# Transition to Advanced Mathematics

#### 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 $w$.

# Statistical Inference

#### Math 472

Textbook: An introduction to mathematical statistics and its applications (Larsen and Marx), 5th edition
Times: TuTh 9-10:15

Homework list

HW1: 3.8: 1, 2, 6 (Transforming and combining random variables); 3.10: 8, 12, 14 (Order statistics)
HW2: 4.6: 1, 4, 5 (Gamma distribution); 5.2: 2, 10, 14 (Method of maximum likelihood)
HW3: 5.3: 1, 13, 22 (Interval estimation); 5.4: 14, 16, 17
HW4: 5.5: 2, 3, 7; 5.6: 1, 5, 6
HW5: 5.7: 3, 4, 5; 5.8: 3, 5, 7
HW6: 6.2: 5, 7, 9; 6.3: 3, 4, 8
HW7: 6.4: 4, 6, 9; 6.5: 2, 4, 6
HW8: 7.3: 4, 6, 8; 7.4: 1, 3, 25
HW9: 9.2: 1, 5, 16
HW10: 10.2: 2, 4, 9; 10.3: 6, 8, 9
HW11: 11.2: 10, 22, 29; 11.3: 10, 18, 19
HW12: 11.4: 1, 5, 14; 12.2: 5, 6, 8

Each homework set is worth the same amount. The top 10 of 12 homeworks count 2% of the course each. The best out of two midterms counts 40%. The final counts 40%.

# Fall 2011 Teaching

#### Math 244

HW1: 14.1: 2,4,15,19,23,25
HW2: 14.2: 3,12,15, 20,23,33, 52, 54,55,58
HW3: 14.3: 8,9,14,18 and
14.4:3,12,13,25,30,32,36
HW4: 14.5: 13, 16, 18, 22, 23, 24, 30, 40, 41, 43
HW5: 14.6: 2, 8, 10, 13, 14, 17, 18, 20
HW6: 14.7: 4, 8, 12, 35, 45, 53, 56, 60, 62, 76 and
14.8: 4, 13, 15, 20, 21
HW7: 15.1: 2, 8, 18, 19, 28, 31
15.2: 2, 8, 13, 21, 26, 34, 39, 43, 45
HW8: 15.3: 7, 16, 18, 20, 25, 33, 34, 36
HW9: 15.4: 1, 3, 9, 20, 22, 30, 33, 37
HW10: 15.5: 1, 8, 12, 19, 22, 25, 28, 36, 41, 42
HW11: 15.6: 11, 13, 14, 18, 21, 24, 37, 38, 42
HW12: 15.7: 2, 4, 7, 22, 25 and
15.8: 2, 8, 9, 21, 23, 30

Each homework set is worth the same amount. The top 10 out of 12 homeworks count 1.5% of the course each for a total of 15% for homework. The two best out of three midterms count 20% each. The final counts 45%.

Math 244 Course calendar

#### Math 471

Midterm III

HW1: Chapter 1:
2,3,4,13,15,19,23,25,26,35,37,40,43,46
HW2: Chapter 1: 51, 56 and Chapter 2:
8,9,18,21,23,30,33,35,40,41,44,45,49,56,62,67,68,70,71,79,80,85
HW3: Chapter 3:
11,12,13,14,18,19,21,24,29,37,38,42,43,44,46,50,59,60,66
HW4: Chapter 5: 1,3,7,9,20,22,23
HW5: Chapter 5: 28, 33, 36, 39
HW6: Chapter 6: 2,6,8,11,12,19,21,25,28,30,31,39,42
Each homework set is worth the same amount. The top 5 homeworks count 2% of the course each. The two best out of three midterms count 25% each. The final counts 45%.