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# Upper division undergraduate mathematics

This page describes *major-specific* or *upper division* parts of undergraduate mathematics, in contrast with lower division undergraduate mathematics (that includes calculus, multivariable calculus, linear algebra, and ordinary differential equations).

Major-specific material typically includes the following. In cases where the learning benefits and learning recommendations pages are missing, we haven't found enough topic-specific demand to investigate and find the best learning resources, but are open to doing so if people ask us questions about it.

See also:

- Upper division undergraduate mathematics course structure
- Upper division undergraduate mathematics learning recommendations

Topic | Brief description | Learning benefits | Learning recommendations |
---|---|---|---|

Undergraduate analysis | A year-long sequence that includes some topological, measure-theoretic, and metric concepts associated with the real line, and an understanding of the real numbers and spaces like in that context. Some multivariable calculus and linear algebra may be covered here. | Undergraduate analysis learning benefits | Undergraduate analysis learning recommendations |

Abstract algebra | A year-long sequence that includes group theory, ring theory, and field theory. Some linear algebra may be covered here. | Abstract algebra learning benefits | Abstract algebra learning recommendations |

Topology | A single course covering point set topology + a glimpse of algebraic topology | Topology learning benefits | Topology learning recommendations |

More analysis | Courses in complex analysis, functional analysis, partial differential equations, analytic number theory, Fourier analysis | -- | -- |

More algebra | Courses in ommutative algebra, algebraic geometry, algebraic number theory | -- | -- |

More geometry/topology | Courses in differential geometry and Riemannian geometry. | -- | -- |

Set theory, logic | Course in logic | -- | -- |

Discrete mathematics and combinatorics | Courses in discrete mathematics and combinatorics (offerings are not standardized) | -- | -- |

Probability theory (close to statistics) | See our probability and statistics learning recommendations | ||

Other applied | Numerical analysis, Linear programming and optimization | -- | -- |

Mathematics students may be required or encouraged to take courses in sister subjects such as statistics and computer science.