**Office:**Stevenson 337

**Email:**szchebol@ilstu.eduz (with the two "z"'s removed)

**Office Hours:**By appointment**Class meeting time:**- WIH 313 - 10:00 - 10:50 MWRF

**Text:**Modern Algebra with Applications, 2nd Edition William J. Gilbert (Univ. of Waterloo, Ontario, Canada), W. Keith Nicholson (Univ. of Calgary, Alberta, Canada)

** Announcements: **

- (Sep 21) There will be no class on Thursday and Friday of next week. However, there will be an extra class on Tuesday from 4:00 - 5:00 in the conference room in STV math office.
- (Sep 7) I will be out of for a couple of days at the end of this month. The dates are Sep 27 and 28th. On these days I will have you work on the first class test. More details will be announced later.
- (Aug 17) More than 99.9 % of the people in the world never get this privilege of taking a graduate course in abstract algebra. You are so unique! Congratulations!

**Course links:**

**Project Ideas:** I will collect here some ideas for inclass
projects, some of these were also mentioned in class. These will be
assigned to students on a first-come-first-serve basis.

- Stone's representation theorem on Boolean Algebras. (See reference on Page 40)
- The analysis of the 15-puzzle. (This includes exercises 3.81, 3.82 and 3.83). You can also download a free app for this game on a smart phone. Here is nice paper on this topicPDF
- Sylow theorems: Statements, proofs, and applications.
- Burnside theorem which states that finite groups of order p^n q^m are solvable. (In interested, ask for reference.)
- Wall paper designs. I find it fascinating that are only 17 wall paper designs. This will be a fun topic for a project.
- Polya's enumeration theorem (The general version). See wikipedia.

**Presentations:**

- September 9-12, 2012
- Jessica Cartabuke: Symmetries of a regular octohedron and cube
- Dan Marfise: Symmetries of a regular tetrahedron
- Eric Larson: Symmetries of a regular icosahedron
- Philip Gutbrod: Classification of finite subgroups of SO(3)
- Annmarie Bitter: Classification of finite subgroups of SO(3)

- September 24-26, 2012
- Jessica Cartabuke: Sylow Theorem 1
- Dan Marfise: Sylow Theorem 2
- Eric Larson: Sylow Theorem 3
- Philip Gutbrod: Applications of Sylow Theorems
- Annmarie Bitter: Applications of Sylow Theorems

- October 25-26, 2012
- Jessica Cartabuke: Colouring the vertices of cube
- Dan Marfise: Colouring the faces of a dodecehedron
- Eric Larson: Chemical compounds of a Benzene ring
- Philip Gutbrod: Switching circuits using 3 switches I
- Annmarie Bitter: Switching circuits using 3 switches II

- Final presentations, 2012
- Jessica Cartabuke: Archimedean Solids (Nov 30, 10:00 - 10:50)
- Dan Marfise: Latin Squares (Dec 6, 10:00 - 10:50)
- Eric Larson: Error Correction Codes (Dec 7, 10:00 - 10:50)
- Philip Gutbrod: Geometric Constructions I (Dec 10, 1:00 - 1:50)
- Annmarie Bitter: Geometric Constructions II (Dec 10, 2:00 - 2:50)

**Nov 14**Chapter 11: Read this chapter and solve these problems: 1, 5, 6, 13, 15, 17, 22, 23, 27, 37, 54, 55, 61.**Nov 14**Read Chapter 10 (especially pages 211-214) and do the following problems in this chapter: 3, 4, 5, 8, 15, 16, 21, 23, 24, 33, 41, 44, 46, 51, 58, 59, 60-
**Nov 3**Finish reading Chapter 9 by Wednesday and do the following problems in Chapter 9: 5, 9, 13, 14, 18, 22, 37, 43, 45, 52, 53, 54, 56, 57, 63, 65, 67. -
**Oct 29**Skip Chapter 7 on Monoids and Machines and read all of chapter 8 (skip convolution fractions) by Wednesday. Exercises for this week from Chapter 8: 1, 3, 7, 8, 9, 13, 15, 18, 23, 27, 31, 32, 35, 37, 39, 43, 50, 51, 57 -
**Oct 19**Read whole of Chapter 6. Do the following exercises: 6.1, 6.5, 6.7, 6.9, 6.13, 6.21, 6.25 -
**Oct 5**Read up to Theorem 5.13. Exercises: let us try to do ALL problems! -
**Sep 24**Do the following exercises from the Sylow theorems packet: Section 1: 1-9,Section 4: 1, 2, 3,6, 9, 11 (a--c), 13, 15. -
**Sep 21**Prepare for your presentations next week and study for upcoming class test I which will cover everything done so far. -
**Sep 17**Start reading the material handed in class on Sylow theorems. -
**Sep 11**Complete reading the whole of Chapter 4 by the end of this week. Exercises for this chapter: 4.9, 4.12, 4.16, 4.17, 4.18, 4.21, 4.22, 4.25-4.29, 4.30, 4.31, 4.32, 4.33, 4.36, 4.40, 4.43, 4.45, 4.48, 4.62, 4.63, 4.64. -
**Sep 7**Complete solving the assigned problems in Chapter 3. Start reading Chapter 4; read at least up to the definition of Normal subgroup on Page 82. -
**Sep 5**Finish reading Chapter 3 and do these exercises: 3.1, 3.4, 3.5-3.16, 3.19, 3.20, 3.22, 3.24, 3.26-3.29, 3.38, 3.39, 3.43, 3.44, 3.46, 3.47, 3.54, 3.55, 3.57, 3.59, 3,63, 3.72, 3.73, 3.75, 3.76, 3.78, 3.79,3.85 -
**Aug 31**Start reading Chapter 3 on Groups. You should be done reading this Chapter before our next meeting on Wednesday. -
**Aug 27**Read the material on Circuits and Transistor gates. I think it is fun and exciting material. Do the exercises: 2.33, 2.36, 2.39, 2.40, 2.41, 2.47, 2.48, 2.59, 2.60, 2.63, 2.64, 2.68. -
**Aug 24**Complete reading the rest of Chapter 2 (optional reading: cirucits and transistor gates) and also do exercises 2.19, 2.25, 2.26 and 2.27 -
**Aug 22**Chapter 2: Read sections on Boolean Algebras and Propositional Logic and do exercises 2.16, 2.17, 2.20, and 2.24. -
**Aug 20**Read Chapter 1. (Pleasant Bed time reading, mostly a historical survery giving you the bird's eye-view)