Abstract Algebra
General Information | Syllabus | HW Assignments | Course Resources |
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Syllabus
The following is a tentative syllabus for the course. This page will be updated irregularly.On the other hand, the weekly syllabus contained in the Homework Assignments page will always be accurate.
Lectures | Sections in Text | Brief Description |
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9/12 | 1.1, 1.2 | Introduction, sets and equivalence relations |
9/14 | 2.1, 2.2 | Properties of $\mathbb Z$: induction, division and Euclidean algorithm |
9/16 | 3.1, 3.2 | $\mathbb Z_n$: Integers modulo $ n$, Symmetric groups, Dihedral groups $ D_3$, $ D_4$, matrix groups, Quaternion group |
9/19 | 3.2, 3.3 | Simple properties of groups, subgroups and characterization |
9/21 | 4.1, 4.2 | Cyclic groups, multiplicative group of $\mathbb C$ |
9/23 | 5.1, 5.2 | Symmetric groups, cycle notation, general dihedral groups |
9/26 | 6.1, 6.2, 6.3 | Cosets; Lagrange's theorem, applications |
9/28 | 9.1, 9.2 | Isomorphism; direct products |
9/30 | 10.1, 10.2 | Normal subgroups; factor groups; the alterating group |
10/3 | 11.1, 11.2 | First Isomorphism theorem |
10/5 | Midterm Exam I | |
10/6 (x-hour) | 11.2 | The other isomorphism theorems |
10/7 | 14.1 | Groups acting on sets; Cayley's theorem |
10/10 | 14.2 | The class equation and applications |
10/12 | 15.1, 15.2 | The Sylow Theorems |
10/14 | 13.1 | Fundamental theorem of finite abelian groups; recognizing direct products |
10/17 | 13.2 | Solvable groups; Simple Groups and the Hölder prgram |
10/19 | 16.1, 16.2 | Rings; integral domains |
10/21 | 16.2, 16.3 | Integral domains, homomorphisms, ideals |
10/24 | 16.3, 16.4 | Maximal and prime ideals |
10/26 | Midterm Exam II | |
10/27 (x-hour) | 17.1 | Rings, Polynomial Rings, Finite Fields |
10/28 | 17.2 | The Division Algorithm |
10/31 | 17.3 | Irreducibility, Rational root test, Gauss's lemma |
11/2 | 17.3 | Gauss's lemma, Eisenstein's criterion |
11/4 | 18.1 | Integral domains and fields of Fractions |
11/7 | 18.2 | PIDs are Unique Factorization domains |
11/9 | 18.2 | $D$ UFD implies $D[x]$ UFD |
11/11 | 18.2 | Detecting multiple roots, irreducibility in $\mathbb Q[x,y]$ |
11/14 | Cyclotomic polynomials | |
11/18 | Final Exam | 8-11am |
T. R. Shemanske
Last updated August 11, 2020 16:04:41 EDT