Computer Algebra Systems (Math 119)

Syllabus: Computer Algebra Systems (Math 119)

Course Description: This one hour, one credit course has been designed as an introduction to computer algebra, or symbolic algebra systems, using the application Mathematica. The focus is immersive learning engagement in using computational calculation and graphic tools in scientific and technical problem solving.

Learning Objectives: Upon successful completion of this course, the student should be able to use Mathematica as a mathematical computing package to support their numerical and symbolic computing efforts in the physical sciences, engineering and social sciences. The emphasis will be on how to gain facility in using it as a mathematical and scientific calculator, scripting engine, and as an end-user computer progarmming language (EUP).

1. Familiarization and Overview via Review of Intermediate Algebra

Tool package: Workspace Access & Use, Control and Management

Concepts: Numbers, Arithmetic; Basic Geometry, Algebra, Trigonometry

2. Calculations with Manipulations of Data Types, Structures and Collections

Numbers, Symbolizations, Variables, Expressions, Formulas, Equations
Lists, Vectors, Matrices, Tables, sigma-pi reductions, Computational Statistics
Functions and Functional Programming, Recursion, Algebraic Calculus
Graphics, Plots, Presentation and Visualization Graphics

3. End User "Programming" (EUP) and Scripting for Science and Technology Calculations

Procedural and Imperative, Program Control Structures, Patterns
Recursive Programming, Divide and Conquer, Greedy Algorithms
Rule-based Programming & Table-driven programming
Graphics Programming, Animation

4. Advanced Topics (if time permits)

Front Ends, Interfacing to the Package, Integration with other CAS (e.g. Excel)
3-D Graphics, Simulations
Packages, "Modular" Programming
Multi-paradigm Script Programming
Matrix Computation, Analytics, Numerical Analysis

Textbook (required)
Don, Eugene; Mathematica (Second Edition); McGraw Hill; ISBN: 978-0-07-160828-2

Grading Policy: All students are expected to attend all lectures. Students are expected to do most of the programming exercises outside of the lecture hours. There will be four, equally weighted exams. In addition, projects and homework will be periodically assigned.

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