How does the emphasis in Acme work? I mean you already have to take differential equations for most science and engineering so why not just get a full major in that field?
-My Name Here
Before I answer how emphases in ACME work, I want to address some common misconceptions about math, some of which are implied in your answer. And I want to say thank you for allowing me to talk a bit about what it really means to do applied math.
First, math is not about numbers. If someone were to take a passing glance at my ACME homework, it would like a series of short, hand-written essays. I don't think this point is really encapsulated in your question, but this is a chance for me to get up on my math pedestal and lecture the world (or rather, the minuscule portion that will read this) about what math really is and gosh darn it, I'm going to lecture! It's true that particularly for lower forms of math, mathematics is often clothed in numbers. But the numbers aren't the purpose of math. What the essence of math is is logic. It is taking information and expressing it in such a clear way so that there can be no doubt as to the implications. Math is one of the instruments by which people are able to gain precise understanding of the total sum of reality. And understanding of things not within the sum of reality--theory is fun. Notice that this definition of math is very broad. It includes things like the double bubble conjecture, number theory--the list goes on and on and on. If I wanted, I could say my major really is the study of the language of the universe.
Now, to get to an actual implied misconception in your question: that differential equations is as high a math as ACME gets. Differential equations isn't even the highest prerequisite students have to take before they get into the core program. Math 334 is like a little baby in comparison the depth that ACME goes into with differential equations in the Senior core.
Focusing in on misconceptions surrounding applied math: many people think that applied math is engineering. And it's true that engineering is one of the types of applied math. However, applied math is a subject that covers literally any area where math is applied. This includes bio-informatics, biology, physics, psychology, statistics, economics, cognition, computer science, cryptography--really any type of science, plus other subjects. Now the type of applied math that ACME teaches is most closely linked to computer science. If someone wanted to get the closest approximation of skills taught in ACME without taking ACME, then they would have to do a double major in CS and pure math.
Alright, I'm finally getting to how ACME emphases work. The nice thing about the emphasis is that cuts out unnecessary classes. Like, every major has some classes that are so specific to just one area that most of the students who take the class will never use what they learned there ever again. Really, the emphases are like fine-tuned minors. People don't choose to major in their emphases (well, there are some crazy people who manage a double major with ACME, but they aren't common) for the same reason people don't major in their minors: the major is different from the minor, and offers things the person wants.
Another cool thing about emphases is that they can be pretty much anything. The most common emphasis is CS, but people also have emphases in areas like linguistics, bio-informatics, cryptography, chemistry, economics, statistics, or even create a new emphasis.
The purpose of having an emphasis in ACME is that is builds the context for you to know how to set up and apply all your crazy math skills. Basically, it makes you even more attractive to prospective employers.
I am an engineering major, and I have seen the stuff that ACME majors do. I can testify to what Anathema said: ACME is waaay more in depth. The Linear Algebra, Diff Eq, and Multi Variable classes we engineering majors take don't even come close to ACME.