Calendar
| Week | Monday | Wednesday | Friday |
|---|---|---|---|
| 1 |
Review on Proofs (if, for all, there exists, uniqueness, contrapositive, contradiction), Sets, Functions (injective, surjective, bijective) Ch 1.1,1.2 (excluding equivalence relations). Reading question 5, and do the same for proving a function being injective or surjective. Judson calls a function a ''mapping''. We sometimes also call a function a ''map''. |
Review on Equivalence Relations, Congruence Ch 1.2 - Equivalence relations. Reading question 3. Ch 1.4 Q25. Ch 3.1 up to Proposition 3.4. Reading questions 1-2. Ch 3.6 Q1. I dislike the notation ''Z_n'' a lot. In this class we always use the notation Z/n or Z/nZ. |
Review on Induction, Division Algorithm, Euclidean Algorithm Ch 2. Reading questions 2-3. |
| 2 | MLK | Check 1; Definition of Groups, examples Ch 3.1 - Symmetries. Ch 3.2 (excluding Basic Properties of Groups). Reading questions 3,5,6. |
More examples on groups, abelian and nonabelian Ch 3.5 Q13, Q39, Q40 (ignoring the term ''subgroup''). Ch 12.1. |
| 3 | Properties of groups Ch 3.2 - Basic Properties of Groups. |
Check 2; Subgroups Ch 3.3. Reading question 4. Ch 3.5 Q34-36. |
Cyclic Subgroups, Order Ch 4.1, excluding Subgroups of Cyclic Subgroups. Reading questions 1-2. |
| 4 | Catch-up / Review | Midterm 1 Solution | Properties of cyclic subgroups Ch 4.1 - Subgroups of Cyclic Subgroups. Ch 4.5 Q26, 35. |
| 5 | More examples on cyclic groups Ch 4.2. Reading question 4. Ch 4.5 Q20, 21. |
Permutation Groups Ch 5.1 up to Remark 5.11. Ch 5.4 Q1, 2ab. |
Transpositions; Even and Odd Permutations Ch 5.1 - Transpositions. Reading questions 2-3. Ch 5.4 Q3ab |
| 6 | Alternating Groups, Dihedral Groups Ch 5.1 - Alternating Groups. Ch 5.2. Reading question 4. Ch 5.4 Q11. |
Cosets Ch 6.1. Ch 6.5 Q5. |
Lagrange's Theorem Ch 6.2. Reading question 1, 4. Ch 6.5 Q1. |
| 7 | President | Isomorphism, Cayley's Theorem. Ch 9.1, skipping Theorem 9.7 - Theorem 9.10. Reading question 2. Ch 9.4 Q1. |
Classification of cyclic groups rest of Ch 9.1. Reading question 4. |
| 8 | Direct Product Ch 9.2. Reading question 3. Ch 9.4 Q15, 17. |
Midterm 2 | Finite Abelian Groups Ch 13.1. Reading questions 1-4. |
| 9 | Normal subgroups Ch 10.1 - Normal Subgroups. Reading questions 1-4. |
Quotient Group Ch 10.1 - Factor Groups. Judson calls quotient groups as ''factor groups''. We will always say ''quotient groups''. Reading questions 5, Ch 10.4 Q1. |
Group Homomorphism Ch 11.1, Reading questions 1-3. |
| 10 | Properties of Group Homomorphism, examples Ch 11.4 Q2. |
Check 7; Isomorphism Theorems Ch 11.2, Reading questions 4-5. |
Catch-up / Review |
| 11 | Final Exam: Mar 22 (Wed), 3-5pm |
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