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Bookmark or Share- reference request - Roadmap for self-learning pure mathematics from ...At this stage, one needs to know how to solve linear equations, systems of linear equations, quadratic equations, factor polynomials, algebra identities, and inequalities. You don't learn elementary algebra separately but learn it along with calculus. Cautions: Just as in Olympiad geometry, don't spend too much time with inequalities.
- Do most mathematicians know most topics in mathematics?I still only know "a bit" about it, most of it I don't know, and most of what I had learned is already forgotten. (Actually FEM-Theory is still a huge topic, that contains e.g. different kinds of PDEs [elliptic, parabolic, hyperbolic, other]. So you could do the "zooming" several times more.)
- "Does everyone want coffee?" propositional logic problemThe solution is that the first two professors who say they don't know if everyone wants coffee are the ones who want coffee. However, I don't understand the logic. For example, the first professor may not want coffee, but does not know if the other professors want coffee, and thus can answer "I do not know."
- Pigeonhole Principle Question - Group of 6 people, do 3 either know ...The pigeonhole principle applies because every person is related to every other person in two ways, (either they know the person or they do not). So when we consider any of the $6$ people we know that they know $3$ people or they don't know $3$ people.
- A good way to retain mathematical understanding?Just my two cents, don't know if it'll help you. Oh and one more thing, if you have less than one month left, the best thing you can do is just try and work out old sample papers, questions and homework problems. That is the best strategy, I know of, to pass the exams with a good grade, if that's what you are looking for.
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