Intro. to Computing for Mathematics and Statistics
Course Outline
This course introduces students to computer-based problem solving techniques that can be used to approach problems in Mathematics and Statistics. Through a combination of lectures and laboratory sessions, students become familiar with a scientific computing environment that combines numeric and symbolic computation, high-level programming, scientific libraries, graphics, and a variety of visualization tools. Topics include:
1. Working with the Environment
a. Opening MAPLE
b. Saving your program
c. Getting help
2. Basic Aspects of Maple
a. MAPLE as a programming language
b. Variables, constants
c. Expressions and assignments
d. Lists
e. Sets
f. Arrays
3. Control Structures (looping, repetition, branching)
a. Do loop
b. For loop
c. If statement
d. Conditional and logical operators
4. Procedures
a. What a procedure is
b. Defining a procedure
c. Calling a procedure
d. Parameters and local variables
e. Library procedures, loading a package (example: Linear Algebra)
f. User-defined procedures
5. Data Structures
a. Expressions and operands
b. Strings
c. Lists
d. Arrays and tables
6. Plots and other Visualization Tools
a. Accessing the MAPLE plotting package
b. Plotting tabular data
c. Approximating curves and surfaces
d. The GRID and MESH objects
e. Animations: Display and Animate commands
f. Generating Reports
g. Converting MAPLE plots into images (such as gif, jpeg) and incorporating them into web pages
h. Putting MAPLE Notebooks on the Web
7. Recursion
a. Recurrence relations
b. Reduction formulas from integration
c. Sorting (bubble sort, quick sort)
d. Calculation of numbers with recursive formulas.
8. Math and Statistics Applications, including possibly topics from:
Algebra, Calculus, Probability and Statistics, Matrix Algebra, Trigonometry. Such topics may include, but are not limited to:
(Algebra) solve equations and systems of equations, simplify expressions, find roots of polynomials; (Calculus) calculate limits, find derivatives, compute finite sums, evaluate integrals; (Probability and Statistics) Generate and animate: Poisson distribution, exponential distribution, normal distribution, Pseudo-randomly generated data from distributions; (Matrix Algebra) Vectors, operations involving vectors (difference, dot product, cross product), Matrices, operations involving matrices (define a matrix, build a matrix from column vectors and from row vectors, add two matrices, multiply two matrices, add, multiply, divide entries of a matrix by a value, transposition, determinants); (Trigonometry) MAPLE’s trigonometry functions and examples.