REU Meeting  20240705
This following is a brief summary of our research meeting on 20240705.
What happened

Liam presented a solution to Exercise 1a in Section 1.2. By first completing the squares, he was able to rewrite the equation
as the equation
He then recognized this as an equation of an ellipse, centered atwith "horizontal radius" and "vertical radius" : 
Nicholas presented a solution to Exercise 1b in Section 1.2, noting that the equation
was equivalent to the conditions that either or . (This can be seen either by solving the equation for , or by factoring as .) Thus, the solution set was the union of two lines: 
Aaron presented a solution of Exercise 4d, noting that the equation
is equivalent to the conditions that either or . Thus, the solution set was the union of the plane and the parabolic cylinder :
(Ignore the janky edges. Those are rendering errors in the Desmos 3D visualizer.) 
Aaron also sketched the solution to Exercise 8 in Section 1.2, following the solution strategy outlined in the book. The crux of the argument relied on the fact that a polynomial in one variable has at most a finite number of zeroes.
Tasks for next meeting
 Read/skim Section 1.4, 4.1β4.3, and Sections 5.1, 5.2 and 5.4
 Work through the following exercises:
 1.4: 1, 3, 5, 7, 8, 15
 4.1: 1, 2
 4.2: 3, 5
 5.1: 2