## Math 28b, Spring 2010, Brandeis University

This is the website for the class Math 28b, Introduction to rings and fields, taught in the fall of 2009 at Brandeis University.

### Vital statistics

Lecturer: Thomas Barnet-Lamb
Office: Goldsmith 205
Email: consists of the identifier 'tbl', followed by an at sign, followed by the word brandeis, a dot, and the suffix 'edu'.
Schedule: Mon, Wed, Thurs 12 noon-1pm
Office hours: Wed 10am-11am; Thurs 3.30-4.30pm

Further information can be gleaned by perusal of the syllabus.

Final practice problems and Final practice solutions are available. Please let me know of any typos.

Material from any section of the class, including sections 6 and 7, might be on the final. However, special treatment will apply to (parts of) these sections. In particular:

• The long arguments from section 6 (specifically, the material from lecture 29 and later) will be 'virtually open book': if I ask a question on material from this section, I will reproduce the relevant pages from the online lecture notes as part of the exam.
• The earlier part of section 6 is examinable just as all the earlier sections.
• All of section 7 is 'virtually open book'. If if I ask a question on material from this section, I will reproduce the relevant pages from the online lecture notes as part of the exam. Moreover, I said that this section will be examined more lightly than other sections. In practical terms, you should make sure that you understand all the proofs in this section, and then you will be prepared for the exam.

### Homework

Homework one (integers and divisibility).
Homework two (fields and rings).
Homework three (more rings, unique factorization).
Homework four/five (vector spaces, field extensions).
Homework six (more field extensions).
Homework seven (yet more field extensions).
Homework eight (pi).

### Lecture notes (abbreviated)

Lecture 1 was introductory and has no posted notes.
Week 1: lecture 1, lecture 2., lecture 3.
Week 2: lecture 4, lecture 5., lecture 6.
Week 3: lecture 7, lecture 8, lecture 9
Week 4: lecture 10, lecture 11, lecture 12
Week 5: lecture 13, lecture 14, lecture 15
Week 6: lecture 16, lecture 17, lecture 18
Week 7: lecture 19, lecture 20, lecture 21
Week 7: lecture 22, lecture 23, lecture 24
Week 7: lecture 25, lecture 26, lecture 27
Week 7: lecture 28, lecture 29, lecture 30
Week 8: lecture 31, lecture 32, lecture 33
Week 9: lecture 34, lecture 35