Nowadays, the undergraduate major is pretty standard as far as I can see. Usually it goes something like:
Lower Level courses: calculus sequence, ODEs, linear algebra, some form of discrete math or introduction to set theory course
Upper level courses: Abstract Algebra sequence (covering things like groups, rings, fields), real analysis sequence, introduction to topology, and then some electives or graduate level courses
This obviously varies from school to school, but if you go look up pretty much any US based colleges math major, the requirements will look something like this.
I’m interested in how the undergraduate math major has changed over the past two or centuries. Is there any source on this? I’d be curious to see what courses math majors took in the 19 and 18 hundreds. I’d assume that things like vector calculus, which many students take in their first or second year, may have been relegated to their junior, or senior year, or maybe even graduate school if one goes back far enough.
My internet searches have turned up empty, so I thought I’d ask here. Any help would be appreciated.
Ethan was on the right track, searching on history of math stack exchange led me to this answer, which is more than adequate in my opinion.
To paraphrase, in 1910, the courses offered solely to math majors at Harvard were a lot like high school mathematics (at least in the US), in the sense that the topics covered superficially seem like more difficult versions of standard high school courses. Indeed, the courses offered include things like trigonometry, elementary algebra, another algebra course (which from the course description seems more arithmetic based than that of an abstract algebra course), and many course in planar, solid, and analytic geometry. The courses seem to culminate to an introduction to differential and integral calculus.
The courses offered to undergraduates, and graduates included things like a second course in differential and integral calculus, differential equations, vector calculus (and quaternions, which I guess makes sense since quaternions were originally used by Maxwell in developing the Maxwell field equations). Things eventually start to seem more upper level undergraduate/intro graduate mathematics courses with some abstract algebra courses (which seem primarily concerned with galois theory), a "theory of functions" course (I presume this is some form of functional analysis?), a calculus of variations course, a differential geometry of curves and surfaces course, and a non euclidean geometry course to name a few. The graduate courses seem to culminate with an advanced theory of functions course, a linear differential equations in physics course, a definite integrals and integral equations course, and a course which seems to essentially be a rudimentary Lie theory course.
All in all this was a very interesting find, I wonder if there exists stuff like this for the mid 20th century, and the mid 19th century, just to bridge the gaps a bit.