Week 1: Introduction to Julia Programming Language - Overview of Julia: Features and Advantages - Setting Up the Julia Environment - Basic Syntax and Data Types - Writing and Running Your First Julia Program
Week 2: Control Flow and Functions - Conditional Statements and Loops - Defining and Calling Functions - Scope and Variable Lifetime - Introduction to Julia Modules
Week 3: Working with Arrays and Matrices - Creating and Manipulating Arrays - Basic Matrix Operations - Array and Matrix Indexing - Using the LinearAlgebra.jl Package
Week 4: Data Structures and DataFrames - Introduction to Data Structures in Julia - Working with Tuples, Dictionaries, and Sets - Introduction to DataFrames.jl - Basic Data Manipulation with DataFrames
Week 5: Introduction to Linear Algebra - Vectors and Matrices in Mathematical Programming - Matrix Operations and Transformations - Solving Linear Systems - Eigenvalues and Eigenvectors
Week 6: Complex Numbers and Trigonometry - Introduction to Complex Numbers - Operations with Complex Numbers - Trigonometric Functions and Identities - Applications of Trigonometry in Julia
Week 7: Set Theory - Introduction to Sets and Set Operations - Working with Sets in Julia - Venn Diagrams and Applications of Set Theory - Examples and Practice Problems
Week 8: Plotting and Visualization - Introduction to Plots.jl - Creating Basic Plots (Line, Bar, Scatter) - Customizing Plots (Titles, Labels, Legends) - Advanced Plotting Techniques
Week 9: Optimization and Numerical Methods - Introduction to Optimization Problems - Using the Optim.jl Package - Numerical Methods for Solving Equations - Gradient Descent Algorithm
Week 10: Capstone Project - Project Planning and Proposal - Implementing a Mathematical Programming Solution - Presenting Your Project - Course Review and Q&A