Mathematics 5251 (Error-Correcting Codes, Finite Fields, Algebraic Curves)



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Required text: The Mathematics of Coding Theory, by Paul Garrett.

Homework: Homework will be posted on the course page after every lecture. Weekly homework assignments are due on Monday of the following week in the beginning of class.

Exams: There will be three midterm exams on Wednesdays, October 12, November 9 and December 7, and a final exam on Saturday, December 17, 10:30 - 12:30, room to be announced.

Make up exams: Will be allowed only under truly exceptional circumstances. You must notify the lecturer at least a week in advance.

Calculators: Calculators are not permitted for the midterms and the final exam. A calculator will be useful for some of the homework problems.

Final grade: Homework counts for 45%, each of the midterm exams for 10% and the final exam for 25%.

Lecture date Homework assignment Due date
Wednesday
September 7 		pp. 29 -- 30:
1.01 -- 1.14, 1.17, 1.21		 Monday
September 12
Friday
September 9 		p. 30:
1.28 -- 1.31, 1.33		 Monday
September 12
Monday
September 12 		p. 31:
1.39, 1.40, 1.45		 Monday
September 19
Wednesday
September 14 		p. 43:
2.01 -- 2.03		 Monday
September 19
Friday
September 16 		Read Sections 2.1 and 2.2;
Exercises p. 43:
2.04, 2.05		 Monday
September 19
Monday
September 19 		Read Sections 3.1 and 3.2;
Exercises p. 60:
3.01, 3.02		 Monday
September 26
Wednesday
September 21 		Read Sections 3.3 and 3.4;
Exercises p. 60:
3.03, 3.04, 3.05		 Monday
September 26
Friday
September 23 		Read Sections 4.1 and 4.2;
Exercises p. 60:
3.06
Exercises p. 80:
4.01, 4.02, 4.03, 4.05		 Monday
September 26
Monday
September 26 		Read Section 4.3
Exercise p. 80:
4.04		 Monday
October 3
Wednesday
September 28 		Read Sections 4.4, and 4.5;
Exercises p. 81:
4.08, 4.09, 4.10, 4.11		 Monday
October 3
Friday
September 30 		Read Sections 5.1 through 5.4;
Exercises p. 92:
5.01 through 5.05, 5.07, 5.08		 Monday
October 3
Monday
October 3 		Read Sections 6.1, 6.2, 6.3 and 6.5 and 6.7;
Exercises pp. 129-131:
6.02 -- 6.07, 6.19, 6.20, 6.37		 Monday
October 10
Wednesday
October 5 		Read Sections 6.7, 6.9 and 6.14;
Exercises pp. 132--133:
6.52, 6.53 and:
Find the multiplicative inverse of 56 modulo 137		 Monday
October 10
Friday
October 7 		Read Sections 6.8, 6.10, 6.13, 6.14 and 6.15;
Exercises pp. 132--133:
6.50, 6.51 and 6.56		 Monday
October 10
Monday
October 10 		Read Sections 6.11, 6.12 and 6.13
Is 32 a primitive root modulo 101? Is the polynomial x^3+x+1 primitive?		 Monday
October 17
Wednesday
October 12 		midterm 1
Friday
October 14 		Let p be a prime number.
Prove that the number of primitive roots modulo p equals the number of non-zero remainders modulo p that are relatively prime to p-1.
How many primitive roots modulo 101 are there?
List all primitive roots modulo 11. 		Monday
October 17
Monday
October 17 		Read Sections 10.1 -- 10.5;
Exercises p. 191:
10.11, 10.13 and:
Find the multiplicative inverse of (x+1) modulo (x^3+x^2+1)		 Monday
October 24
Wednesday
October 19 		Read Sections 13.1
Exercises pp. 232 -- 233:
13.01, 13.02, 13.03
Read Section 12.4
Exercises p. 226:
12.01 and 12.02		 Monday
October 24
Friday
October 21 		Read Sections 13.2
Exercises p. 233:
13.04 -- 13.10 		Monday
October 24
Monday
October 24 		Read Sections 12.5 -- 12.7
p. 226: Exercises 12.07, 12.09, 12.11, 12.13
 Monday
October 31
Wednesday
October 26 		Read Sections 12.7 -- 12.8
p. 227: Exercises 12.18, 12.19
 Monday
October 31
Friday
October 28 		Read Sections 12.7 -- 12.8
p. 227: Exercises 12.16, 12.17, 12.20
 Monday
October 31
Monday
October 31 		Read Sections 14.1 and 14.2
Exercises p. 238:
14.01 and 14.02
Monday
November 7
Wednesday
November 2 		Exercises pp. 238 -- 239:
14.03, 14.04
 Monday
November 7
Friday
November 4 		Exercises pp. 238 -- 239:
14.05
 Monday
November 7
Monday
November 7 		Read Sections 11.1 through 11.5
Exercises p. 198:
11.01 through 11.04
Monday
November 14
Wednesday
November 9 		midterm 2
Friday
November 11 		Read Section 10.3
Exercises p. 190:
10.01 through 10.04
Exercises p. 198:
11.05, 11.06 and 11.07 		Monday
November 14
Monday
November 14 		Read sections 15.1 and 15.2
Exercises p. 259:
15.01, 15.11, 15.12 and 15.13
Read Section 17.1
Exercises p. 295:
17.04, 17.05 and 17.06
 Monday
November 21
Wednesday
November 16 		Read Sections 17.1, 17.2 and 17.3
Exercises p. 295:
17.07, 17.08, and 17.09
Monday
November 21
Friday
November 18 		Read Section 17.4
Exercises p. 295:
17.10
Monday
November 21
Monday
November 21 		Read Section 17.5
Exercise p. 296:
17.14 		Monday
November 28
Wednesday
November 23 		Exercises pp. 295 -- 296:
17.11, 17.12 and 17.13 		Monday
November 28
Monday
November 28 		Read Sections 19.1, 19.2, and 19.3
Exercises p. 333:
19.03, 19.05, 19.07 and 19.09 		Monday
December 5
Wednesday
November 30 		Read Sections 19.4, 19.5, and 19.6
Exercises p. 333:
19.04, 19.06, and 19.08 		Monday
December 5
Friday
December 2 		Read Section 19.7
How many irreducible polynomials of degree 12 with coefficients in $\mathbb F_2$ are there? 		Monday
December 5
Monday
December 5 		Read Section 19.8
How many primitive polynomials of degree 5 with coefficients in $\mathbb F_3$ are there? 		Monday
December 12
Wednesday
December 7 		midterm 3
Friday
December 9 		prepare for final
Monday
December 12 		prepare for final
Wednesday
December 14 		prepare for final