Math 31 Summer Term, 2004

Course and Homework Schedule

 

Friday  June 25:  Introductory Lecture, Overview of Chapter 0 of book. Assignment:  Read Section 0 for Monday.  Note that we do not have class Saturday.

 

Monday June 28:  Class Activity:  Finish Chapter 0.  Assignment: Read Section 1 for Wednesday.

 

Wednesday June 30: Class Activity: Cover Chapter 1.  Assignment: Turn in Problems 7, 8,  9, 11, 13, 14, 15, 16, 17, 21, 26, 29, 36, 37 and 50 (Hint for part d: You may use words to describe a-1.) from Chapter 0.   Here is one more problem.  My written sevens sometimes look like ones.  Suppose I give someone the encoded number 7324501877 with the last two check digits included as in the example on pages 13 and 14 of how to correct a single error.  This person passes it on to someone else as 1324501877.  Use the method shown in the book to correct a single error to convert this received message back into a corrected message.  If you need to solve an equation like 5i mod 11 =2, you can do so by just substituting values for i until you find one that works.  Comment on the result that you get and explain what is happening.

 

Friday July 2:  Class Activity:  Chapter 2.  Read Chapter 2 and Chapter 3 for July 7.

 

Monday July 5:  No class, college holiday.

 

Wednesday July 7:  Class Activity: Chapter 3.  Turn in the following.  Chapter 1. Turn in Problems 1, 2, 3, 6 (Can you explain why a geometric motion that takes only one point of a regular polygon to itself is a rotation?), 9 (read problems 7 and 8), 11, 12, 17, 18.  Chapter 2.  Turn in Problems 2, 3, 4, 5, 6, 7b, 8, 15, 16, 18, 24, 25, 32 a, 33, 34.

 

Friday July 9:  Class Activity: Chapter 4.  Read For Monday, Chapter 4 and start Chapter 5.

 

Wednesday July 14:  Class Activity: Finish Chapter 5.  Turn in the following: Chapter 3, Problems 1, 4, 7, 9, 11, 13, 14, 21, 22, 23, 28, 30, 33, 36. Chapter 4, Problems 1, 3, 7, 8, 9, 13, 22, 23, 29, 32, 34, 53. Chapter 5, Problems 3a,e, 4. 17ab, 18 a, 27.

 

Friday July 16: Class Activity:  Chapter 6 through Cayley’s Theorem.

 

Monday July 19:  Class Activity:  Chapter 6 properties of Isomorphisms, and Chapter 7, Cosets and Lagrange’s Theorem.

 

Wednesday July 21.  Class Activity:  Finish Chapter 7.  From Chapter 5, turn in Problems 7, 19, 22, 35, 45.  From Chapter 6, turn in  Problems 4, 5, 7, 19, 20, 22, 36. From Chapter 7, turn in Problems 1, 2, 5, 8, 14, 15, 20. Exam 1 Classroom portion 7PM Room 105 Bradley.

 

Friday July 23 Turn in take-home portion of Exam.  Class Activity:  Finish Cosets (Chapter 7) and discuss External Direct Products (Chapter 8).

 

Monday July 26 Class activity:  Begin discussion of Normal Subgroups and Factor Groups (Chapter 9). 

 

Wednesday July 28:  Class Activity:  Finish discussion of Normal Subgroups and Factor Groups and introduce Homomorphisms (Chapter 10).  From Chapter 7, turn in problems 22, 25, 34, 39.  From Chapter 8, turn in Problems 4, 5, 7, 10, 11, 14, 22, 24, 29, 30, 32.  From Chapter 9, turn in Problems 1, 3, 4, 5, 7.

 

Friday July 30:  Class Activity:  Homomorphisms

 

Monday August 1:  Class Activity Finish Group Theory with additional topics from Chapters 9 and 10.

 

Wednesday August 4:  Class activity:  Begin Ring Theory, Chapter 12.  From Chapter 9, turn in Problems 6, 9, 12, 14, 17, 22, 27, 30, 32, 40, 44

From Chapter 10, turn in Problems 1, 7, 9, 14, 15, 16, 20, 28, 37 (You also need to show that the intersection of K and N is a normal subgroup of K), 38 (You also need to show that M/N is a normal subgroup of G/N.), 41, 42, 46, 48,

 

Friday August 6:  Class Activity  Chapter 13

 

Monday August 8:  Class activity Chapter 14

 

 

Wednesday August 11.  Exam #2, classroom portion, 7:00PM Room 105 Bradley.  Class Activity:  Chapter 15  From Chapter 12, turn in Problems 4, 6, 11, 15, 22, 31, 36.  From Chapter 13, turn in Problems 2, 3, 5, 6, 9, 10, 18, 28, 29, 35, 43.  From Chapter 14, turn in Problems 3, 5, 6, 8, 9, 10, 11a, 17, 22, 24, 25, 28.

 

Friday August 13.  Exam #2, take home potion, due at beginning of class.

Class activity Chapter 16.

 

Monday August 16.  Class activity: Chapter 17

 

Wednesday August 18.  Class Activity Chapter 19.  From Chapter 15, turn in Problems 8, 9, 11, 18, 22, 23, 35, 36.  From Chapter 16, turn in Problems 2, 3, 6, 11,13, 17, 14, 21, 22. From Chapter 17, turn in  Problems 4, 5,  8, 17, 33.

 

Friday August 20.  Class Activity Chapter 20. 

 

Monday, August 23.  Class Activity, Chapter 22.

 

Wednesday, August 25.  Class Activity, Error Correcting Codes (partly Chapter 31).  From Chapter 19. turn in problems 7, 10, 14.  From Chapter 20 turn in Problems 3, 4 (Hint: 1+i is not a zero, but something closely related is.), 7, 13, 18, 26 (Hint; You can use your knowledge about GF(8) and irreducible polynomials to make an educated guess and check it.) 29.  From Chapter 22, Turn in problems 1, 3, 6, 9, 11, 13, 27