# Basic Courses

Click here for rules regarding basic courses

### Forms:

Course # | Course Title | Semester | Description |
---|---|---|---|

60210 | Algebra I | Fall | Groups, rings, modules |

60220 | Algebra II | Spring | Fields, Galois theory, and topics chosen from modules, multilinear algebra, homological algebra, commutative algebra, and noncommutative algebra |

60350 | Real Analysis I | Fall | Calculus, Lebesgue measure, general measure theory |

60360 | Spring | Functional Analysis or topics chosen at the discretion of the instructor | |

60370 | Complex Analysis I | Fall | Analytic functions, Cauchy integral theorems and formulas, applications. |

60380 | Complex Analysis II | Spring | Topics from complex manifolds, Riemann surfaces, ... |

60330 | Basic Geometry & Topology | Fall | Quick review of point set topology, fundamental groups and covering spaces, manifolds. |

60440 | Basic Topology II | Spring | Algebraic topology, homology, cohomology, duality theorems |

60510 | Logic I | Fall | Model theory and some set theory. |

60520 | Logic II | Spring | Computability theory and more set theory. |

60610 | Discrete Mathematics | Enumeration, graph theory, error correcting codes, and other topics at discretion of the instructor | |

60620 | Optimization | Convex sets, theorems of Caratheodory, Radon, Helly, and Krein-Milman. Facial structure of convex sets. Extreme points. Separation Theorem. Optimality conditions for convex programming problems. Introduction to subdifferential calculus. Chebyshev approximations. | |

60650 | Basic PDE | Linear partial differential equations, including transport, Laplace, heat, and wave equations. Nonlinear differential equations. | |

60670 | Basic Differential Geometry | Spring | Connections, Riemannian geometry, topics chosen from Kahler geometry, symplectic geometry, contact geometry. |

60850 | Probability | An introduction to probability theory, including elements of measure and integration, random variables, central limit theorems, and other topics. | |

70220 | Lie Groups and Lie Algebras | Spring |