An Introduction to Python Jupyter Notebooks

Table of contents :
PREFACE
JMM 2023
JNB LAB: Patterns
Patterns in Nature
Displaying an Image
Displaying a YouTube Video
Patterns in Societal Data
Reading in CPS Data from the Chicago Data Portal
Streamlining the Data
Simplifying the Column Names
Making a Scatterplot with OLS Regression Line
Patterns in Mathematics
Tracing Parametric Curves
Plotting Quadric Surfaces and Level Curves
Connecting Patterns in Mathematics to Patterns in Nature and Society
Identifying Streamlines of Polluted and Freshwater Flow
JNB Lab Solutions
Patterns in Nature
Patterns in Societal Data
Patterns in Mathematics
Connecting Patterns in Mathematics to Patterns in Nature and Society
PRE-COLLEGE - Wheaton College Team
Introduction
Elementary Blackboard Problems
Arithmetic
Positive and Negative Numbers
Addition
Subtraction
Multiplication
Division
Pascal’s Triangle
Fractions
Vectors
Subsets
Polar Coordinates
Cylindrical Coordinates
Symmetry
Fractals
Trees
Circuits
Beginning Python Programming
Getting Started with JNBs
Functions
numpy
The . extension
pandas
File upload
Exercises
matplotlib
for loops
Exercise
if conditional statements
Exercise
dataframes
Exercise
Glimpse of Chicago
Michael Jordan’s Greatest Scoring Game
How Bad is COVID-19?
Exercises
Mapping Famous Chicagoans
Predicting Exemplary Schools
Assignment
The Great Migration
Creating a Map from our Dataframe
ASSIGNMENT
The Chicago Hardship Index
Raw Data and Summary Statistics
Summary Statistics
K-Means Clustering
Arts in STEM (STEAM)
Pixel Images
Assignment
Word Clouds
Assignment
Name That Tune!
Assignment
Random Numbers and Pi
Assignment
Simulating Formula 1
Assignment
Solution to Exercises
Beginning Python Programming
Glimpse of Chicago
Arts in STEM(STEAM)
Simulating Formula 1
JNB LAB: After-School Program Demo
DEMO 1: City of Chicago Budget
Exercise
Demo 2 Pixel Images
Exercise
DEMO 3: Track NFL Player Positions
Exercise
Demo 4 Word Clouds
Exercise
Demo 5 Name that Tune
Exercise
JNB Lab Solutions
PYTHON PROGRAMMING GUIDE - Thomas VanDrunen, Yiheng Liang
Introduction
Introduction to Python
Expressions, types, variables, and statements
Conditionals and while loops
Functions
Anonymous (lambda) Functions
Lists and other indexables and iterables
Thinking through algorithms
Python libraries
Classes and objects
Section on numpy
Trouble shooting libraries
Working with Data
Introduction
An Overview of Data and Data Analysis
Data Operations: Importing and Exporting, Reading and Writing Data
One-dimensional data processing
Two-dimensional data processing
Exporting Data: Writing Data to A File
Introduction to Pandas
Data operations with pandas.Series
Data operations with pandas.Dataframe
Basics of matplotlib
Exercises
Solution to Exercises
Introduction to Python
Working with Data
An Overview of Data and Data Analysis
Data Operations: Importing and Exporting, Reading and Writing Data
Introduction to Pandas
Basics of MATPLOTLIB
JNB Lab: Introduction to Python
Doing it recursively
Exercises
Doing it by comprehension
Exercises
Doing it efficiently: Horner’s rule
Making other operations (requires calculus)
Exercises
Making a class
Exercises
JNB Lab Solutions
EXPLORATORY DATA ANALYSIS - Jonathan Zhu
Introduction to Part I
Why is EDA Important?
How Do We Do EDA?
About the Dataset
Data Investigation I
Cleaning Data
More Exercises
Plotting and Statistical Testing I
Plotting
One Numerical Variable: Histograms
One Categorical Variable: Count Plots
Two Numerical Variables: Scatterplots
One Categorical, One Numerical: Boxplots
Statistical Testing
T-tests
ANOVA
EDA Project
Solutions to Part I Exercises
Introduction to Part II
About the Dataset
What is EDA?
Why is EDA Important?
Integrating Domain Knowledge
Guiding Questions
What Makes EDA Here “Advanced”?
Data Investigation II
Setup
Simple Data Inspection
Dataframe Attributes
Finding NaN values
Removing NA Columns and Rows
Basic Transformations
Substitution
Generation
Outlier Removal
Illogical Value Removal
Advanced Transformations
Saving Data Transformations
EDA Project: Part 1
Plotting and Statistical Testing II
Plotting
Histograms
Barplots
Scatter Plots
Boxplots
Violin plots
Interpreting Plots
Statistical Testing
Numerical Comparisons
One Group Comparisons
Two Group Comparisons
Many-Group Comparisons
Categorical Analysis: Chi-Square Tests of Independence
Normality Tests
EDA Project, Part 2
Making EDA Reports
EDA Writing Principles
Introduction
Data Preparation
Results
Discussion
General Writing Tips
Notebook Preparation
Markdown Basics
Hiding Code
EDA Project, Part 3
Solutions to Part II Exercises
JNB Lab: Housing Equity Initiative
Introduction
Park district facilities in Ward 20
Tax Year 2019 Owner-Occupied Tax Sale Data for Ward 20
Low Income Tract Clustering
JNB Lab Solutions
Park District Facilities
Tax Year 2019 Owner-Occupied Tax Sale Data for Ward 20
Low Income Tract Clustering
PROBABILITY - Laura Gross, Yiheng Liang
Introduction
Random Numbers
Arbitrariness
Pseudo-randomness
Pseudo-random number generation in Python
True randomness
Exercises
Probability
Definitions and Facts
Addition rule
Multiplication rule
Simulation
Law of large numbers
Gambler’s fallacy
Exercises
Conditional Probability
Exercises
Probability Distributions
Uniform distribution
Normal distribution
Binomial distribution
Exercises
Random Walks
Exercises
Agent-based Models
Exercises
Mathematical Games
Craps
Choosing the Right One
Coin-flipping Game
Exercises
References
Solution to Exercises
Random Numbers
Probability
Conditional probability
Probability Distributions
Random walks
Agent-based models
Mathematical Games
JNB Lab: Homicides in Chicago
Historical Context
DATA VISUALIZATION
Monte Carlo Analysis
JNB Lab Solutions
STATISTICAL INFERENCE - Peter Jantsch, Claire Wagner
Introduction
About This Chapter
Statistics Packages in Python
Foundations of Statistical Inference
Sampling and the Central Limit Theorem
Confidence Intervals
Confidence Intervals in Python Libraries
Why Is It Called a Confidence Interval?
Exercise 1
The Central Limit Theorem for Discrete Numerical Random Variables
Confidence Intervals for Categorical Data/Proportions
Hypothesis Testing for Categorical Data
Statistical Decision-Making: The Hypothesis Test
The Wellcome Global Monitor Survey
Making a Hypothesis
How Much Evidence Do We Need?
The Test Statistic: Using Data to Decide
Making a Decision
Confidence Intervals for Proportions
Difference of Two Proportions
Using Python for the Test
Further Exploration of P-Values
Exercises
Exercise 1
Exercise 2
Hypothesis Testing for Numerical Data
The Palmer Penguins
The Student’s T-Distribution
The T-Test
The T-Test in Python
Exercise 1
Two-Sample T-Test
The Test Statistic
Large Sample vs. Small Sample
Robustness to Assumptions
Linear Regression
Simple Linear Regression
World Bank Development Indicators
Simple Linear Regression Models
Minimizing the Sum of Squares Error
Finding the Least Squares Line
R2 and Goodness of Fit Tests
Inference on Model Parameters
Model Diagnostics
Exercise 1
Multiple Regression
Dummy Variables
Model Diagnostics
Inference on Model Parameters
Exercise 2
Solutions to Exercises
Foundations of Statistical Inference
Exercise 1
1. Use the widget above to construct 25 different 90% confidence intervals for the average weekly wages of Premier League players. How many of the 25 contain the true population mean? Is this the number you expect? Would it be possible for exactly 90% of the intervals to contain the true population mean?
2. Choose your own confidence level, and construct a single confidence interval for the average weekly wages of a Premier League player. Describe your interval in a complete sentence.
Hypothesis Testing for Categorical Data
Exercise 1
1. Pick another country (perhaps your country of origin or another country you are interested in) and filter the observations to just include responses from that country.
2. Make a hypothesis about the proportion of all the people in your chosen country that have high trust in scientists. For example, do you think it is over 20%? Under 15%? Make any hypothesis you like.
3. Choose a level of α.
4. Compute the value of p.
5. Run a hypothesis test using statsmodels.
6. Write your conclusion in a complete sentence. Be sure to report the test statistic and the P-value. If you found a significant result, give a confidence interval for the proportion.
Exercise 2
1. Pick a second country of interest.
2. Write hypotheses to test whether the proportion of people in the first country with high trust in scientists is higher than the same proportion in the second country.
3. Choose a level of α.
4. Run the hypothesis test using statsmodels.
5. Write your conclusion in a complete sentence. Be sure to report the test statistic and the P-value. If you found a significant difference, give a confidence interval for the difference in proportions.
Hypothesis Testing for Numerical Data
Exercise 1
1. Find the average bill length for Gentoo penguins from the Encyclopedia of Life. Use this information to form null and alternative hypotheses, making sure to note the units.
2. What is the sample size you have? Does the distribution of bill lengths appear to meet the normality assumption needed to perform the T-test?
3. Perform the test and report the test statistic and P-value.
4. What do you conclude? If you find a significant difference, give a confidence interval for average bill length.
Linear Regression
Exercise 1
1. Make a scatter plot of the number of goals a team scored (goals_for) versus the number of points they accrued in the standings (points). How would you describe the relationship?
2. Fit a linear model to these two variables, and print out the summary.
3. Use the summary to write down the estimated slope and intercept of the model. Interpret these values in the context of the problem. How many points, on average, is each additional goal scored in the standings worth?
4. What is the value of r2? Does the model seem to be a good fit? Explain your reasoning.
5. Provide diagnostic plots and comment on the results.
6. Repeat this analysis with another variable or variables. Do your new models seem to be a better or worse fit? Why or why not?
Exercise 2
1. How many different levels (i.e., possible categories) are in the species variable? How does the software handle the species variable?
2. Are all the variables providing useful information in your model? How can you tell?
3. Describe the typical characteristics of a very large or very small penguin.
4. Provide diagnostics for your model and comment on the validity of the regression assumptions.
JNB Lab: The Framingham Heart Study
Part 1: Explore the data
Part 2: Two Sample T-tests
JNB Lab Solutions
Part 1: Explore the data
Part 2: Two Sample T-tests
APPLIED CALCULUS FOR DAILY LIFE - Wheaton College Team
Introduction
Linear Systems and the Two-commodity Model
Two-Commodity Model
Sensitivity Analysis
Marginal and Average Cost
Derivative Rules
Marginal Functions
Fixed Cost
Demand Function
Average Cost
Graphical Intersections
Exercises
Optimization and Object Design
Example 1: Cathedral Door
Example 2: Office Space Design
Exercises
Optimization and Cobbs-Douglas Production
Exercises
Related Rates and Volumes
Exercise
Related Rates with Trig Functions and Football
Definition of Trig Functions
Derivatives of basic trig functions
Example
Radian Measure
Example
Python trig functions
Example
Questions
Exercises
Probability Distributions and Drive Thrus
Introduction
Distributions
Use of Random Numbers
A=Length of time before next arrival
O=length of time to place an order
Exercises
Normal Distribution and Process Control
Derivatives of Exponential Functions
Rule of 68-95-99.7
Exercises
Partial Derivatives and OLS Regression
Exercises
Area Between Curves and the Gini Index
Computing Area Between Two Curves
Example
Lorentz Curve and GINI Index
Exercises
Integral Test and Income Streams
Integral Test
P-Series
Income Streams
Exercises
Ordinary Differential Equations and Exponential Growth/Decay
Initial Value Problems
Separation of Variables
Exponential Growth
Exponential Decay
Exercises
Solutions to Exercises
Linear Systems and the Two-Commodity Model
Marginal and Average Cost
Optimization and Object Design
Optimization and Cobbs-Douglas Production
Related Rates and Volumes
Related Rates with Trig Functions and Football
Probability Distributions and Drive Thrus
Normal Distribution and Process Control
Partial Derivatives and OLS Regression
Area between curves and the GINI index
Integral Test and Income Streams
Ordinary Differential Equations and Exponential Growth/Decay
JNB Lab: Calculus of Entropy in Daily Life and Monte Carlo Simulations
Derivative Optimization
Exercises
Series
Exercises
Probability Distributions
Exercises
Monte Carlo Simulation
Exercises
Random Number Simulation of a Drive-thru
Model Distributions
A=Length of time before next arrival
O=length of time to place an order
P=length of time to pay for the food
By Cash
By Credit
F=length of time to pick up food
JNB Lab Solutions
CALCULUS - Inne Singgih
Introduction
Functions
Function Definition and Terminology
Function Behaviors
Increasing, Decreasing, and Constant Function
Concave Up and Concave Down Function, Inflection Point
Common Functions (Linear, Exponential, Logarithm, Logistic)
Linear Functions
Exponential Functions
Logarithm Functions
Logistic Functions
Function Operations, Compositions, and Inverse
Function Operations
Function Compositions
Inverse Functions
Exercises
Limits, Continuity, and Rates
Limits
Limit Properties
Continuity
Intermediate Value Theorem
Measures of Change over an Interval
Measures of Change at a Point
Secant and Tangent Lines
Exercises
Derivatives
Derivatives and Derivative Notations
Properties, Formulas, and Rules
Derivative Properties
Basic Derivative Formulas
Product, Quotient, and Chain Rule
Derivative Rules - Examples and Code
L’Hospital’s Rule and Indeterminate Forms
Derivative Graphs
Increasing and Decreasing
Concave Up and Concave Down
Extrema
Definition
Extreme Value Theorem
Finding Extrema
The Mean Value Theorem
Linearization
Implicit Differentiation
Exercises
Integrals
Antiderivatives and Indefinite Integrals
Properties of the Indefinite Integral
Basic Antiderivative Formulas
Integration by U-substitution
Integration by Parts (IBP)
Area Problem and Definite Integrals
Properties of Definite Integral
Fundamental Theorems of Calculus (FTC)
FTC Part 1
FTC Part 2
Improper Integrals
Average Value
The Mean Value Theorem for Integrals
Area Between Curves
Exercises
Parametric Equations
Parametric Equations - Curves and Tangents
Parametric Curves
Tangents with Parametric Equations
Parametric Equations - Area and Arc Length
Area with Parametric Equations
Arc Length with Parametric Equations
Polar Coordinates - Conversion and Tangents
Polar to Cartesian Coordinates Conversion
Cartesian to Polar Coordinates Conversion
Equations Conversion
Tangents with Polar Coordinates
Polar Coordinates - Area and Arc Length
Area with Polar Coordinates
Arc Length with Polar Coordinates
Exercises
Sequences and Series
Sequences
Properties of Sequences
Limit of Sequences
Theorems
Series
Convergence and Divergence of Series
Properties of Convergent Series
Geometric Series
Harmonic Series
Convergence Tests
Integral Test
The p-series Test
Comparison Test
Limit Comparison Test
Alternating Series Test
Absolute and Conditional Convergence
Ratio Test
Root Test
Convergence Test with Python
Power Series
Exercises
Solution to Exercises
Functions
Limits, Continuity, and Rates
Derivatives
Integrals
Parametric Equations
Sequences and Series
JNB LAB: Calculus Animations
Tangent Lines
Exercise
Riemann Sums
Exercise
Parametric Curves
Exercise
JNB Lab Solutions
LINEAR ALGEBRA - Soheil Anbouhi
Introduction
Linear Systems
Systems of Linear Equations
Linear Systems
Solving a Linear System
Exercises
Matrix Equation.
Vector Equation
Matrix Equation Ax=b
Exercises:
Solution set of linear Systems.
Homogenous Linear Systems
General Case: the solution set of non-homogenous linear system:
Matrices and Determinants
Matrix Algebra
Matrices
Basic Algebraic Operations
Matrix Product
Numerical Note
Transpose, Inverse and Trace of matrices
Transpose of a matrix
Inverse of a square matrix
Trace of Square Matrices
Determinant
Cofactor expansion
Determinants as Area or Volume
Numerical Note
Linear Transformations
Subspaces of Rn
Column space and null space
Basis, Dimension, and Rank
Exercises
Introduction to Linear Transformations
Motivation
The standard matrix representation of a linear transformation
Exercises
Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
Motivation
Eigenspace and characteristic polynomial
Exercises
Diagonalization
Computing powers of a matrix
Diagonalization
Diagonalization as a change of basis
Exercises
Discrete Dynamical Systems
Modeling Dynamical Systems as sequence of linear systems
Long-term behavior of dynamical systems
Exercise
Orthogonality
Inner Products and Orthogonality
Inner product
Angles and Orthogonality
Exercises
Orthogonal Projection
Orthogonal Set
Orthogonal Projections onto 1-dimensional spaces
Orthogonal Projections onto a general subspace
The Best Approximation Theorem
Exercises
The Gram–Schmidt Process
Idea: construction of an orthogonal basis from a basis with two elements
Construction of an orthogonal basis from a basis with three elements
The Gram_Schmidt Process
Exercises
Least-Squares Problems
Numerical Note
Exercises
Solutions to Exercises
JNB Lab: Linear Algebra
Linear Systems
Matrices and Determinants
Linear Transformations
Eigenvalues and Eigenvectors
Orthogonality
JNB Lab Solutions
Linear Systems Solutions
Matrices and Determinants Solutions
Linear Transformations Solutions
Eigenvalues and Eigenvectors Solutions
Orthogonality Solutions
LINEAR ALGEBRA AND OPTIMIZATION FOR DATA ANALYSIS - Wheaton College Team
Introduction
OLS Linear Regression
Least-Squares Solutions
OLS LINEAR REGRESSION OPTIMIZATION PROBLEM
Minimizing the OLS Loss Function via Normal Equations
Example 2.1.
Equivalence of Gradient-Based Optimization
Example 2.2.
Exercises
K-means Clustering
Clustering of Data
Optimization by Gradient Descent
Example 3.1.
Coordinate Descent
Optimization by Coordinate and Block Descent
Example 3.2.
Block Descent
K-MEANS CLUSTERING OPTIMIZATION PROBLEM
Example 3.3.
Proof of Block Descent’s Stepwise Minimization of J
Exercises
Dimension Reduction by Principal Component Analysis
Variance and Covariance for Mean-centered Data
Covariance Matrix
Example
Projected Variance
Example 4.2.
Maximization of Projected Variance by Principal Component Analysis
Exercises
Binary Classification of Labeled Data by Support Vector Machines
Intuition Underlying SVM
Mathematical Formalism
Separating Hyperplanes
Signed Distance
Optimization for Linearly-Separable Data
Optimization for Non-Separable Data
Exercises
Conclusion
References
Acknowledgements
Solution to Exercises
OLS Linear Regression
K-means clustering
Dimension Reduction by PCA
Binary Classification by SVM
JNB LAB: Linear Algebra for Data Analysis
Exercise
K-Means Clustering
Assignment
PCA
Exercise
Support Vector Machines
Image Recognition
Exercise
JNB Lab Solutions
Section 1 Exercise
Section 2 Exercise
Section 3 Exercise
Section 4 Exercise
DIFFERENTIAL EQUATIONS - Rachel Petrik
Overview of Chapter
Introduction to Differential Equations
Basic Terminology
Example 1
Example 1 (continued)
Example 1 (continued)
Example 2
Exercises
First-Order Differential Equations
Separable First-Order Differential Equations
Linear First-Order Differential Equations
Slope Fields
Autonomous Equations
Exercises
Second-Order Differential Equations
General Theory
Linear Homogeneous Differential Equations with Constant Coefficients
Nonhomogeneous Linear Equations and Undetermined Coefficients
Exercises
Systems of First-Order Differential Equations
Introduction to Systems of Linear Differential Equations
Solving Homogeneous Linear Systems with Constant Coefficients
Solving Non-Homogeneous Linear Systems with Constant Coefficients
The Phase Plane for Autonomous Systems
Geometric Behavior of Homogeneous Linear Systems
The Phase Plane for Nonlinear Autonomous Systems
Exercises
Laplace Transforms
Introduction to Laplace Transforms
The Inverse Laplace Transform
More Laplace Transforms & the Heaviside Function
Exercises
Solutions to Exercises
Section 2 Solutions
Section 3 Solutions
Section 4 Solutions
Section 5 Solutions
Section 6 Solutions
JNB Lab: Differential Equations
Chapter Review
Section 2 Questions
Section 3 Questions
Section 4 Questions
Section 5 Questions
Section 6 Questions
Python Questions
First and second order equations
Direction Fields
Phase Planes and Phase Portraits
Nullclines
Laplace Transforms
JNB Lab Solutions
Chapter Review
Section 2 Questions
Section 3 Questions
Section 4 Questions
Section 5 Questions
Section 6 Questions
Python Questions
First and second order equations
Direction Fields
Phase Planes and Phase Portraits
Nullclines
Laplace Transforms
DIFFERENTIAL EQUATIONS FOR THE BENEFIT OF SOCIETY - Wheaton College Team
Introduction
Logistic Growth and COVID-19
Introduction
Exponential Growth
Logistic Growth Model
Exercises
Reference
The Basic SIR Model
Introduction
Numerical Solutions
Exercises
Cholera in Haiti
Introduction
SIR Model
Exercises
References
CWS Model of Alzheimer’s Disease
Introduction
Simple Model of the Great Lakes
The CWS Model
Equilibrium Analysis
Parameter Estimation
A Simplified CWS Model
Analysis of Treatments
Treatment 1
Treatment 2
Conclusion
Exercises
References
Gravity Fed Water Delivery
Introduction
Derivation of Bernoulli’s Equation
Application to Gravity-Fed Water Delivery Systems
Basic Case
Break-Pressure Tanks
Water-Flow Rates
Viscous Flow in Pipes
Head Loss
Reynold’s Number
Laminar Flow
Turbulent Flow
Pipe Selection
Designing a System
Case Study: Honduras
Further Directions
Exercises
References
Earthquake Resistant Construction
Introduction
The Fundamental Equation of Structural Dynamics
Homogeneous Equation
Damping
Forcing and Resonance
Blast Loading
Convolution Integral Method
The Laplace Transform Method
Ground Motion
Two Degree of Freedom Models
Undamped Two-Story Building with Ground Motion
2-DOF Forced Free Vibration
Solving Undamped 2-DOF Systems
One Story Damped-Building with Ground Motion and a Tilting Tower
References
Solutions to Exercises
Logistic Growth and COVID-19
The Basic SIR Model
Cholera in Haiti
CWS Model of Alzheimer’s Disease
Gravity-Fed Water Delivery
Earthquake Resistant Construction
JNB Lab: HIV-AIDS
Introduction
UNAIDS Fact Sheet
Perelson’s Immunological HIV Model
Equilibrium Analysis
Analysis in Python
Sensitivity Analysis
Exercises
Bibliography
JNB Lab Solutions
COMPLEX VARIABLES IN GROUNDWATER MODELING - Wheaton College Team
Setting the Scene
Complex Analysis Background
The Complex Function f(z)
Exercises
The Derivative f'(z)
Exercises
The Cauchy-Riemann Equations
Polar Form of the Cauchy-Riemann Equations
Exercises
Harmonic Conjugates
Example
Exercises
Orthogonality
Exercises
Idealized Groundwater Flow
Two-Dimensional Flow and the Continuity Equation
Exercise
Darcy’s Law and the Velocity Potential Φ
Exercises
The Stream Function Ψ and Complex Potential Ω
Example
Exercise
Uniform Flow
Exercise
Sources and Sinks
Example
The Rankine Oval
Exercises
Contaminant Extraction Modeling
Model Assumptions
Methods
Model Output
Sensitivity Analysis
Discussion
Exercises
Supplemental JNBs
References
Solutions to Exercises
JNB LAB: Complex Potentials and Contaminant Flow
Complex Potentials
Introduction
Uniform Flow
Source
Five-Spot Pattern
Exercises
Fischer-Calo Contaminant Model
Setting the Scene
Model
Exercise
JNB Lab Solutions
Complex Potentials
Fischer-Calo Contaminant Model
ADVANCED DATA ANALYSIS - Jonathan Zhu, Claire Wagner, Ying Li
Introduction
Preprocessing
Tasks
Levels of Processing
Procedures
Stemming
Tokenizers
Named Entity Recognition
String Operations
About Text Data
Transformation
Vectorizations
Bag of Words
One-Hot Vectors
Numeric Count Vectors
Document-Term Matrices
N-Grams
Probabilistic Language Modeling
Natural Language Generation
Features
TF-IDF (Term Frequency, Inverse Document Frequency)
Feature Effectiveness
More Exercises
Document Embedding
Universal Sentence Encoder
Classification of Texts
A Machine Learning Overview
The Algorithms
The Perceptron
Naive Bayes Algorithms
Ridge Classification
More Exercises
Evaluating Classification
The ROC Curve
Multiclass Classifiers
One vs Rest
One vs One
More Exercises
Applications
Classifying a given text
Similarity Retrieval
More Exercises
Solutions to Exercises: Sections 1 to 4
Preprocessing
About Text Data
Document Embedding
Solutions to Exercises: Sections 5 to 7
Classification of Texts
Evaluating Classification
Applications
JNB Lab: United States Grant Data
Lab Exercises, Part 1: Supervised Learning and Vectorizations
Unsupervised Learning
Lab Exercises, Part 2: Unsupervised Learning
Lab Exercises, Part 3: Similarity
Generative AI and Language Models
Lab Exercises, Part 4: Generative AI and Language Models
JNB Lab Solutions
Lab Exercises, Part 1: Supervised Learning and Vectorizations
Unsupervised Learning
Lab Exercises, Part 2: Unsupervised Learning
Lab Exercises, Part 3: Similarity
Generative AI and Language Models
Lab Exercises, Part 4: Generative AI and Language Models
COMPLEX SYSTEMS - Wheaton College Team
Introduction
Setting the Scene
Complex System Science
Fundamental Concepts
Homogeneity of Constituent Parts
Exercise
System Classification
Open, Closed, and Isolated Systems
Random, Correlated and Coherent Systems
Emergent Global Behavior
Exercises
Linearization
Logistic Growth
Exercises
Bifurcations
Exercises
Normal vs Power Law Behavior
Exercise
Mathematical Concepts from Equilibrium Statistical Physics
The Hamiltonian
Spring Mass Problem
Total Energy (Hamiltonian)
Properties of the 1D Hamiltonian Dynamics
Exercises
Ising Spin Models and Entropy
Isolated Paramagnetic Spin Model
Canonical Ensembles
Grand Canonical Ensembles
Exercises
Maximum Likelihood and Phase Transitions
Fully Connected Ising Model
Exercises
Simplified Schelling Model and Segregation
Exercises
Societal Applications
Incarceration and Parole
Exercise
Urban Productivity
Exercise
Job Diversification
Exercise
A Simple IDP Response Model
IDP Data
Simplifying Assumptions on IDP System Complexity
A Basic Response Model
ENTROPY IN SOCIETAL APPLIATIONS
Exercises
References
Solution to Exercises
Section 2
Section 3
Section 4
JNB LAB: Complex Systems
Bifurcations in the Rozenzweig-MacArthur Predator Prey (RMPP) Equations
Exercises
Sensitive Dependence on Initial Conditions in a Fitzhugh Nagumo System
Exercise
Random Walks
Exercise
Scale Adjusted Metropolitan Index (SAMI)
Exercise
Internally Displaced People (IDP) in Tigray, Ethiopia
Exercises
JNB Lab Solutions
Bifurcations
Sensitive Dependence on Initial Conditions
Random Walks
Scale Adjusted Metropolitan Index
IDP
References