Fall, 2016

Class | Date | Instructor | Topic |
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Part 1 – Linear Analysis and Optimization (Notes) |
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1 | August 29 | Fuentes | Preliminaries — Algorithmic Complexity, BLAS |

2 | August 31 | Fuentes | Vector and Function Spaces |

3 | September 2 | Fuentes | Metric Spaces |

September 5 | Labor Day Holiday | ||

4 | September 7 | Fuentes | Entropy, Mutual Information |

5 | September 9 | Fuentes | Linear Independence, Equivalence of Norms |

6 | September 12 | Fuentes | Linear Operators, Null Space, Range Space |

7 | September 14 | Fuentes | Point Spread Function, Operator Inverse |

8 | September 16 | Fuentes | Rank and Nullity |

9 | September 19 | Fuentes | Bounded Operator, Matrix Conditioning and Stability of Linear Systems |

10 | September 21 | Fuentes | Inner Product, Orthogonality, Least Squares |

11 | September 23 | Fuentes | Adjoint Operators, Eigen-formulation |

12 | September 26 | Fuentes | Optimization, Characterization of Solution |

13 | September 28 | Fuentes | Line Search, Newton - CG Trust - Region Methods |

14 | September 30 | Fuentes | Applications: L1 Minimization |

15 | October 3 | Fuentes | Exam on Optimization |

Part 2 – Transforms |
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16 | October 5 | Ma | Where Nature Does or Calls for the Fourier Transform, Definition of FT, Notations, Symmetry and FT, Interpretation of FT |

17 | October 7 | Ma | Some Useful Functions and Calculating Their FTs |

18 | October 10 | Ma | Convolution, Correlations and the Central Limit Theorem |

19 | October 12 | Ma | LTI Systems, More on Convolution, FT as a Linear System, What is Special about e^{-i2πxy}? |

20 | October 14 | Ma | Convolution Theorem and other Fourier Theorems |

21 | October 17 | Ma | The δ-Function, Distributions and Generalized Functions, Re-defining the FT |

22 | October 19 | Ma | Discrete Fourier Transform and Cyclic Convolution |

23 | October 21 | Ma | The Fast Fourier Transform Algorithm |

24 | October 24 | Ma | The Sampling Theorem, Ghost Function and Nyquist Frequency |

25 | October 26 | Ma | Drawbacks of the FT, Wavelets, Continuous Wavelet Transforms, Wavelet Transform as a Cross-correlation and Constant-Q Filtering |

26 | October 28 | Ma | Discrete Wavelet Transforms and Orthogonal Wavelet Decomposition, Multi-Resolution Analysis |

27 | October 31 | Ma | More on Multi-Resolution Analysis, Scaling Function, Digital Filtering |

28 | November 2 | Ma | Haar Wavelets, Filters, Filter Banks, Multistage Filter Banks and Perfect Reconstruction |

29 | November 4 | Ma | Medical Physics Applications of Fourier and Wavelet Transforms |

30 | November 7 | Ma | Exam on Transforms |

Part 3 – Statistics |
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31 | November 9 | Zhou | Introduction to Statistics: Population, Sample, Randomized Trials, Descriptive Statistics, Grouped Data and Graphical Methods |

32 | November 11 | Zhou | Introduction to Probability: Definitions and Notations, Conditional Probability, Bayes Rule, ROC Curves |

33 | November 14 | Zhou | Random Variables, Distribution Convergence, Discrete Probability, Binomial Distribution |

34 | November 16 | Zhou | Continuous Probability, Normal Distribution |

35 | November 18 | Zhou | Estimation: Mean and Variance of a Distribution, Binomial Distribution, One-Sided Confidence Interval |

36 | November 21 | Zhou | Hypothesis Testing: General Concepts, One-Sample t-Test |

37 | November 23 | Zhou | Hypothesis Testing: Sample Size Determination, Relationship between Hypothesis Testing and Confidence Interval, t-Tests for Two Samples and for Two Independent Samples, Interval Estimation |

November 24-25 | Thanksgiving Holiday | ||

38 | November 28 | Zhou | Hypothesis Testing: Testing for Equality of Two Variances, Two-Sample t-Test for Independent Samples with Unequal Variances, Outliers, Estimation of Sample Size and Power for Comparing Two Means |

39 | November 30 | Zhou | Non-Parametric Methods: Sign Test, Wilcoxon Signed-Rank Test, Wilcoxon Rank-Sum Test |

40 | December 2 | Zhou | Hypothesis Testing of Categorical Data: Fisher's Exact Test, McNemar's Test, RxC Contingency Tables, Χ^{2} Goodness-of-Fit, Kappa Statistic |

41 | December 5 | Zhou | Regression and Correlation Methods: Fitting Regression Lines, Assessing the Goodness-of-Fit of Regression Lines, Stastistical Inference, Multiple Regression |

42 | December 7 | Zhou | Multi-sample Inference, One-way Analysis of Variance, Fixed Effects Model |

43 | December 9 | Zhou | Hypothesis Testing in One-way ANOVA, Two-way Analysis of Variance, the Kruskal-Wallis Test, the Random Effects Model |

44 | December 12 | Zhou | Introduction to Survival Analysis, Estimation of Survival Curves, Kaplan-Meier Estimator, Log Rank Test |

45 | December 14 | Zhou | Exam on Statistics |

46 | December 16 | Ma | Class Wrap-up (No Final Exam) |