There are things you learn in Tensor Calculus that take us back to first grade where you learned addition. We can build games that push your thinking in ways that prepare you for the things you need to understand in Tensor Calculus.

We can connect games that teach addition to ideas you need for Vector Algebra. We can introduce Physics in a simple version that considers time, displacement and velocity. The exercise sets the stage for learning about Invariance.

We can push hard on the idea that certain things in the Algebra textbook are more important than the rest of the contents in the book. We hope you like that--and we'll be asking you to learn everything else in the textbook. Such an attitude is a part of your valor and honor.

When you get to Linear Algebra you will see all those things again. Those ideas become "structures" that help you build a Vector Space. Linear Algebra will give you some experience with vectors that is needed for Physics. You will do things with vectors and matrices. As one example, we can use a matrix to take an old vector and make a new vector with a particular important math technology.

When we get to Dual Vectors Spaces we will ask everyone to move slowly, carefully, like we are walking through a mine field. In Phase One, we'll learn that you can do all kinds of things in a Dual Vector Space. In Phase Two, we'll discover that there's only one thing you want to do, and that one thing you want to do is handed to you by a calculation.

Part of Tensor Calculus is learning notation, and if you look at several references you will notice that the authors don't all do their superscripts and subscripts the same way. We will discuss the differences in details and attempt to dull the pain a bit by showing what we learn after looking at the differences.

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