The answer depends on the university. Usually, you need at least a Master's degree to teach at a university. I've never heard of a college professor with only a Bachelor's degree.
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To teach at the college level (or at a private high school), a minimum of a master's degree in mathematics (or a closely related field) is required. Some colleges will allow teachers to teach as adjuncts (meaning they are not official professors, do not have offices, teach only a few classes, and make a much lower salary than official professors) if they are in the process of getting a master's degree. To teach at the high school level, the requirements vary from state to state in the US. Most require a bachelor's degree in mathematics education. The main difference is that colleges do not require any education background whatsoever (just math) while high schools require more education than math (in some districts with a shortage of teachers, a history teacher with no math background could be allowed to teach calculus).
College Algebra is the required math for all college students.
Albert Einstein taught math, English and science at the college campus of Medaille College?
The best is to have a college degree and be a math major. Many math teachers do not have degrees in math, however, my personal opinion is that formal math education is a big plus (pun intended) for math teachers. Some math teachers have computer science backgrounds. In many cases, teachers who want to teach math without a math degree need to pass a test to do so. So if you want to be a math teacher, go to college and major in math! Then you also have to get a teaching credential. Some schools have combined math bs and teaching programs.
The math class(es) you are required to take in college are based on your area of study, so someone studying engineering may have to take certain math classes that a chemistry major may not have to take.