PMATH 741
Algebraic Number Theory
Winter 2025
Topics
- Rings of integers and Dedekind domains
- Ideal factorization and ideal class groups
- Computing rings of integers
- Kummer’s theorem
- Splitting of primes
- Cyclotomic fields
- Minkowski’s geometry of numbers
- Dirichlet’s unit theorem
Readings
- Matthew Baker, Algebraic Number Theory Course Notes, revised February 23, 2022; the first three chapters are closely followed.
- Instructor typed notes posted on LEARN.
Undated
Topics
- Factorization in Rings
- Algebraic Number Fields
- Galois theory
- Trace, Norm and Discriminant
- Cyclotomic Number Fields
- Dedekind Domains
Readings
- Chapter 1. Factorization in Rings — https://www.math.uwaterloo.ca/~snew/PMATH441/chap1.pdf
- Appendix 1. Continued Fractions — https://www.math.uwaterloo.ca/~snew/PMATH441/app1.pdf
- Chapter 2. Algebraic Number Fields — https://www.math.uwaterloo.ca/~snew/PMATH441/chap2.pdf
- Chapter 3. Galois theory — https://www.math.uwaterloo.ca/~snew/PMATH441/chap3.pdf
- Chapter 4. Trace, Norm and Discriminant — https://www.math.uwaterloo.ca/~snew/PMATH441/chap4.pdf
- Chapter 5. Cyclotomic Number Fields — https://www.math.uwaterloo.ca/~snew/PMATH441/chap5.pdf
- Chapter 6. Dedekind Domains — https://www.math.uwaterloo.ca/~snew/PMATH441/chap6.pdf
Sources
- Course catalogue ↗2026–2027
- course_outline ↗Winter 2025
- course_website ↗Undated
- Winter 2025. No required main textbook. PDF identifies PMATH 441/741; a departmental index has a conflicting 641 label.
- Public lecture-note archive by Stephen New. Topics are the chapter headings in the posted notes; this is not a current-term syllabus. Source term/year not established.