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Advanced Mathematics Past Papers
When it comes to the concept of advanced mathematics, it depends on the context.
Some people consider calculus to be advanced mathematics but to someone majoring in math calculus is pretty basic stuff.
There are two big transitions on the road to become a research mathematician.
The first occurs early in undergrad, usually after calculus and differential equations when emphasis shifts from solving problems to reading and writing proofs, i.e. proving theorems using rules of logic.
Most people who are not math majors never are exposed to this or only are a little.
This includes engineers and even physicists, who don’t really need the rigor of proofs and are content to just utilize theorems proved by mathematicians.
Given that probably 99.9% percent the world population never reach this point I think this transition is probably the best candidate for separating “basic” math from “advanced” math.
There is a second transition point as well that comes usually during grad school (in mathematics) where you start coming up with your own definitions and theorems (and proving them) rather than proving things where the conclusion is given to you and you are asked to provide the proof.
This is the essence of mathematical research. Though I am certainly not to this point yet I have read that it is a very different skill from either of the first two phases of math education even though those phases are certainly prerequisites.
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