Linear Algebra is Scary, Even for Future Mathematicians

The Calculus of Friendship: What a Teacher and a Student Learned about Live While Corresponding about Math (2009) is a delightful book by Steven Strogatz. Strogatz is Jacob Gould Schurman Professor of Applied Mathematics at Cornell University, and he writes beautifully. The book is about his decades-long correspondence with one of his high-school mathematics teachers, … Read more

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

Atoms in Mathematics and Science; The Concept of a Basis

One of the most important tools that mathematicians and scientists use to cope with the daunting complexity of the world goes by the name of reductionism. That is, one first identifies the key parts of a complex system, then one strives to understand the parts, and finally one strives to understand how the parts fit … Read more

How It Came To Pass That Students In Linear Algebra III Did Not Know What A Basis Is

Once upon a time, an instructor (whom I shall call Professor “A”) went on sabbatical leave. As a result, another instructor (whom I shall call part-time instructor “b”) was called upon to teach Linear Algebra III, which was normally taught by Professor “A.” All 16 of the students who attended Linear Algebra III had successfully … Read more