<p>Why is Real Analysis taught in year 3 as undergrad? I have found Real Analysis to be extremely useful in writing proofs, why is it that they make you wait for three years to take it? All you really need as a prerequisite is linear algebra and Calc 2. I could have done so much better in my linear algebra 2 class if I took real analysis prior.</p>
<p>What are you talking about? I thought it was the norm that if you had the prerequisites you were good to go. That’s how it is at my school. It just so happens that a lot of people end up taking it their junior year due to a variety of reasons. I’m not taking it until my senior year. Here you have to take an intro proofs class before you can take that class. I was a transfer student and they did not offer Real Analysis at my community college. </p>
<p>In my linear algebra class we were taught proof techniques and used them throughout the course. Idk how useful Real Analysis would’ve been but what we were taught was enough to get through the proofs.</p>
<p>Some math departments think that most undergraduates will find real analysis to be a more difficult proof-oriented course than proof-oriented linear algebra or some other proof-oriented course, so they suggest taking another proof-oriented course before real analysis.</p>
<p>While it is possible to qualify for Real Analysis after Calculus II and Linear Algebra (if the Linear Algebra course had a great deal of proof-writing), the overall difficulty of the course may be a tad too much for sophomores. On top of that, the usual math schedule for most math majors and many engineering majors is:</p>
<p>Calculus I (freshman/fall semester), Calculus II (freshman/spring semester), Linear Algebra (sophomore/fall semester), Calculus III (sophomore/spring semester) with Differential Equations somewhere in the sophomore year.</p>
<p>For EE, CompE, CS, Math/CS, add in programming courses (Java or C++) in both semesters of freshman year and Discrete Math/Structure and Computer Organization.</p>
<p>EE’s and CompE’s also have the Electric Circuits sequence during sophomore year and many Math, Science and Engineering majors also have the Physics sequence during sophomore year…especially if the Math major wants a B.S.</p>
<p>I am not even mentioning Chemistry courses for the schools who require Chemistry to fulfill science requirements.</p>
<p>Probably only the Pure Math major (going for a B.A.) who has no intentions on taking any additional applied academic areas can really take Real Analysis as a sophomore and even then, you are looking at a 3-math-course semester as a sophomore.</p>
<p>Probably too much.</p>
<p>All you really need for RA is a background in calculus and the ability to write proofs. Lots of math majors take calculus in high school, and basic proof-writing is something that can be picked up in a week if you’re motivated. Unfortunately, lots of schools have weird prerequisites for various classes, and not just in math. That being said, there are schools that offer real analysis to freshman as well (Princeton and Chicago are two examples).</p>
<p>Plenty of universities won’t stop a frosh from enrolling in real analysis, since there are frosh who come in having already completed the usual frosh and soph math courses.</p>
<p>Caltech and Harvey Mudd “frosh calculus” might as well be real analysis, since they are filled with proofs.</p>
<p>Not everyone is on the same schedule. Univ. math departments have to assume their freshman have not taken calculus yet. Years 1-2 are spent learning Calc I-III and then differential equations and linear algebra. Second years also usually get a basic introductory course on how to write proofs. Year 3 and upwards then jumps into proof writing math–RA, abstract algebra, logic, functional analysis, etc.</p>
<p>OP even though real analysis may help you to write proofs, the content (as many have said in their own different ways) is often times very difficult for undergraduates. I can safely say Real Analysis was the hardest course I took while in undergrad. I have a few friends doing PhDs in math and they still can’t figure out real analysis completely. </p>
<p>I took it my senior year (made a ‘B’ don’t ask me how). I honestly believe, for the average math student, Real Analysis should be done your junior year (second semester) or senior year; when you are a more mature student of mathematics.</p>