PMATH 347

Groups and Rings

Undergraduate

Undated

Topics

Groups and Rings
Subgroups and Cyclic Groups
The Symmetric and Alternating Groups
Group Homomorphisms and Isomorphisms
Cosets, Normal Subgroups and Quotients
The Classification of Finite Abelian Groups
Group Action and the Sylov Theorems
The Classification of Groups of Small Order
Rings and Subrings
Ring Homomorphisms, Ideals and Quotients
Factorization in Commutative Rings
Polynomial Rings

Readings

Chapter 1. Groups and Rings — https://www.math.uwaterloo.ca/~snew/PMATH347/Chap1Groups.pdf
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Chapter 2. Subgroups and Cyclic Groups — https://www.math.uwaterloo.ca/~snew/PMATH347/Chap2Subgroups.pdf
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Chapter 3. The Symmetric and Alternating Groups — https://www.math.uwaterloo.ca/~snew/PMATH347/Chap3SymmetricGroup.pdf
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Chapter 4. Group Homomorphisms and Isomorphisms — https://www.math.uwaterloo.ca/~snew/PMATH347/Chap4Homomorphisms.pdf
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Chapter 5. Cosets, Normal Subgroups and Quotients — https://www.math.uwaterloo.ca/~snew/PMATH347/Chap5QuotientGroups.pdf
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Chapter 6. The Classification of Finite Abelian Groups — https://www.math.uwaterloo.ca/~snew/PMATH347/Chap6FiniteAbelianGroups.pdf
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Chapter 7. Group Action and the Sylov Theorems — https://www.math.uwaterloo.ca/~snew/PMATH347/Chap7GroupAction.pdf
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Chapter 8. The Classification of Groups of Small Order — https://www.math.uwaterloo.ca/~snew/PMATH347/Chap8SmallGroups.pdf
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Chapter 9. Rings and Subrings — https://www.math.uwaterloo.ca/~snew/PMATH347/Chap9Rings.pdf
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Chapter 10. Ring Homomorphisms, Ideals and Quotients — https://www.math.uwaterloo.ca/~snew/PMATH347/Chap10QuotientRings.pdf
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Chapter 11. Factorization in Commutative Rings — https://www.math.uwaterloo.ca/~snew/PMATH347/Chap11Factorization.pdf
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Chapter 12. Polynomial Rings — https://www.math.uwaterloo.ca/~snew/PMATH347/Chap12Polynomials.pdf
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Sources

Course catalogue ↗2026–2027
course_website ↗Undated
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.