I have taught History of math regularly at my university. I recommend "Math Through the Ages" as well as the BBC documentary "Story of Maths". The following are good supplements:
1) Man of Numbers by Keith Devlin, about Fibonacci , who introduced Hindu-Arabic numerals to the West to replace the Roman numeral system, and revolutionized Western mathematics
2) The Mathematical Universe by William Dunham; (Description from amazon.com) The Mathematical Universe is a solid collection of short essays, with each addressing a particular mathematical topic. Titles range from "Isoperimetric Problem" to "Where Are the Women?" Author Dunham manages to maintain a conversational tone while referencing diagrams, equations, and rigorous arguments throughout the book.
3) "Fermat's Last Theorem" documentary by Simon Singh, as well as his book "Fermat's Enigma"
Re: women in math - I am one of the few women in my subfield of mathematics. It is still rare to find women at the top of the profession even though roughly 35-40% of all PhD's in math are awarded to women. Many women. like myself, find careers at teaching universities. Doing theoretical math at the top research level is highly competitive. There are a few "superstars", and many math PhD's , both male and female, drop out of the research stream at a higher rate than other disciplines. I would encourage your daughter to research current women mathematicians like Ingrid Daubechies and Eugenia Cheng.
