#### Math 321

Textbook: Numbers, groups, and codes (Humphreys and Prest), 2nd edition

Times: TuTh 12-1:15

Each homework set is worth the same amount. The top 8 out of 10 homeworks count 2.5% of the course each for a total of 20% for homework. The best out of two midterms counts 40%. The final counts 40%.

**HW1**: 1.1: 3, 6 (Greatest common divisors); 1.2: 3, 7 (Induction)

**HW2**: 1.3: 6, 7, 8 (Unique factorization); 1.4: 5, 6, 7 (Congruence classes)

**HW3**: 1.5: 1, 4 (Solving linear congruences); 1.6: 1, 4, 7, 10, 12 (Cryptography)

**HW4**: 2.1: 3, 7, 8; 2.2: 7, 8, 9, 11

**HW5**: 2.3: 2, 3, 5, 10; 2.4: 2, 4

**HW6**: 3.1: 2, 4; 3.2: 1; 3.3: 3

**HW7**: 4.1: 2, 5; 4.2: 3, 4, 5, 8, 12

**HW8**: 4.3: 3, **4**, 7; 4.4: 3, **4**, 5, 6, 8, 14

**HW9**: 5.1: **1**, 2, 6, 7; 5.2: **1**, 3

**HW10**: 5.3: 2, **3**, 5, 8; 5.4: **2**, 3, 5

Note on 5.4: The syndrome of $w=(x|y)$ ($x$ followed by $y$) is $xA+y$ (whereas juxtaposition denotes matrix multiplication). If $z$ is a coset leader with $z=u|v$ and the same syndrome $uA+v=xA+y$, then $w+z=(x|y)+(u|v) = (x+u)|(y+v) = (x+u)|((x+u)A)$, so $w+z$ is a codeword. Moreover since the coset leaders are low weight (sparse), $w+z$ is close to $w$.