GS02-1183 — APPLIED MATHEMATICS FOR MEDICAL PHYSICS
Fall, 2016

Syllabus

Lecture Schedule, Location to be Determined

Class Date Instructor Topic
Part 1 – Linear Analysis and Optimization (Notes)
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
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
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, Χ2 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)
Last updated: 2016-09-21