rramosp/20161.mmod

Tools for Mathematical Modelling

This course will have three themes, described below.

Grading

Exercises from each theme will weight 1/3 in the total final grade. Each exercise is to be delivered through a single IPython notebook and will be graded according to the following equally-weighted criteria (from 0 to 5):

• 1. Completion: it contains what was requested
• 2. Clean code: the code is clean, commented and understandable
• 3. Expressivity: exploits the notebook documentation capabilities to offer sufficient verbose decription
• 4. Difficulty: of the problem/dataset/algorithm/approach chosen

Dates

31/Mar: Drafts for exercises Theme 1
17/Apr: Exercises Theme 1: 1A + 1B
3/May: Drafts for exercises Theme 2
23/May: Exercises Theme 2
2/Jun: Drafts for exercises Theme 3
17/Jun: Exercises Theme 3

17/Jun: Classes end
20/Jun: Grade submissions closes

Drafts must include a description of the chosen use case (dataset/algorithm, etc.) for each exercise and a first approach (albeit incomplete) to the solution. Failure to deliver drafts will incur in a 50% penalty in the theme grade

Theme 1. Visualization

1.1 Introduction to Jupyter Notebooks Learn Python - Wakari Notebooks Gallery - Numpy Quickstart - Pandas Cookbook

1.2 Libraries: Matplotlib, Bokeh, Plotly Matplotlib Gallery - Bokeh notebooks Gallery - Plotly notebooks Gallery

1.3 Interactivity and Data Streaming: Bokeh Widgets - Bokeh server examples - Linking and brushing

1.4 Big Data Visualization Big Data plotting problems - Plotting NYC taxi data - Datashader

EXERCISE 1.A: Tell a story through data visualization in one notebook. The story must use:

• Pandas and Numpy for data loading and cleaning (see Pandas Cookbook - Chapter 7)
• Matplotlib and Plotly for creating several views on the same data (contours and scatters), sub-sampling data, show data interpolations
• Bokeh for Interactive multi-selection in subplots and interactive widgets

EXERCISE 1.B: Use datashader to build a meaningful visualization of at least 1 million data points

EXERCISE 1.C: Select time series data and build a data streaming example, using Bokeh or Plot.ly

SOME DATASOURCES: https://data.cityofboston.gov/ https://data.nasa.gov/ https://data.cityofchicago.org/ http://transtats.bts.gov/ http://catalog.data.gov/ http://www.kaggle.com example story Boston data

Theme 2. Computing for mathematical modelling

2.1 Symbolic Computing [SymPy Website] (http://www.sympy.org/) - SymPy Tutorial - Lecture Notes on SymPy

2.2 Solving ODEs ODEs in SymPy - Introduction to Differential Equations

2.3 Numerical methods SciPy Cookbook - SciPy Tutorial

2.4 Animating mathematical models Matplotlib animations

EXERCISE 2.A: Choose a problem solvable with ODEs:

• Define, solve and visualize a mathematical model
• If you use a numerical method, show first that the symbolic solver fails.

EXERCISE 2.B: Use matplotlib animations to:

• Create two animations illustrating key aspects of your model.

EXERCISE 2.C: Disseminate your work:

• Create a presentation from your notebook in 2.A)
• Use Git and nbviewer for publishing and sharing notebooks online.

Theme 3. Scaling computing

3.1 Vectorizing functions NumPy ufuncs

3.2 IPython parallelization IPython parallel

3.3 Python fast like C Numba Cython

3.4 Theano: Fast symbolic computing Theano

EXERCISE 3.A: Vectorization and Just in time compilation (in Problemset 03 A)

EXERCISE 3.B: Monte Carlo with IPython Parallel (in ProblemSet 03 B)

Extra grading:

• Run your code in Guane at www.sc3.uis.edu.co (5% additional in the total course grade for each exercise up to a maximum of 15%)
• Only valid for the following exercises: 1A, 2A, 3A, 3B