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# Difference between applied mathematics and pure mathematics?

Registered User Posts: 304 Member
edited July 2012
What is the difference between applied mathematics and pure mathematics majors? I've seen that applied mathematics has been repeatedly ranked within the top ten highest paying majors, and don't get me wrong pure mathematics is at points, but not most. I was wondering what the differences between these are, and whether it really matters that much. Thanks.
Post edited by Cokelly on

## Replies to: Difference between applied mathematics and pure mathematics?

• Registered User Posts: 1,183 Senior Member
Sometimes the differences can be quite theoretical. Pure math deals with abstract structures essentially, proving theorems for the sake of mathematics and aesthetics with no applications necessary. Applied math relates to applicable things, modeling real world processes with differential equations, finding ways to solve such equations, finding optimal solutions to problems, coming up with efficient algorithms for various number crunching things, and proving theorems related to all these.

An acquaintance of mine, who in another life was a probabilist by training, got a job in a business school. She did consulting for some finance researcher, on some pricing problem. She came up with an analytical solution to the problem in 2 days, which the finance guy gave to his computer whiz to implement. The program worked, but it took 24 hours to spit out numbers meant to decide whether to buy/sell on the stock market, where things change by the minute. That was her first adventure in the wonderful world of applications. A pure mathematician is happy to have an exact solution, or often just knowing that a solution exists, number crunching be damned. In applications, an approximation that is good enough and involves the simplest computations are preferred, because at the end of the day, someone else has something useful to do with those numbers.
• Registered User Posts: 62,143 Senior Member
Pure math and applied math will typically have the same core junior and senior level courses like real analysis, complex analysis, abstract algebra, etc., but pure math will typically include courses like logic and set theory, geometry and topology, etc. in preparation for PhD study in math, while applied math will typically include a concentration in an area of application, which is often pre-professional in nature (e.g. actuarial science) but can lead to PhD study, depending on the area of application. As the requirements are not extremely heavy and mostly overlap, it is usually possible to take the courses for both, although they will typically only give you a degree in one.
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