MATH 611: Modern Algebra (Fall 2023)

Instructor: Nha Truong

Office hours: MWF 11:00-12:00 PM- Keller 410

Course information:

Time: MWF 12:30-01:20 PM

Room:  Keller 313 

Textbook: Abstract Algebra by Dummit and Foote.

Other textbooks/ Notes:  Algebra by Hungerford, Romyar Sarifi's notes, Keith Conrad's expository papers

Grade: Bi-weekly Homework (30%), Take-home Midterms (30%), Take-home Final (40%).

Topics: 

1. Group theory: basics of group actions, semidirect products, class equation, Sylow theorems

2. Ring theory: factorization in domains, simplicity of matrix algebras

3. Module theory: basics, projectivity, injectivity, tensor products, flatness, Noetherian property, exact sequences, commutative diagrams, structure theory of modules over a PID 

4. Field and Galois theory: finite fields, separable and normal extensions, Fundamental theorem of Galois theory

5. Language of category theory: objects, arrows, Hom, functors, natural transformations, universal objects, products, coproducts, Yoneda lemma

Additional topics if time allows: 

6. Multilinear algebra: pairings, wedge products, symmetric products, multilinear forms over rings

Resources:

• UH Manoa, Qualification exam in algebra information

• Lecture notes

• Problem sets 

• Exams