# Analysis

## Real Analysis

### Walter Rudin, Real and Complex Analysis

• Useful as a general reference, but there are more useful techniques in other books.

### Stein and Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces

• Has more useful techniques than Rudin.
• Doesn’t include $L^p$ spaces or convexity.

### Lieb-Loss, Real Analysis

• Good source for $L^p$ spaces, convexity, and Fourier analysis.

### Stein and Shakarchi, Fourier Analysis

• Very elementary.

## Differential Equations

### Evans, Partial Differential Equations

• Good source for Sobolev spaces.

# Algebra

## General/Introductory

### Dummit and Foote, Abstract Algebra

• Standard reference, encyclopaedic!

## Commutative Algebra

### Altman-Kleiman, A Term of Commutative Algebra

https://www.mi.fu-berlin.de/en/math/groups/arithmetic_geometry/teaching/exercises/Altman_-Kleiman---A-term-of-commutative-algebra-_2017_.pdf

https://www.mi.fu-berlin.de/en/math/groups/arithmetic_geometry/teaching/exercises/Altman_-Kleiman---A-term-of-commutative-algebra-_2017_.pdf

## Homological

### Peter J. Hilton and Urs Stammbach, A Course in Homological Algebra

• Recommended by Dan Nakano

### Kirillov, Lie Groups and Lie Algebras

• Recommended by Daniel Litt

# Number Theory

### Algebraic Number Theory

#### J. Neukirch, Algebraic Number Theory

• Large number of exercises here

#### J. Milne, Algebraic Number Theory

• Not a textbook: actually notes

### Uncategorized

#### J. Milne, Class Field Theory

• Not a textbook: actually notes

# Topology

## Algebraic Topology

### Hatcher, Algebraic Topology

• Standard reference.

### Dodson and Parker, A User’s Guide to Algebraic Topology

• Covers more advanced topics than a usual course: some sheaf theory, bundles, characteristic classes, obstruction theory
• Appendices on algebra, topology, manifolds/bundles, and tables of homotopy groups

### Glen Bredon, Topology and Geometry

• Blends differential and algebraic topology, can be disorienting as a first pass

### Milnor, Topology from the Differentiable Viewpoint (Princeton)

• Classic reference.

### Bott and Tu, Differential Forms in Algebraic Topology (Springer)

• Classic reference.

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