Math 3140 Fall 16
MATH 3140: Abstract Algebra 1 (Fall 2016)
Syllabus
Final Exam:
Thursday 12/15, 1:30-4 pm, in class
Discussion of results: Friday 12/16, d10-11 am
Office hours:
Tuesday 3-4 pm
Wednesday 11-12 am
Friday 10-11 am
Schedule
Numbers are for orientation and refer to sections with related material
in Goodman, Algebra: Abstract and Concrete.
- 08/22: symmetries, multiplication table (1.1-1.3)
- 08/24: linear maps, matrices (1.4)
- 08/26: permutations (1.5)
- 08/29: cycle notation, order of permutations (1.5)
- 08/31: perfect shuffle (1.5),
- 09/02: Z_n (1.7)
- 09/07: gcd, Euclidean algorithm, Bezout's coefficients (1.7)
- 09/09: Euler's Theorem (1.9), RSA (1.12)
- 09/12: groups (1.10), uniqueness of identity, 2.1.1, inverses 2.1.2, 2.1.3, 2.1.4
- 09/14: subgroups, homomorphisms
- 09/16: REVIEW
- 09/19: MIDTERM
- 09/21: isomorphisms, cyclic subgroups 2.2.9, 2.2.20, 2.2.21
- 09/23: 2.4.12, Cayley's Theorem
- 09/26: dihedral groups D_2n, generators and relations 2.3
- 09/28: left cosets, Lagrange's Theorem 2.5.6, index
- 09/30: kernel, image of homomorphisms 2.4.16
- 10/03: abelian groups, conjugacy, normal subgroups
- 10/05: center 2.5.11,
- 10/07: quotient groups 2.7.1
- 10/10: quotients
- 10/12: homomorphism theorem 2.7.6
- 10/14: correspondence theorem 2.7.13
- 10/17: direct products 3.1
- 10/19: finitely generated abelian groups 3.6
- 10/21: Fundamental Theorem of finitely generated abelian groups 3.6.21
- 10/24: REVIEW
- 10/26: MIDTERM
- 10/26: discussion of midterm
- 10/31: Fundamental Theorem of finitely generated abelian groups (2)
- 11/02: Group actions, orbits, transitivity 5.1
- 11/04: stabilizers, orbit size (5.1.14)
- 11/09: fixed points, counting orbits (5.2.2)
- 11/09: Burnside-Frobenius lemma (5.2.2)
- 11/11: conjugation (5.1.17), class equation (5.4), p-groups (5.4.2)
- 11/14: groups of size p^2 (5.4.3)
11/16: Sylow subgroups (5.4.7), 1st Sylow Theorem
- 11/18: 2nd and 3rd Sylow Theorem (5.4.10-11), groups of size pq (5.4.12)
- 11/28: rings (6.1)
- 11/30: units, fields, subrings
- 12/02: ring homomorphisms, ideals, principal ideals (6.2), quotient rings (6.3)
- 12/05: direct product, Chinese Remainder Theorem
- 12/07:
- 12/09: REVIEW
Assignments
- due 08/24 [pdf]
- due 08/31 [pdf]
- due 09/09 [pdf] [tex]
- due 09/14 [pdf] [tex]
- due 09/21 [pdf] [tex] [solutions]
- due 09/28 [pdf] [tex] [solutions]
- due 10/05 [pdf] [tex] [solutions]
- due 10/12 [pdf] [tex] [solutions]
- due 10/19 [pdf] [tex] [solutions]
- due 10/26 [pdf] [tex] [solutions]
- due 11/02 [pdf] [tex] [solutions]
- due 11/09 [pdf] [tex] [solutions]
- due 11/16 [pdf] [tex] [solutions]
- due 11/30 [pdf] [tex] [solutions]
- due 11/30 [pdf] [tex] [solutions]
Handouts
- Basic definitions in group theory [pdf]
- Quizzes:
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
- List of topics [pdf]
Textbooks
There are many good textbooks on the topic, including the ones listed below. We will mainly follow Goodman's book.
You can find the others online or at the Mathematics Library for additional reading.
- J. Fraleigh, A First Course in Abstract Algebra (Seventh Edition), Addison Wesley 2002.
- F. Goodman, Algebra: Abstract and Concrete (Edition 2.6), 2015.
[pdf]
- T. Hungerford, Abstract Algebra: An Introduction (Second Edition), Brooks Cole 1996.
- I. Herstein, Abstract Algebra, John Wiley 1996.
- T. Judson, Abstract Algebra: Theory and Applications. [pdf]
- S. Lang, Undergraduate Algebra (Third Edition), Springer 2005.
[pdf]