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Introduction to pure mathematics
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[QUOTE="MidgetDwarf, post: 6853357, member: 536423"] If you have a bit of freedom, maybe a proof based euclidean geometry course, and adding basic things such as what a set is (what they are and how to prove a set is a subset of another or equal), relation (equivalence relation/partial ordering), definition of function, what it means for a function to be surjective/injective/bijective? I say Euclidean Geometry, since many of these students should be familiar in using some theorems of geometry, but have maybe not seen proofs. Plus it's visual which can aid in student understanding. Theres a book Moise: "Elementary Geometry From an Advance Standpoint." That you can use as teacher resource, but would not recommend it to students first learning proofs. It covers a lot, so you have great freedom of what to include/exclude. But this would require you to hand out notes, so the students have something to read. Or even have students read Moise more basic geometry book. There are many people, myself included, who never learned basic geometry proper while in undergrad. Maybe look at Pommersheim : A Lively Introduction To the Theory of Numbers. It's one of the most well written, but basic number theory books. At my school, we took a discrete math course, then a number theory course which used this book, to have students practice what they learned in the discrete math course. The problems are not too difficult, and will teach them things that are useful for algebra, but not analysis.But hey, at least they will begin reading and doing mathematics. [/QUOTE]
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