<p>I love your scale – “from 1 to Terry Tao.” I’m also a huge fan of the genius professor. Excuse my linguistic meandering. There is simply a wealth of tangential topics I can pursue here.</p>
<p>To Business: My background in finance can only partially answer your question; specifically, I can tell you what kind of quantitative competency is expected for banking and finance. </p>
<p>Note that any maths (yes, maths) from calculus and beyond will never be invoked in investment banking, private equity or hedge funds. But why do firms expect you to take this and other courses and, moreover, do well in them? It turns out financial firms are much more interested in the general penumbra of aptitude that comes packaged with each academically high-performing applicant. What do I mean by this? </p>
<p>Well, to do well in an introductory calculus, ordinary differential equations, and linear algebra (the standard mathematical fare for underclassmen), it takes a certain intelligence and mental acuity. But what separates the budding mathematicians who codify their logic and arguments in epsilon-delta proofs from the “blue collar”-smart future investment bankers is very different from what separates those successful Goldman Sachs/Morgan Stanley applicants from the inclusive population of non-maths majors. Those who earn a coveted slot at an investment bank tend to be the ones who aren’t necessarily able to digest Rudin ([Principles</a> of Mathematical Analysis (International Series in Pure and Applied Mathematics): Walter Rudin: 9780070542358: Amazon.com: Books](<a href=“http://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/007054235X]Principles”>http://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/007054235X)) in a single setting; rather, they are the ones who find a way to cram the minimum amount of material required to secure a top mark on an exam in the minimal amount of time (an optimization problem in itself!), juice extra points from positive off-line interactions with the teaching staff and professors (we are known for our charisma and preternatural ability to launch into rapport with just about everyone), and continually buffer their final score tally with “cruise points,” which are almost passively-earned points from a variety of minority contributions to your final grade, such as homework assignments, class participation, in-class pop quizzes, etc. </p>
<p>Your ability to master these softer skills are not clear from the single data point of your final grade. Instead, it is just another tiny diamond on the enormous histogram of trials and tribulations suffered during your undergraduate years that encode your entire life, which is eligible for professional scrutiny. </p>
<p>Ultimately, the maths (look, the UK uses this term, and it just stuck) you need to know for finance will never even exceed algebra, as many of the models you construct for valuation or capitalization require basic arithmetic operations at best. [Side note: a good example to see is the set of quant questions tested on the GMAT]. So, if you aspire for finance, and when you finally do take calculus, remember that even if you will never need to consider situations that involve dangling catenaries or proving the existence of fixed points for continuous functions on the job as an Investment Banking Analyst, you can be sure that your academic and soft-skills success in securing high grades will have been responsible for your future successful candidacy at the Bulge Bracket.</p>