f computer applications.
In summary, we want students to come to college thinking that mathematics makes sense, that they can solve nontrivial problems (both in pure mathematics and within real-life contexts) by reasoning and using powerful mathematical tools, and that they are expected to communicate their solutions effectively. They need to be on top of arithmetic and algebraic skills. But perhaps most important of all, students need to develop some degree of love and enthusiasm for mathematics. We would like to see a typical high school student think like a mathematician, develop his or her critical thinking, apply the critical thinking skills in solving problems, and be able to see the interconnections among different areas of mathematics and between mathematics and the real world.
To accomplish this, students should be encouraged to take as much mathematics as possible (at least learning well the content of two years of algebra and a year of geometry, so that we don't have to offer remedial courses in college). A fourth or fifth year of college-preparatory mathematics is to be strongly encouraged, such as some advanced concepts of algebra (e.g., including mathematical induction, set theory, formal logic, the binomial theorem, functional transformations, advanced work with exponential and logarithmic functions, matrices, and lots of applications to real-life situations), trigonometry, discrete mathematics, probability, and statistics. (Students should not be rushed to take calculus in high school, and studying calculus outside the AP program makes no sense at all.) It may well be that not doing a mathematics course in their senior year is likely the single most damaging choice students can make in high school with regards to their success in college.