| 2025.01.06 |
Induction |
|
|
| 2025.01.08 |
Peano arithmetic |
§1.1 |
notes01 |
| 2025.01.09 |
Well-ordering principle |
§1.1 |
problems01 |
| 2025.01.13 |
Equivalence relations |
§2.1 |
|
| 2025.01.15 |
Negative integers |
§1.2 |
notes02 |
| 2025.01.16 |
Division with remainder |
§1.3 |
problems02 |
| 2025.01.20 |
Euclidean algorithm |
§1.4 |
|
| 2025.01.22 |
Congruence |
§2.2 |
notes03 |
| 2025.01.23 |
Modular arithmetic |
§2.3–2.4 |
problems03 |
| 2025.01.27 |
Fermat's Little Theorem |
§2.5 |
|
| 2025.01.29 |
Rings |
§3.1–3.2 |
notes04 |
| 2025.01.30 |
Subrings |
§4.2 |
problems04 |
| 2025.02.03 |
Domains and Fields |
§3.3 |
|
| 2025.02.05 |
Polynomials |
§7.1 |
notes05 |
| 2025.02.06 |
Roots |
§7.2 |
problems05 |
| 2025.02.10 |
Ring homomorphisms |
§4.3 |
|
| 2025.02.12 |
Ideals |
§5.1–5.2 |
notes06 |
| 2025.02.13 |
Quotient Rings |
§5.3–5.4 |
problems06 |
| 2025.02.13 |
Midterm |
|
|
|
Winter break |
|
|
| 2025.02.24 |
Isomorphisms |
§4.4 |
solutions06 |
| 2025.02.26 |
First isomorphism theorem |
§5.5 |
notes07 |
| 2025.02.27 |
Ideals in a quotient |
§5.7 |
problems07 |
| 2025.03.03 |
Direct decomposition of a ring |
§5.6 |
solutions07 |
| 2025.03.05 |
Rings of fractions |
§6.5 |
notes08 |
| 2025.03.06 |
Recognizing fields |
§13.1 |
problems08 |
| 2025.03.10 |
Prime ideals |
§6.1 |
|
| 2025.03.12 |
Euclidean domains |
§6.3 |
notes09 |
| 2025.03.13 |
Extended Euclidean algorithm |
|
problems09 |
| 2025.03.17 |
Principal ideal domains |
§6.2 |
|
| 2025.03.19 |
Unique factorization domains |
§6.4 |
notes10 |
| 2025.03.20 |
Non-Euclidean principal ideal domains |
|
problems10 |
| 2025.03.24 |
Factoring polynomials |
§7.3 |
|
| 2025.03.26 |
Irreducibility criteria |
§7.4 |
notes11 |
| 2025.03.27 |
Counting irreducibles |
§7.5 |
problems11 |
| 2025.03.31 |
Gaussian primes |
§10.4 |
|
| 2025.04.02 |
Sums of two squares |
§10.4 |
notes12 |
| 2025.04.03 |
Review |
|
problems12 |
| 2025.04.15 |
Extra tutorial (in 201 Jeffery Hall) |
14:00–15:00 |
|
| 2025.04.16 |
Exam |
19:00–22:00 |
|
