Contents

A L G E B R A:

Selected Solutions to "Abstract Algebra" Dummit and Foote, 3rd edition:

Chapter 0: Preliminaries
Chapter 1: Introduction to Groups
Chapter 2: Subgroups
Chapter 3: Quotient groups and Homomorphisms
Chapter 4: Group Actions
Chapter 5: Direct and Semi-direct Products and Abelian Groups
Chapter 6: Further Topics in Group Theory
Chapter 7: Introduction to Rings
Chapter 8: Euclidean Domains, Principal Ideal Domains, and Unique Factorization Domains
Chapter 9: Polynomial Rings
Chapter 10: Introduction to Module Theory
Chapter 11: Vector Spaces
Chapter 12: Modules Over Principal Ideal Domains
Chapter 13: Field Theory
Chapter 14: Galois Theory
Chapter 15: Commutative Rings and Algebraic Geometry
Chapter 16: Artinian Rings, Discrete Valuation Rings, and Dedekind Domains
Chapter 17: Introduction to Homological Algebra and Group Cohomology
Chapter 18: Representation Theory and Character Theory
Chapter 19: Examples and Applications of Character Theory


Review Guides:

Sylow's Theorem
First Isomorphism Theorem
Normal Subgroups
Jordan Canonical Form

Selected Solutions to "Linear Algebra" Friedburg, Insel, Spence, 4th edition:

Chapter 1: Vector Spaces
Chapter 2: Linear Transformations and Matrices
Chapter 3: Elementary Matrix Operations and Systems of Linear Equations
Chapter 4: Determinants
Chapter 5: Diagonalization
5.4.18
Chapter 6: Inner Product Spaces
Chapter 7: Canonical Forms


A N A L Y S I S:

Selected Solutions to "Real Analysis" by Stein and Shakarchi :

Chapter 1: Measure Theory
26
Chapter 2: Integration Theory
9, 11, 19,
Chapter 3: Differentiation and Integration
7, 12, 32,
Chapter 4: Hilbert Spaces: An Introduction


Other math references:

Sean Breckling's Analysis Blog (some solutions to Stein and Shakarchi, Real Analysis)