I'm aware of her, and saw the link to the programme. I think it might have been more a case of Babbage collaborating with her though.
For the avoidance of doubt I'd intended "collaboration" to imply an equal contribution, rather using the word "helped". Whilst I don't really know about the split in the glory, I gather Ada was a proper mathematician, presumably far surpassing Babbage, but on the other hand I've not heard any great claim for her mechanical engineering prowess, where presumably Babbage was the expert.
My understanding was that "programmability" was the mostly her thing; very much ahead of its time. I know too little on the maths as to how much if at all, it anticipated Turing.
Another lady mathematician you might want to look up is Emmy Noether. Very poorly treated by the sexist establishment of the day, particularly so in her native Germany, but her tieing together of Group Theory / Symmetry with conservations laws in physics underpins a hell of a lot, maybe most, of most modern particle physics - Higgs boson etc. Sadly this is mostly beyond me though is on my reading list