All ISU undergraduate students are invited to participate in the Problem of the Week Contest.
| MONTH WEEK | DAY | Topics, Reading Assignment | Practice Problems | Assigned Problems, Due at 2nd following class | |
|---|---|---|---|---|---|
| January | |||||
| Chapter 0: Preliminaries Chapter 1: Introduction to Groups | |||||
| WEEK 1 | 10-14 January | ||||
| Mon 10 | Course Introduction Communicating Mathematics The Symmetries of an Equilateral Triangle | Ch 1 #2,3 | Ch 1 #4 | ||
| Wed 12 | Integers:
| Ch 0 #1,2,4,10 | Ch 0 #8 | ||
| Fri 14 | Modular Arithmetic | Ch 0 #3,11,16-18 | Ch 0 #13 | ||
| WEEK 2 | 17 - 21 January | ||||
| Mon 17 |  Martin Luther King Day Holiday No class meeting | ||||
| Wed 19 | Induction | Ch 0 #22,23,28 | Ch 0 #24 For full credit, give a proof by induction. | ||
| Fri 21 | Equivalence Relations | Ch 0 #52,53,55 | Ch 0 #54 | ||
| WEEK 3 | 24 - 28 January | ||||
| Mon 24 | Functions | Ch 0 #51,57 | Let f: A → A. Prove: if ff is one-to-one, then f is one-to-one. | ||
| Wed 26 | The Dihedral Groups | Ch 1 #9,10,11,21 | Ch 1 #14 | ||
| Chapter 2: Groups | |||||
| Fri 28 | Groups | Ch 2 #3,5,6 | Ch 2 #8 (due Fri 04 Feb) | ||
| WEEK 4 | 31 January - 4 February | ||||
| Mon 31 | Elementary Properties of Groups | Ch 2 #12,14,15,23 | Ch 2 #26 (due Mon 07 Feb) | ||
| February | |||||
| Wed 2 | ISU CLASSES CANCELED UNTIL NOON | ||||
| Chapter 3: Finite Groups; Subgroups | |||||
| Fri 4 | Finite Groups; Subgroups | Ch 3 #1,8,10,17,36,58 | Ch 3 #18 (due Fri 11 Feb) | ||
| WEEK 5 | 7 - 11 February | ||||
| Mon 7 | In-class Exercise: REVIEW of Chapters 0-3 | Ch 0 #53 Ch 2 #17 Ch 3 #4, 11 | |||
| Wed 9 | FIRST MIDTERM EXAM Covers Chapters 0-3. Objectives for 1st midterm exam. | ||||
| Chapter 4: Cyclic Groups | |||||
| Fri 11 | Cyclic Groups | Ch 4 #1,3,8 | Ch 4 #10 | ||
| WEEK 6 | 14 - 18 February | ||||
| Mon 14 | Subgroups of Cyclic Groups | Ch 4 #9,32 | Ch 4 #33 | ||
| Chapter 5: Permutation Groups | |||||
| Wed 16 | Definition; Cycle Notation | 1(c), 2, 6 | Ch 5 #2(b) | ||
| Fri 18 | Properties of Permutation Groups, Even and Odd Permutations | Ch 5 #6, 10, 11, 12, 18, 20 | Ch 5 #19 | ||
| WEEK 7 | 21 - 25 February | ||||
| Chapter 6: Isomorphism | |||||
| Mon 21 | Isomorphisms; Cayley's Theorem | Ch 6 #1,4,5,8 | Ch 6 #24 | ||
| Wed 23 | Properties of Isomorphisms; Automorphisms | Ch 6 #10, 15, 17 | Ch 6 #20 | ||
| Chapter 7: Cosets and Lagrange's Theorem | |||||
| Fri 25 | Cosets and Their Properties Lagrange's Theorem | Ch 7 #1, 2, 9, 15 | Ch 7 #16 | ||
| WEEK 8 | 28 February - 4 March | ||||
| Mon 28 | Application to Permutation Groups; Cube and Soccer Ball Symmetry Groups | Ch 7 #33, 35, 45 | Ch 7 #40 (Due Mon Mar 7) | ||
| March | |||||
| Wed 2 | REVIEW Chapters 4-7 | Suppl Ex Ch 1-4: #5 (pg 92) Ch 5: #8 Ch 6: #40 Ch 7: #45. | |||
| Fri 4 | SECOND MIDTERM EXAM Chapters 4-7 Objectives for 2nd midterm exam. | ||||
| WEEK 9 | 7 - 11 March | ||||
| Chapter 8: Direct Products | |||||
| Mon 7 | Direct Products of Groups | Ch 8 #1, 4, 9, 20 | Ch 8 #24 | ||
| Wed 9 | Direct Product Decomposition of U(n) Articles on line thru ISU Library:
J. Gallian & D. Rusin,
Y. Cheng,
| Ch 8 #11, 16, 18, 38, 47 | Ch 8 #20 (Due Wed 23 Mar) | ||
| Fri 11 | In-Class Exercise: External Direct Products | Ch 8 #38, 48
Supplementary Exercises | |||
| 14 - 18 March: WINTER RECESS | |||||
| WEEK 10 | 21 - 25 March | ||||
| Chapter 9: Normal Subgroups; Factor Groups | |||||
| Mon 21 | Normal Subgroups; Factor Groups | Ch 9 #4, 7, 10, 26 | Ch 9 #54 | ||
| Wed 23 | Applications of Normal Subgroups; Cauchy's Theorem for Abelian Groups | Ch 9 #21, 44, 46, 48 | Ch 9 #60 (a), (b) | ||
| Fri 25 | Internal Direct Products | Ch 9 #31, 34 | Ch 9 #42 | ||
| WEEK 11 | 28 March - 1 April | ||||
| Chapter 10: Homomorphisms | |||||
| Mon 28 | Homomorphism and Kernel; The Kernel is a Normal Subgroup | Ch 10 #5, 7, 8, 14, 48 | Ch 10 #10 | ||
| Wed 30 | First Isomorphism Theorem | Ch 10 #35, 38, 39, 40, 42 | Ch 10 #24 | ||
| Chapter 11: Finite Abelian Groups | |||||
| April | |||||
| Fri 1 | Fundamental Theorem on Finite Abelian Groups | Ch 11 #2, 5, 10 | Ch 11 #24 | ||
| WEEK 12 | 4 - 8 April | ||||
| Mon 4 | Proof of the Fundamental Theorem | Ch 11 #32 | Ch 11 #36 (due Mon 11 Apr) | ||
| Wed 6 | REVIEW of Chapters 8-11 | Suppl Ex Chs 5-8 (pp 174ff) #26 Suppl Ex Chs 9-11 (pp 230ff) #6,14,22. | |||
| Fri 8 | THIRD MIDTERM EXAM, Chapters 8-11 Objectives for 3rd midterm exam. | ||||
| Chapter 24: The Sylow Theorems | |||||
| WEEK 13 | 11 - 15 April | ||||
| Mon 11 | Conjugacy Classes; The Class Equation | Ch 24 #1, 2, 4 | Ch 24 #41 | ||
| Wed 13 | Sylow Theorems | Ch 24 #10, 11, 12 | |||
| Fri 15 | Sylow Theorems, Concluded | ||||
| WEEK 14 | 18 - 22 April | ||||
| Mon 18 | Applications of Sylow's Theorems | Ch 24 #40 | |||
| Chapter 29: Symmetry and Counting | |||||
| Wed 20 | not-Burnside's Theorem | Ch 29 #1, 3, 5, 10 | Ch 29 #4 | ||
| Fri 22 | Applications | Extra Credit: Ch 29 #6 Due Fri 29. | |||
| WEEK 15 | 25 - 29 April | ||||
| Mon 25 | REVIEW | Ch 9 #55 Ch 10 #33 Ch 24 #4 Ch 29 #3 | |||
| Wed 27 | REVIEW | Ch 10 #40 Ch 11 #8 Suppl Ex 9-11 #8 Ch 24 #20 | |||
| Fri 29 | REVIEW | Ch 10 #48, 49 Ch 11 #15 Ch 24 #2 | |||
| May | |||||
| FINAL EXAM WEEK | 2 - 6 May | ||||
| Tue 3 | FINAL EXAM 9:45 - 11:45 a.m. Objectives for Final Exam
| | |||
