What This Document Is
These are lecture notes from MCS 320, Introduction to Symbolic Computation at the University of Illinois at Chicago. The notes focus on utilizing a specific computational software package – Maple – to explore advanced concepts in symbolic mathematics. This material delves into techniques for manipulating and simplifying complex mathematical expressions, going beyond standard polynomial algebra. It builds upon previously learned concepts and introduces methods for handling trigonometric and exponential functions within a symbolic computation environment.
Why This Document Matters
This resource is ideal for students currently enrolled in an introductory symbolic computation course, or those seeking to deepen their understanding of how to leverage software for mathematical problem-solving. It’s particularly valuable when you’re working on assignments that require precise symbolic manipulation, simplification of expressions, or the application of assumptions to arrive at solutions. These notes can serve as a helpful companion to textbook readings and in-class discussions, offering a focused perspective on practical application within Maple.
Topics Covered
* The ‘assume’ facility for defining and utilizing mathematical assumptions.
* Techniques for working with properties and queries within the software environment.
* Application of assumptions in arithmetic and root-finding algorithms.
* Simplification of expressions, including trigonometric and exponential functions.
* The use of ‘expand’ and ‘combine’ commands for expression manipulation.
* Exploring an algebra of properties and utilizing verification tools.
What This Document Provides
* A focused exploration of Maple’s capabilities for symbolic computation.
* Illustrative examples demonstrating the application of key commands and techniques.
* Guidance on how to impose constraints and assumptions to achieve desired simplifications.
* A discussion of how to utilize properties to solve mathematical problems programmatically.
* A foundation for more advanced work in areas like constrained optimization and term rewriting.