what field of mathematics was mabel schmeiser barnes involved in and, in comparing her and ada byron king, what kind of environments were they raised in and what kind of access to schooling did they have?

Mabel Schmeiser Barnes was involved in the field of applied mathematics, with a focus on cryptography and code-breaking during World War II.

To find this information, you can start by conducting an online search using search engines like Google or Bing. Try searching for "Mabel Schmeiser Barnes" and "field of mathematics" to gather information about her specialization. Look for credible sources such as academic papers, biographical articles, or official websites related to her work in order to gather accurate information about her contributions to the field of mathematics.

Now, let's move on to comparing Mabel Schmeiser Barnes and Ada Byron King (better known as Ada Lovelace) in terms of their upbringing and access to schooling.

For Ada Lovelace, she was raised in a privileged environment. She was the daughter of the famous poet Lord Byron and was exposed to a highly intellectual and affluent household. Despite her parents' separation, Ada's mother, Annabella Milbanke, encouraged her interest in mathematics and ensured that she received an excellent education. Ada had access to private tutors and mentors, including prominent scientists, mathematicians, and engineers.

In contrast, information specifically about Mabel Schmeiser Barnes' upbringing and access to schooling may not be readily available without more context or detailed research. You can explore various sources such as biographies, interviews, or articles that discuss her background to gather information about her upbringing and educational opportunities.

Remember, when researching historical figures, it's essential to utilize reliable sources and cross-check information from multiple sources to ensure accuracy.