| 2023.01.09 |
Induction |
|
|
| 2023.01.11 |
Peano arithmetic |
§1.1 |
notes01 |
| 2023.01.12 |
Well-ordering principle |
§1.1 |
problems01 |
| 2023.01.16 |
Negative integers |
§1.2 |
|
| 2023.01.18 |
Division |
§1.3 |
notes02 |
| 2023.01.19 |
Fundamental Theorem of Arithmetic |
§1.4 |
problems02 |
| 2023.01.23 |
Equivalence relations |
§2.1 |
|
| 2023.01.25 |
Congruence |
§2.2 |
notes03 |
| 2023.01.26 |
Modular arithmetic |
§2.3–2.4 |
problems03 |
| 2023.01.30 |
Fermat's Little Theorem |
§2.5 |
|
| 2023.02.01 |
Rings |
§3.1–3.2 |
notes04 |
| 2023.02.02 |
Subrings |
§4.2 |
problems04 |
| 2023.02.06 |
Domains and Fields |
§3.3 |
|
| 2023.02.08 |
Polynomials |
§7.1 |
notes05 |
| 2023.02.09 |
Roots |
§7.2 |
problems05 |
| 2023.02.13 |
Ring homomorphisms |
§4.3 |
|
| 2023.02.15 |
Ideals |
§5.1–5.2 |
notes06 |
| 2023.02.16 |
Quotient Rings |
§5.3–5.4 |
problems06 |
|
Winter break |
|
|
| 2023.02.27 |
Isomorphisms |
§4.4 |
|
| 2023.03.01 |
First isomorphism theorem |
§5.5 |
notes07 |
| 2023.03.01 |
Midterm |
|
midterm |
| 2023.03.02 |
Ideals in a quotient |
§5.7 |
problems07 |
| 2023.03.06 |
Direct decomposition of a ring |
§5.6 |
|
| 2023.03.08 |
Rings of fractions |
§6.5 |
notes08 |
| 2023.03.09 |
Recognizing fields |
§13.1 |
problems08 |
| 2023.03.13 |
Prime ideals |
§6.1 |
|
| 2023.03.15 |
Euclidean domains |
§6.3 |
notes09 |
| 2023.03.16 |
Extended Euclidean algorithm |
|
problems09 |
| 2023.03.20 |
Principal ideal domains |
§6.2 |
|
| 2023.03.22 |
Unique factorization domains |
§6.4 |
notes10 |
| 2023.03.23 |
Non-Euclidean principal ideal domains |
|
problems10 |
| 2023.03.27 |
Factoring polynomials |
§7.3 |
|
| 2023.03.29 |
Irreduciblity Criteria |
§7.4 |
notes11 |
| 2023.03.30 |
Counting irreducibles |
§7.5 |
problems11 |
| 2023.04.03 |
Gaussian primes |
§10.4 |
|
| 2023.04.05 |
Sums of two squares |
§10.4 |
notes12 |
| 2023.04.06 |
Review |
|
problems12 |
| 2023.04.10 |
Extra tutorial |
09:30–10:20 |
|
| 2023.04.25 |
Extra tutorial |
13:00– |
|
| 2023.04.26 |
Exam |
09:00–12:00 |
Bartlett Gym |
