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Programming for Mathematical Applications
1. Introduction to Julia
1.1. Julia as a Calculator
1.2. Variables and Assignments
1.3. Functions
1.4. For-Loops
1.5. Conditionals
1.6. While-Loops
1.7. Function Arguments
2. Arrays and Dictionaries
2.1. Introduction to Arrays
2.2. Multi-dimensional Arrays
2.3. Dictionaries
3. Plotting
4. Debugging
5. Random Numbers
5.1. Distributions
5.2. Histograms
5.3. Monte Carlo
6. Vectorization
6.1. Constructing Arrays
6.2. Array Functions
6.3. Logical Indexing
7. Data Types
7.1. Arbitrary Precision Integers
7.2. Arbitrary Precision Floats
7.3. Complex Numbers
7.4. Rational Numbers
7.5. Data Types of Arrays
8. Recursion
9. Linear Algebra
9.1. Matrix Operations
9.2. Special Matrices
9.3. Linear Systems and Regression
10. Strings and File Processing
10.1. String Basics
10.2. String Functions
10.3. File Processing
11. Structs and Objects
12. Computational Geometry
12.1. Convex Hull
12.2. Line-segment Interactions
12.3. Triangulations
13. Image Processing
13.1. Reading and Plotting Images
13.2. Image Scaling
13.3. Filtering
13.4. Fourier Transform
14. Differential Equations
14.1. Initial Value Problems
14.2. Higher Order Derivatives and Systems of ODEs
14.3. Boundary Value Problems
14.4. DifferentialEquations Package
15. Optimization
15.1. Gradient Based Optimization
15.2. Optim Package
16. Graphs
16.1. Graph Basics
16.2. Graph Algorithms
17. Sparse Matrices
17.1. Matrix Designs
17.2. Sparse Matrices in Julia
17.3. Application; Graphs
17.4. Application; Google Page Rank
18. Appendices
18.1. Floating Point Arithmetic
18.2. Algorithmic Efficiency
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