<p>At my college, there is no applied math major, so I'm considering designing my own. Regular math majors are required to take 2 semesters in analysis. Is this really necessary for a career in applied math? Also, will I be able to get into graduate programs in Operations Research (e.g.) without analysis?</p>
<p>Why don’t you man up and take it anyways?</p>
<p>It’s a big shame that programs DON’T require analysis and algebra. My understanding is that most good programs require them. While you might not be fond of algebra, at least take analysis. The rigorousness should prepare you adequately for working with higher level math.</p>
<p>But then again, I’m super biased towards math, so take my commentary with a grain of salt. : )</p>
<p>I’m not shying away from the difficulty. I’d be replacing the 6 hours at the 400 level with 6 hours of statistics at the 500 level.</p>
<p>If the concepts in analysis are the basis for graduate-level math, that’s one thing. However, I haven’t seen analysis as an entrance requirement for any of the operations research programs I’m interested in, including some of the top programs in the country. Are you suggesting I take analysis only to be exposed to the rigor, or will the concepts in fact lay the foundation for grad math?</p>
<p>I don’t know anything at all about operations research, so I will talk about applied mathematics in general. Analysis is useful for applied mathematics in at least three different ways:</p>
<ul>
<li><p>You get the hang of epsilon-delta proofs. Error bounds for numerical algorithms are all about epsilon-delta arguments and you will be glad that you have done it before in a more familiar calculus setting.</p></li>
<li><p>You get a first exposure to measure theory, which is the language that graduate-level probability theory is done in.</p></li>
<li><p>A rigorous foundation in real analysis is useful for applicable analysis classes like PDEs.</p></li>
</ul>
<p>You can get through all of the courses mentioned above without taking an actual analysis class, but it might make your life much easier. The concepts, methods and results will crop up all over the place in graduate-level mathematics.</p>
<p>For what it’s worth, I just googled “operations research phd” and two of the first three programs I clicked on required a real analysis course in their PhD program for students who hadn’t taken it in their undergraduate years (Cornell and Stanford; Cornell also requires abstract algebra).</p>
<p>This is exactly what I wanted to know.</p>
<p>Thank you.</p>
<p>If you are at all interested in a research career in applied mathematics (whether in a corporate or academic setting), I would highly encourage you to get a solid foundation in pure mathematics, ideally at least up through first-year graduate classes. It might look like abstract non-sense right now but it will be tremendously helpful later on. Many advances in applied mathematics rely on results in pure mathematics and you want to be in a position to understand those. I know several applied mathematicians who regret not having taken more pure math classes in college and grad school, and not a single one who would give their pure training back. </p>
<p>
Just as a heads up, graduate-level applied math is just as rigorous as pure mathematics. The difference between pure and applied mathematics is not the rigor but the objective: pure mathematicians develop mathematical theory, and applied mathematicians use that theory to develop models and methods (i.e. more theory) to solve problems outside of mathematics.</p>
<p>To clarify: I’m interested in OR Master’s programs. Cornell’s [Ph.D</a>. requirements](<a href=“http://www.orie.cornell.edu/orie/academics/phd/programdescription/phdreq.cfm]Ph.D”>http://www.orie.cornell.edu/orie/academics/phd/programdescription/phdreq.cfm) differ from their [MS</a> requirements](<a href=“http://www.orie.cornell.edu/orie/academics/meng/programdescription/requirements.cfm]MS”>http://www.orie.cornell.edu/orie/academics/meng/programdescription/requirements.cfm) in that the MS doesn’t require analysis. The same appears to be true at Stanford (see [Ph.D</a>. requirements](<a href=“Management Science and Engineering”>Management Science and Engineering) appendix 2 vs. [MS</a> requirements](<a href=“Management Science and Engineering”>Management Science and Engineering)) and other universities such as Georgia Tech.</p>
<p>This seems to fit with your advice. If I want to develop theory, I need at least analysis. If I want to use theory, they aren’t entirely necessary, but they’re helpful as you said:</p>
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</p>
<p>Now the question is, what is more valuable? Undergraduate exposure to theory and methods used in grad math, or specialization at the undergrad level as I would be doing if I skipped out on analysis? I can free up hours from pure math for applied statistics and computational math, both of which are useful in OR. I’m leaning towards building a solid foundation with a BS, then getting into the meat of OR in grad school, like you have suggested, but remain unconvinced.</p>
<p>My own observation based on a very limited sample: Pure math majors get into more selective applied math programs than applied math majors. This even extends to other fields such as computer science, economics, etc.</p>
<p>But my opinion doesn’t matter here. You need to figure out a path that works for you. There are good reasons for either option. (If you do end up taking analysis, be sure to take the full sequence. The first semester feels like Calc 1 all over again, and you don’t get to new interesting topics until the second.)</p>