In that case, applicants should have taken modules that demonstrate these skills. If they haven't, it seems to me they're not the ideal candidates in the opinion of the graduate school.