8 problems.
- Contrapositive and negation of “if all birds swim or some fish fly, then no whales walk”
- Alternating sum of squares \(1^2-2^2+\cdots+(-1)^{n-1}n^2\)
- One-sided \(\varepsilon\)-\(\delta\) limit, and \(\lim_{x\to 0^+} 1/\ln x = 0\)
- Taylor series of \(\ln(2+x)\) about the origin
- Line integral of \(y\,dx+2x\,dy\) along a quarter circle closed by the axes
- A \(C^\infty\) function vanishing on \((-\infty,0]\) but not on \((0,\infty)\), an infinite-dimensional vector space over \(\ZZ/2\ZZ\), a non-diagonalizable matrix in \(M_2(\CC)\), and a power series with radius of convergence \(0\)
- \(\dim\ker A\) and \(\dim\operatorname{im} A\) for a given \(3\times 3\) matrix
- Spectral theorem and an orthogonal diagonalization of \(\begin{pmatrix}2&-2\\-2&5\end{pmatrix}\)