Math Vista: motivation, theme, illumination
Lebanon Valley College
Welcome to the Math Vista project home page! Math Vista is a collection
of videos that address motivation, theme, and illumination of important
ideas in undergraduate mathematics courses.
Math Vista videos supplement course texts and classroom lectures with:
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.
- "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.
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
The fall semester 2013 pilot project was made possible with funding from the Lebanon
Valley College President's Innovation Fund.