# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

**Approved:**2017-03-14, Jesus De Loera

**Units/Lecture:**

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

**Prerequisites:**

**Course Description:**

**Suggested Schedule:**

Lecture(s) | Comments/Topics | |

Week 1 | Lecture 1: Overview of the course. What is data analytics? What is operations research? Discuss at least two examples of applications (e.g., optimal assignment marriage stable problem and medical school applicants). Singular value decomposition model for classification (briefly recall SVD if they do not remember it). Quick review of MATLAB. Lecture 2: Convex sets and convex functions, convex optimization (Section 8.1- 8.3 in main textbook). Introduction to ZIMPL/SCIP software. Lecture 3: Optimality conditions of convex problems (section 8.4 main textbook). Continue introduction to ZIMPL/SCIP | |

Week 2 | Lecture 4: Duality: Lagrange dual, Karush-Kuhn Tucker (section 8.5 main textbook). More examples on using ZIMPL/SCIP. Lecture 5 and 6: Linear and quadratic optimization models (section 9.2-9.5 main textbook) | |

Week 3 | Lecture 7: Discuss basics of supervised learning LASSO (section 13.2 main textbook). Lecture 8 and 9: Discuss basics of binary classification (Support vector machines) (Section 13.3 main textbook). | |

Week 4 | Lecture 10: Basics of robust optimization, (sections 10.1, 10.3 main textbook). Lecture 11: Semidefinite models (discuss matrix completion problem) (section 11.1 and 11.2 main textbook). Lecture 12: More on semidefinite programming applications (Section 11.4 main textbook). | |

Week 5 (halfway) | Lecture 13, 14: Discuss basics of unsupervised learning models PCA, graphical models. Non-negative Matrix factorization. (section 13.5 main textbook). Lecture 15: Clustering models: K-means and first mention of discrete models for partitioning, packing problems, Knapsack models. | |

Weeks 6 | Lecture 16: Ranking algorithms. Massey and Colley's methods (Chapters 1 to 3 of Langville-Meyer book). Lecture 17-18: Discrete models: Shortest path problem, minimum cost perfect matching. (Sections 1.4-1.5 in Guenin et al book). Lecture 18: More discrete models: Traveling salesman, ranking ordering models through binary integer optimization (this portion is in in Chapter 15 Langville-Meyer book and chapter 6 of Guenin et al.) | |

Weeks 7 | Lecture 19: Quick survey of convex optimization algorithms. Smooth unconstrained minimization. (Sections 12.1-12.2 main textbook). Lecture 20: Algorithms for convex constrained optimization. Gradient descent. (Sections 12.3 and 12.4 main textbook). Lecture 21: Coordinate descent methods. Brief mention of interior point methods (Section 12.5 main textbook). Assign f | |

Weeks 8 | Lecture 22: Integer Discrete models versus continuous models (see Guenin et al book in chapters 6,7 and appendix for this material.) Lecture 23: Cutting planes and the simplex method. Branch and bound. (Guenin et al chapter 6). Lecture 24: Discuss non-convex optimization problems. Karush-Kuhn Tucker for non-convex problems. (Guenin et al. chapter 7) | |

Weeks 9 | Lecture 25: More Discrete models, polynomial versus exponential algorithms. NP-hardness. (appendix Guenin et al book). Assign Lectures 26-27: Business finance applications, portfolio optimization (section 14.1-14.2 main textbook).
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Weeks 10 | Lectures 28-30: These three extra days can be used to catch up, or for holding in class midterm(s), or to do course review, e.g., before an in class final exam, if the instructor chooses to have one instead of final project. |

**Additional Notes:**

**Learning Goals:**

**Assessment:**