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Abstract Algebra I - 1st semester - 2015

The lectures of the abstract algebra course will be based on a book by the same title, written by Dummit and Foote (Los Andes biblioteca # 512.02 D855 2004). We will cover the first 9 chapters. In the process, we might skip some sections or add topics from external resources. The lectures will be mostly in English but students also are welcome to ask quesions, have discussions with their peers or give presentations in Spanish.

Download the coures outline here.

Evaluation policy


Office hours

Martes 11:30-1:30 y Jueves 8-10
H 007

Projects

Group theory in cryptography Juan Camilo Chavez and Andres Camilo Paz
link
Lattices, Minkowski's theorem and the sum of four squares theorem David Stiles, Juan Camilo Azuero, Juan Pablo Lievano and Ivan Felipe Herrara
link
Group rings and Maschke's theorem Daniel Rodriguez, Juan Felipe Ceron and Gloria Buritica
link
Burnside's theorem and Escher's patterns Juan Esteban Perez and Santiago Villegas
link 1 y link 2
Symbolic computations with GAP Christian Poveda and German David Cardozo
link
Presentation file
PGL and PSL and their simplicity Nicolas Cuero, Paula Rodriguez, Juan Felipe Uribe and Daniel Tamayo
link 1 y link 2
Topological Groups Juan Sebastian Aguirre, Daniel Bermudez, Diego Alejandro Murillo and Juan Felipe Ariza
link

Homeworks, Quizzes and Midterms

HW #1, Friday Jan 30 - Tuesday Feb 3
Solutions here
Quiz #1 on Friday Feb 13
Solutions here
Parcial #1 on Sat Feb 21
HW #2, Friday Feb 27 - Tuesday Mar 3
Solutions here
Quiz #2 on Friday Mar 13
Solutions here
Parcial #2 on Fri Mar 20
HW #3, Friday Mar 27 - Tuesday Apr 7
HW #3 Solutions
HW #4, Friday Apr 17 - Friday Apr 24
HW #4 Solutions
HW #5, Para Viernes, 8 Mayo
HW #5 Solutions
Final Exam
Final Exam Solutions

Practice Homework

These are some suggested homework questions to get you started.
1.1 1, 7, 12, 19, 22, 24, 30, 31, 36
1.2 1, 4, 9, 14, 17
1.3 2, 5, 10, 14, 20
1.4 2, 3, 8, 10, 11
1.5 1, 2, 3
1.6 4, 7, 9, 17, 19, 20, 26
1.7 3, 4, 5, 8, 12, 15, 16, 21
2.1 3, 9, 12, 15, 17
2.2 2, 4, 6, 7, 13
2.3 2, 6, 9, 10, 21, 23
2.4 2, 6, 7, 9, 14, 19
2.5 2, 8, 9, 11, 16, 18
3.1 1, 3, 6, 12, 19, 22, 28, 34, 41
3.2 2, 4, 5, 10, 11, 17, 20, 22
3.3 1, 3, 7, 8
3.4 1, 3, 7, 8
3.5 3, 6, 10, 17
4.1 1, 2, 4, 6, 10
4.2 2, 3, 4, 8, 13
4.3 3, 4, 6, 8, 9, 17, 20, 25
4.4 1, 2, 5, 6, 8, 11
4.5 1, 2, 3, 4, 5, 13, 19, 26, 29
4.6 1, 2, 5
5.2 1, 2, 7, 14
5.5 1, 2, 3, 5, 9, 11
6.1 3, 7, 8, 9, 10, 12, 13, 16
7.1 7, 11, 13, 21, 22, 26, 27
7.2 3, 5, 10, 12
7.3 2, 6, 8, 10, 13, 14, 15, 16, 22, 29, 34

Miscellaneous

Mathematics on a distant planet
Who wanted to make the Heisenberg group abelian?
Fun with F_{un}
or just let Allan Connes tell you about it