The Online Math 51 Project

This page will contain the links to an expanding set of videos covering various topics in Math 51.  We are starting with just a few, but will be steadily adding more. These videos are meant to be used in a variety of ways:  we want you to use them as an enhancement of the lectures and of the textbook.  Some topics from the standard lectures may be covered more briefly in class because you have these videos available; other topics will be covered fully in lecture, but these videos will present a slightly different discussion of the same topics, which will hopefully help you to understand the material better. Other videos may just contain a number of worked examples that you can use for review.

This is a new project and we do not yet know what parts of this will be the most useful to you.  We will be surveying you from time to time and we hope that you will give us some useful feedback.  There will also be a way for you to give unsolicited comments about this project through a link that will be set up soon on this website.

This first video contains a description of the determinant of 2 by 2 matrices. The emphasis is on motivating the formula and showing that it corresponds to something geometric:  the area of a certain parallelogram.  This is all done without assuming that you have seen cross-products.  The goal of this video is to show you that the perhaps strange looking definition of determinants in this simplest case has a good motivation.

This second video presents the definition of cross-products of vectors in three-dimensional space. Here we present the formula for the cross-product, then explain some of the main uses of this construction. This material is needed, in particular,  for the remaining videos about determinants of 3 by 3 and larger matrices.

The final video about determinants will be posted here in the next few days, before the lecture of Monday, Feb. 4. It discusses more about the algebra of determinants and how to calculate them.

This next video discusses the case of 3 by 3 matrices and their determinants. We use the language of cross-products and explain that there is a close relationship between the two concepts. This discussion is meant to motivate the large algebraic expression for the determinant of a 3 by 3 matrix and show that it is a reasonable thing to study.