Syllabus

**Homework**

__For Exam 1__

**HW1 (due **~~17 Jan~~22 Jan) [soln]: p. 142: #5, 6, 7, 8, 11, 15, 31; p. 174: #1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 14, 15, 16, 17, 20, 23, 24, 25

*(for graduate students): p.143: #33; p.174: #22, 27, 28*

**HW2 (due 28 Jan)** [soln]: p.175: #35, 38, 44; p.182 #1, 2, 3, 5, 6, 9, 10, 11, 12, 24

__For Exam 2__

**HW3 (due 14 Feb)** [soln]: p.189: #4, 5, 10, 11, 12, 13, 14, 15, 16

*(for graduate students): p.190: #27, 28*

**HW4 (due 21 Feb)** [soln]: p.196: #1, 2; p.207: #1, 2, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 20, 21, 24, 27

*(for graduate students): p. 197: #30, 31*

__For Exam 3__

**HW5 (due 11 March)** [soln]: p.218: #1,2,3,4,9,10,11,14; p.243: #17, 26, 27, 30, 34, 37

*(for graduate students): p.243: #19, 20, 29*

**HW6 (due **~~16 March~~ 25 March) [soln]: p. 252: #1, 2, ~~3, 4,~~ ~~5, 6~~, 16, 17, ~~18, 19~~, 24, 27, 34; ~~p. 272: #1, 2, 3, 4, 5, 9, 10, 11, 12, 33, 34~~

*(for graduate students): p.254: #36; *~~p. 273: #29~~

**HW7 (due 1 April)** [soln]: p. 272: #1, 2, 3, 4, 5, 9, 10, 11, 12, 33, 34

*(for graduate students): p.273: #29*

**HW8 (due 19 April)** [soln]: p.273: #25; p.280: #4, 5, 6, 7, 8, 9, 10

*(for graduate students): p.273: #33; p.281: #18*

**HW9 (due 27 April)** [soln]: p.291: #1, 2, 3, 4, 5, 6, 11, 12

**Quizzes**

__For Exam 1__

Quiz 1 [soln]: Find all solutions in $\mathbb{Z}_6$ to the polynomial equation $x^2-3x+2=0$.

Quiz 2 (due 25 Jan on Blackboard) [soln]: Find the characteristic of the product ring $\mathbb{Z}_3\times\mathbb{Z}_3$.

*For Exam 2*

Quiz 3 (due 8 Feb on Blackboard) []: Compute $29^{25}\text{ mod }11$.

Quiz 4 (due 15 Feb on Blackboard) []: Find the sum and product of $f(x)=2x^2+3x+4$ and $g(x)=3x^2+2x+3$, where $f, g \in \mathbb{Z}_6[x]$.

Quiz 5 (due 23 Feb on Blackboard) []: Divide $f(x)=x^4+3x^3+x^2+2x+1$ by $g(x)=3x^2+5x+4$ in $\mathbb{Z}_7[x]$.

*For Exam 3*

Quiz 6 [soln]: Let $R=\mathbb{Z}\times\mathbb{Z}\times\mathbb{Z}$ and $N=\left\{(0,0,n) \colon n \in\mathbb{Z}\right\}$. Show that $N$ is an idea and describe the factor ring $R/N$ (i.e. what do its elements look like? what is it isomorphic to?)

**Exams**

Exam 1

Exam 2

Exam 3