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Course |
Title |
Crs. |

MATH 6201 | Modern Algebra | 3 |

MATH 6261 | Real Variables I | 3 |

MATH 6150 | Linear Algebra | 3 |

MATH 6202 | Modern Algebra II | 3 |

MATH 6301 | Functions of a Complex Variable. | 3 |

Course |
Title |
Crs. |

MATH 6540 | Introduction to Topology | 3 |

MATH 6271 | Mathematical Analysis I | 3 |

MATH 6262 | Functions of Real Variables II | 3 |

MATH 6551 | Algebraic Topology I | 3 |

MATH 6272 | Mathematical Analysis II | 3 |

MATH 8309 | Complex Analysis II | 3 |

MATH 6460 | Functional Analysis I | 3 |

MATH 8469 | Functional Analysis II | 3 |

MATH 8465 | Spectral Theory and D.E | 3 |

Courses in Specialization Area | 12 | |

Elective Courses | 6 |

Course |
Title |
Crs. |

MATH 8001 | Graph Theory | 3 |

MATH 6881 | Linear Programming | 3 |

MATH 8005 | Enumerative Combinatorics | 3 |

MATH 8015 | Discrete Algorithms | 3 |

MATH 8051 | Convex Polytopes | 3 |

MATH 8021 | Algebraic Combinatorics | 3 |

MATH 8031 | Combinatorial Optimization | 3 |

MATH 6656 | Applied Algebra I | 3 |

MATH 8041 | Matroid Theory | 3 |

Courses in Specialization Area | 12 | |

Elective Courses | 6 |

Course |
Title |
Crs. |

MATH 6601 | Probability and Statistics I | 3 |

MATH 6271 | Mathematical Analysis I | 3 |

MATH 6681 | Data Structures I | 3 |

MATH 6602 | Probability and Statistics II | 3 |

MATH 6272 | Mathematical Analysis II | 3 |

MATH 6682 | Data Structures II | 3 |

MATH 6680 | Computational Analysis I | 3 |

MATH 6690 | Computational Analysis II | 3 |

Courses in Specialization Area | 15 | |

Elective Courses | 6 |

Course |
Title |
Crs. |

Seminars | 6 | |

Doctoral Dissertation | 3 |

- An exam in Real and Complex Analysis, based on the corresponding core courses of the first year.
- An exam in Modern and Linear Algebra, based on the corresponding core courses of the first year.
- An exam specific to the chosen option in one of the following areas:
- Pure Mathematics Option: Real Analysis and Complex Analysis, Topology, Functional Analysis.
- Discrete Mathematics Option: Graph Theory, Linear Programming, Applied Algebra, Enumerative and Algebraic Combinatorics, Discrete Algorithms, Combinatorial Optimization, Convex Polytopes, Matroid Theory.
- Computational Mathematics Option: Mathematical Analysis, Probability and Statistics, Data Structures and Algorithms, Computational Analysis

- Demonstrated a competent knowledge of Spanish and English. A reading knowledge of French, German, or Russian is strongly recommended.
- Maintained a
*B*average or better in formal course work, with grades of at least*B*in the courses related to the chosen option. - Passed the written qualifying examinations at the doctoral level, as described in Section V of the Departmental Rules.
- Passed the oral examination for advancement to the Ph.D. candidacy.
- Satisfied the specific requirements of the option committee governing the field of principal interest.
- Obtained the consent of a faculty member who will accept the responsibility 0€ directing a dissertation.