I’m currently an undergrad student trying to figure out what route to go and what classes to take. Right now I’m a math major and considering picking up a comp sci minor, since I’m thinking about about future jobs possibly in programming or other computer science fields (maybe cryptology). Would an applied math or pure math major pair better with the comp sci minor? Also, how employable would pure or applied math be without the minor?
Either way (pure or applied math), it depends on what in-major electives and out-of-major electives you choose. For example, if you are interested in cryptography, choosing algebra and number theory electives within math, and appropriate electives within computer science, would be desirable. The common destinations in finance or actuarial jobs would need statistics, economics, and finance electives. High school teaching would require course work as needed for teacher credentialing in your area.
Depending on the differences in requirements between pure and applied math at your school, one may be better than the other for fitting in all of the desired elective courses.
The line between pure and applied math isn’t squeaky clean, and their respective contents vary a bit from school to school. Generally speaking, pure math encompasses more math subjects, including the more esoteric ones, while applied math focuses on more practical techniques in fewer number of fields where they can be applied. Even on the same subject, a pure math major will learn more about the theoretical aspects of the subject, while an applied math major will focus more on the applications and less on abstractions.
For classical cryptography specifically, the most relevant math for now is number theory and probability. Number theory is obviously a pure math subject and probability is a subject in both pure math and applied math. However, cryptography is about to experience seismic and foundational changes. Quantum computing will render the current technique that relies on prime number factorization (a number theory subject) obsolete.
Traditionally, most cryptographers come from either the math community or the computer science community or a combination of the two. That said, a background in physics, specifically quantum mechanics, is helpful working on post-quantum cryptography.
Data science is also a hot field that combines mathematics (applied) and computer science. Not a lot of schools are offering degrees in data science yet, so entry into the field with a math degree and a computer science minor is possible.