(Class originally scheduled for January 18, but was cancelled due to inclement weather.)
We discussed vector spaces and solutions to homogeneous linear equations in general (including in more than two variables). We also discussed how to solve inhomogeneous linear equations. The homework and answers are available (solutions are hidden if you print).
This is the last lecture of the term, and we will not be continuing the subject in the next term (as there may be new students in the class). You may read the algebra lesson plan as a reference.
This lecture was taught by Eric Xiao. We discussed vectors, in particular their sums and scalar multiplication, and learned how to solve homogeneous linear equations in two variables. The homework and answers are available.
We discussed polynomials of degrees higher than 2, and propose various tools like long division, the remainder theorem, and the rational root theorem to help us factor (and hence solve) these polynomials. Lectures were taught by Eric Xiao and Zed Li.
This lecture was taught by Eric Xiao. We discussed the vertex form of quadratic equations, and used this to derive the quadratic formula.
We reviewed linear equations, talked about a graphical method of solving them, and then introduced quadratic polynomials and their associated equations. We talked about standard form and factored form and the trial and error method of converting from standard form to factored form.
On November 2, we discussed some basics of sets, including their definition, membership, equality, and subset relationships.
On November 9, we continued the discussion by introducing Venn diagrams, set union, and set intersection.
We discssed square roots of integers that are not perfect squares, like . We found that they do not exist as rational numbers. We made a graph showing the relationship between rational numbers and their squares, and noted that if we could draw a continuous curve, then there should exist a square root of . We define the “real numbers” to represent this concept of a continuum.
This lecture was taught by Eric Xiao. We discussed some exponent rules and introduced polynomial equations.
We discussed some of the problems from last week’s homework. We then gave many examples of word problems with a single variable. We noticed the similarities between these problems, and discussed a solution to linear equations with one variable in general.
We reviewed the integers (including negative numbers) and introduced variables. We then covered fractions using this new vocabulary and reviewed various operations on them.
If you would like more practice with fraction arithmetic, check out Khan Academy. Don’t worry if the variables don’t make sense yet — we will continue to practice them in future lectures.
Feel free to email me with any questions about the course.