Introduction to Pure Mathematics for Advanced High School Students consists of a series of lessons in Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra.
Lesson 1 from this series covers the basics of mathematical logic. In this lesson we will learn about statements, logical connectives, truth assignments, the construction of truth tables, how to determine truth without a truth table in an efficient yet rigorous way, and the notion of logical equivalence.
This version of the lesson includes a PDF file with notes followed by a problem set. The problems are broken down into five levels of difficulty. The paid version of this product also includes a second PDF file consisting of solutions to all the problems.
This series is intended to give high school students who are advanced in math an honest and rigorous introduction to pure mathematics. It is unfortunate that most students will not be exposed to real theoretical mathematics until their sophomore year of college and after they have already declared themselves math majors. My hope is that students wishing to explore real theoretical mathematics before committing to becoming a math major will now have the opportunity to do so. And of course I hope that they enjoy experiencing pure mathematics as much as I enjoy writing about it.
|11th Grade, 12th Grade, Higher Ed
|EBooks, Lecture notes
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