What is Linear Algebra?

Solving systems of equations Solving a single linear equation with one unknown quantity is a task that is studied in elementary school. One proceeds in high school to study more complex equations involving more involved functions. Many problems in mathematics and its scientific applications amount to solving equations, and especially to solving systems of equations. … Read more

On teaching how to prove mathematics theorems

For four consecutive years I taught a fourth-semester course called “Introduction to Analysis,” in which we looked at differential calculus for a second time, stressing the foundations, the logical structure, and proving all the key theorems. We used Stephen Abbott’s excellent book, Understanding Analysis. The course was intended primarily for math majors, although we had … Read more