9 problems.
- De Morgan: complement of an intersection is the union of complements
- Differentiability implies continuity, and the product rule
- Existence of nonabelian groups of order \(5\) and \(6\)
- Cube roots of \(8\) in \(\mathbb{C}\)
- The winding number of a circle about the origin
- The chain rule for \(f(g(t))\) and perpendicularity of \(\nabla f\) to the tangent of an implicit level curve
- Bounds on alternating partial sums of a decreasing positive sequence
- Diagonalize \(\begin{pmatrix} 8 & 9 \\ -6 & -7 \end{pmatrix}\) as \(ABA^{-1}\)
- Binomial theorem and \((x+y)^p \equiv x^p+y^p \pmod{p}\)