Syllabus

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Quiz 1 [soln]: Define a function that is one-to-one, but is

Quiz 2 (due 8 Sep) [soln]: Complete the following table so that it makes $*$ into a commutative binary operation: $$\begin{array}{l|l|l|l} *&a&b&c \\ \hline a&b&&c \\ \hline b&&b& \\ \hline c&&&b \end{array}$$

Quiz 3 (due 14 Sep) [soln]: Let $*$ be defined on $\mathbb{R}^+=(0,\infty)$ (positive real numbers) by letting $a*b=\sqrt{ab}$. Does the structure $\left\langle \mathbb{R}^+, * \right\rangle$ obey all of the group axioms $\mathscr{G}_1$, $\mathscr{G}_2$, and $\mathscr{G}_3$? If not, then which ones does it not satisfy?

Quiz 4 (due 19 Sep) [soln]: Does the binary operation $*$ defined in the following table obey the group axioms $\mathscr{G}_2$ and $\mathscr{G}_3$ of a group on the set $G=\{a,b,c\}$? Is it a commutative operation? Explain.

$$\begin{array}{l||l|l|l} * &a&b&c \\ \hline\hline a&a&a&b \\ \hline b&b&b&b \\ \hline c&c&b&c \end{array}$$

Quiz 5 (due 25 Sep) [soln]: Argue why $\pi\mathbb{Z}=\left\{\pi n \colon n \in \mathbb{Z}\right\}$ is a subgroup of $\left\langle \mathbb{R},+\right\rangle$.

Exam 1 (20 September)

Exam 2 (18 October)

Exam 3 (15 November)