# Suggested topics for a math DRP

Below is a list of suggested areas for your DRP reading:

- Algebraic Geometry
- Analysis_Harmonic
- Analysis_Geometric
- Analysis_PDE
- Applied Math_Physical Math
- Applied Math_Numerical Analysis
- Category theory
- Computer Science
- Combinatorics
- Differential Geometry
- Game Theory
- Geometry & Topology
- Logic
- Number Theory_Algebraic
- Number Theory_Analytic
- Machine learning
- Probability
- Representation Theory_Lie Groups
- Representation Theory_Combinatorial
- Statistics
- Topology_Algebraic
- Topology_Geometric
- Topology_Symplectic
- Topology_Combinatorial

Once you choose an area, you may specify a topic of interest from this list (courtesy of the University of Chicago math department's DRP program). These are only suggestions, and you are welcome to come up with others!

- algebra/combinatorics
- algebra/number theory
- algebraic curves
- algebraic curves and riemann surfaces
- algebraic geometry
- algebraic graph theory
- algebraic k-theory
- algebraic number theory
- algebraic topology
- algorithms of algebra and number theory
- analytic number theory
- applied mathematics
- bass-serre theory
- categorical logic
- category theory
- combinatorial game theory
- combinatorial topology
- combinatorics
- combinatorics/number theory
- commutative algebra and algebraic geometry
- compact lie groups
- complex algebraic curves
- complex algebraic geometry
- complex analysis
- complexity theory
- computability and algorithmic information
- diffential forms in algebraic topology
- differential geometry
- differential geometry and general relativity
- elementary number theory
- elliptic curves
- elliptic curves and cryptography
- ergodic theory in number theory
- euler characteristic and gauss-bonnet theorem
- existence and uniqueness for ordinary differential equations
- first-order logic and model theory
- flows on manifolds
- fourier analysis
- galois theory of differential equations
- game theory
- geometry and differential forms
- geometry of surfaces
- geometry/topology
- graph colorings
- grÃ¶bner bases
- group theory
- harmonic analysis
- homological algebra
- hyperbolic geometry
- introduction to characteristic classes
- introduction to logic
- introduction to manifolds
- introduction to probability
- knot theory
- lie groups
- lie groups and geometry
- linear algebra
- linear differential equations
- local class field theory via lubin-tate theory
- manifolds and lie groups
- mathematical physics
- matrix groups
- model theory
- models of peano arithmetic
- mordell's theorem
- nonstandard analysis
- number fields and class groups
- number theory
- number theory and combinatorics
- optimization theory
- p-adic analysis
- partial differential equations
- probability
- representation theory
- representation theory and quantum mechanics
- riemann surfaces
- riemann surfaces and elliptic curves
- sheaves, complex analysis and gaga
- special (co)limits and kan extensions
- stochastic processes
- the borsuk ulam theorem
- the fundamental group
- the prime number theorem
- the spectral theorem
- topoi and logic
- topological genericity
- topology from the differential viewpoint
- topology/analysis
- topos theory in physics
- tropical geometry
- van der waerden's theorem
- visual introduction to complex analysis
- young tableaux
- young tableaux and representations of the symmetric group
- zeta functions of number fields