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Welcome to the Fall EMC2 Python Labs¶

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Lab 1: Introduction to Python, Part I
- What is Programming?
- Setting up Google Colab
  - Running Code in Cells
- Python Basics
  - Arithmetic
  - Output and Print Statements
  - Variables
- Task 1
- Python Types
- Booleans and Comparison Operators
- Conditionals
- Functions
- Task 2
- Task 3
- Task 4
- Compound Conditions
- Task 5
- Task 6
- Strings
- Task 7
- Task 8
- Lists
- Task 9
- Review
Lab 2: Introduction to Python, Part II
- Functions, Part 2
  - Global and Local Variables
- Task 1
- Lists
- Task 2
- Task 3
- For Loops
- Task 4
- Task 5
- Exceptions
- Task 6
- Task 7
- List Comprehension
- Task 8
- Task 9
- Task 10
Lab 3: Introduction to Python, Part III
- Function Docstrings
- Task 1
- Task 2
- Task 3
- Challenge Problems
Lab 4: Introduction to LaTeX
Lab 5: Matrix Operations and Intro to NumPy
- Nested For Loops
- Task 1
- Task 2
- Double and Nested List Comprehensions
- Task 3
- Task 4
- Intro to Numpy
- Task 5
- Vectors and Matrices
- Task 6
- Conclusion
Lab 6: The Caesar Cipher
- The Mod Operator
- Task 1
- Task 2
- Task 3
- Task 4
Lab 7: NumPy and Matrix Row Reduction
- NumPy
- Application: Matrix Row Reduction
- Task 1
- Task 2
- Task 3
- Challenge
Lab 8: The Vigenère Cipher
- Task 1
- Task 2
- Task 3
- Finding the key length
- Task 4
- Task 5
Lab 9: Solving Systems of Linear Equations
- Jacobi’s method
- Task 1
- Task 2
- Gauss-Seidel method
- Task 3
- Task 4
- Error and Convergence
- Task 5
- Cases where convergence isn’t reached
Lab 10: Counterexamples
- “Proposition” 1: Fermat Primes
- “Proposition” 2: Mersenne Primes
- “Proposition” 3: Prime Number Races
- “Proposition” 4: Cyclotomic Polynomials
Lab 11: Dimensional Analysis
- Balancing Units
- Rayleigh’s Method and the Buckingham \(\pi\) Theorem
  - A Simple Pendulum
- Task 1: Solve the System
- G. I. Taylor and the Atomic Bomb
- Task 2: Find the Exponents
- Task 3: Estimate the Energy Yield
Lab 12: Recursion
- Writing a Recursive Function
- Task 1
- Task 2
- Task 3
- Task 4
- Task 5
Lab 13: Linear Transformations
- Linear Transformations
  - Types of Linear Transformations
- Task 1
  - Compositions of Linear Transformations
- Affine Transformations
- Task 2
- Linear Transformations in 3-D
- Task 3
- Task 4
Lab 14: Applications of Eigenvectors
- Transition Matrices
- Task 1
- Eigenvalues and Eigenvectors
- Task 2
- Simulating Populations
- Task 3
- Black Bear Population Demo
- Task 4
- Task 5
Lab 15: The Euclidean Algorithm
- Task 1: Iterative GCD
- Task 2: Recursive GCD
- The Extended GCD Algorithm
  - Recursive Case
  - Base and Switch Cases
- Task 3: The Extended GCD, nonnegative inputs
- Task 4: The Extended GCD, general inputs
- Task 5
Lab 16: The Gram-Schmidt Process
- Task 1
- Task 2
- Task 3
Lab 17: Recursion Reloaded
- Systems of One-Way Roads
- Task 1
- Valid Paths
- Task 2
- A Problem with Recursion
- Task 3
- Task 4: Towers of Hanoi
Lab 18: Networks and Eigenvector Centrality
- Graph Theory Background
- Adjacency Matrices
- Task 1
- PageRank Centrality
- Task 2
- Task 3
- Task 4
- Task 5
- Conclusion
Lab 19: Cracking the Vigenère Cipher
- Task 1: Split the ciphertext
- Task 2: Measure letter frequencies
- Task 3: Maximize the dot product
- Task 4: Decrypt the ciphertext
Lab 20: Applications of SVD
- Application 1: Image compression
- Task 1
- Task 2
- Application 2: Principal Component Analysis (PCA)
- Task 3
- Task 4
Lab 21: Pandas
- DataFrames
- Task 1
- CSV Files
- Task 2
- Accessing Data
- Task 3
- Basic Data Manipulation
- Masking
- Task 4
- Basic Statistical Functions
- Task 5
Lab 22: The Lean Theorem Prover Part I
- Successor Function
- Task 1
Lab 23: The Lean Theorem Prover Part II
- Task 1
Lab 24: Least Squares Lab
- Polynomial Regression
  - Task 1
  - Task 2
  - Task 3
- Computing Linear Regression for Diabetes Data
  - Task 4
  - Task 5