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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
2. Arrays and Other Collections
2.1. Introduction to Arrays
2.2. Multi-dimensional Arrays
2.3. Tuples
2.4. 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. Vectorized Functions
6.3. Logical Indexing
7. Special Number Types
7.1. Arbitrary Precision Integers
7.2. Arbitrary Precision Floats
7.3. Complex Numbers
7.4. Rational Numbers
7.5. Arrays of Special Numbers
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. Composite Types and Objects
12. Computational Geometry
12.3. Convex Hull
12.4. Line-segment Interactions
12.5. 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. Graphs
15.1. Graph Basics
15.2. Graph Algorithms
16. Sparse Matrices
16.1. Matrix Designs
16.2. Sparse Matrices in Julia
16.3. Application; Graphs
16.4. Application; Google Page Rank
17. Optimization
17.1. Gradient Based Optimization
17.2. Optim Package
18. Appendices
18.1. Floating Point Arithmetic
18.2. Algorithmic Efficiency
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Symbolic Algebra
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