## Math Vista Videos: motivation, theme, illumination

Welcome to the Math Vista Video Project home page! Math Vista Videos address motivation, theme, and illumination of important ideas in undergraduate mathematics.

Math Vista videos supplement course texts and classroom lectures with:

• "big picture" talks that span entire courses or large pieces of courses; and
• enrichment on important topics aimed at providing insight and understanding where texts emphasize technique and procedure.
Textbooks tell you how; we aim to elucidate why and explore basic workings behind important ideas in some key places in the undergraduate mathematics curriculum. Math Vista is not a replacement for textbooks or class lectures. It is an additional resource aimed at bringing topics to life.

### The Videos

• #### Sequences of Approximations

Using examples from a second semester calculus course, we illustrate this powerful concept that pervades mathematical theory and application.
• #### Why Linear Algebra?

Linear algebra studies the dynamics of the simplest possible interactions among multiple variables. Its fundamentals are essential to all areas of mathematics.
• #### The Cross Product

This workhorse of classical vector calculus is an elegant solution to a natural problem. This video brings into focus what the cross product is about and why it works.
• #### Zeno's Paradox, Part I: A Puzzle and A Flaw

One of the most powerful and basic strategies in problem solving is: (1) break a large, complicated problem into smaller, simpler pieces; (2) solve the smaller problems, and; (3) reassemble those small solutions into one large solution. Zeno of Elia (a Greek philosopher in the 400s BCE) posed stark thought experiments that go right to the heart of what can go wrong with this process. We continue to learn valuable lessons by studying Zeno's paradoxes.
• #### Zeno's Paradox, Part II: Geometric Sequences

A closer examination of details of the smaller and larger problems of Zeno's paradox leads to an amazingly useful pattern called geometric sequence.

### Acknowledgments

The fall semester 2013 pilot project was made possible with funding from the Lebanon Valley College President's Innovation Fund.