Math 113 Tentative Syllabus
| Week of | Mon | Wed | Fri | Topics |
| 1/21 | Holiday | §1: A.3-4 | §1.1 | Integers: Induction, Divisors, |
| 1/28 | §1.2 | §1.3 | §1.4 | Primes. Congruences. Integers modulo n. |
| 2/4 | §2: 2.1 | §2.2 | §2.2 | Sets, functions, and relations. |
| 2/11 | §2.2-3 | §2.3 | 2.3 | Equivalence relations. Permutations. Quiz.. |
| 2/18 | Holiday | §3.1-3.2 | §3.2 | Groups. Definition of a group. Subgroups. Examples. |
| 2/28 | §3.3-3.4 | §3.5 | §3.5 | Isomorphisms. Cyclic Groups |
| 3/3 | §3.6--3.7 | §3.8 | §4 : §4.1 | Permutation groups. Homomorphisms. Cosets and Factor groups. Polynomials. |
| 3/10 | §4.1 | §4.2 | Midterm 1 | Factors. Roots. |
| 3/17 | §4.2 | §4.3 | §4.4 | Existence of roots. Integral polynomials. |
| 3/24 | Spring Break | |||
| 3/31 | §5: 5.1-5.2 | §5.3 | §5.3-5.4 | Commutative Rings. Homomorphisms. Ideals and factor rings.Quotient fields. |
| 4/07 | §7: §7.1,7.3 | §7.2-7.3 | §7.2,7.4 | Structure of groups. Group actions. Cojugacy. |
| 4/14 | §7.4-7.5 | §6: 6.1--6.2 | Midterm2 | Sylow theorems. Finite abelian groups. Fields. Algebraic elements and extensions. |
| 4/21 | §6.2, §6.4 | §6.4 | §6.4 | Algebraic extensions. Splitting fields. |
| 4/28 | §6.5 | §6.5 | §9: 9.1 | Finite fields. Unique factorization. Eucidean domains. |
| 5/5 | §9.2 | §9.3 | §9.3 | Unique factorization domains. Diophantine equations. |
| 5/12 | §9.3 | X | Final |
The above schedule is just a rough guide and subject to change as the course progresses.
1. This midterm will cover chapters 1--3.
2: This midterm will cover chapters 1--5 and sections 7.1 and 7.2.