<p>"Auburn, could you give examples of what you and other math snobs (no offense) consider to be “real math”? "
- No offense taken. I think most of “us” know we’re being snobbish when we have these exclusionary opinions…</p>
<p>To answer your question, real math… it’s sort of like love. Nobody can tell you you’re in love, but you know. I’m actually being more serious than you’d think…</p>
<p>You can teach just about any “mathematical” subject in a variety of ways, some of which would count as “mathematics” and some of which wouldn’t. Prime examples of this include differential equations and probability and statistics. You can teach both as applied subjects for scientists and engineers, and you can learn both like that. What is differential equations besides all the techniques? What is probability and statistics besides knowing how to calculate averages and odds? Well, the typical engineer would say “nothing more”, whereas the (decent) math (and, to a lesser extent, CS) major would say “a lot more”.</p>
<p>What subjects typically count as “real” math? Well, real analysis, abstract algebra, and topology are good candidates. Things like graph theory, combinatorial designs, coding theory, and game theory may also count, depending on how they are taught. Other courses, such as numerical analysis, cryptography, etc… can also be taught as mathematics courses, but this will depend on treatment.</p>
<p>In CS, courses like Discrete Math, Algorithms, and Formal Languages are usually safe bets, depending on how they’re done. Other courses will have some math mixed in with non-mathematical subjects…</p>
<p>The differences can be subtle, but the following questions can normally guide you…
- Is the goal of most exercises to calculate a number, or a specific instance of some other well-defined mathematical structure?
- Do the mechanics required to solve most exercises come from high-school algebra, trig, pre-calculus, or calculus?
- Does the problem rely mostly on solving specific differential equations or using techniques from linear algebra on specific structures?
- Do you not know what the “answer” is supposed to be before you begin the exercises (if answers are given simply for self-check purposes, this still applies)?
- Can you write down answers to exercises without providing a logical explanation, either in practice or in theory?</p>
<p>If you answered yes to most of the questions, you’re probably not in an actual mathematics class.</p>