Are courses like real analysis required for an undergrad math degree?

Question

are courses like advanced calculus/real analysis required for an undergraduate degree in math? i've always liked math but i believe that there are some upper division courses i will not be able to pass. i am a community college student who is thinking of transferring in as a math major, but i am very nervous because i know there are classes at the upper division level over my head and some that i can do well in.

i hope i can get some serious responses. thank you.

Answer 1

Traditionally, math programs require real analysis, but there are actually some math programs that don't - it depends mostly on what the university calls "math". At my university (University of Waterloo in Canada) there is a "Faculty of Math" but not really a single math major. Most of the faculty is for computer science, various business programs, and actuarial science, but even within the more fundamental programs, only "pure math" requires real analysis. There are still "math" degrees like applied math, combinatorics/optimization, statistics, etc. that don't require analysis. However, other universities like the University of Toronto require analysis (in fact they substitute 2 years of calculus with very hard analysis courses). To them "math" is theoretical math, not stats or computer science.

Real analysis (or abstract algebra, etc.) is hard. I wish I could tell you otherwise. In fact I'm in computer science now largely because I've checked out real analysis and algebra textbooks from the library, tried to study them on my own, and gave up. It's distressing to me considering that I was the top 1 or 2 in math in high school and I still sometimes want to enjoy math for its own sake.

BUT please don't let that block you if you want to major in math - if you can work hard and are more ambitious than I am then I believe you can succeed. Math is a beautiful subject and if you can do it then I'll be very proud of you.

Keep in mind that a course like real analysis is all about proofs and is very different from what's usually taught at community college or engineering/science programs. If you haven't seen proofs try looking for a book that introduces them or see if your calculus textbook has proof examples. But again, there are some universities that have "math" programs that are more applied and don't require it, and you could definitely do a math-related field like actuarial science, financial math, computer science, engineering, etc.

"Advanced calculus" though is not necessarily real analysis - different universities refer to different things as "advanced calculus" but often it's just the 3rd calculus course (multivariable calculus) which is not necessarily much harder than single-variable calculus.

Answer 2

Yes, you need advanced calculus and analysis is often an elective or required course.  If you like math but don't want to get into the really upper-level stuff, consider a science field - like physics, astronomy, or geology.