MCS 320: Introduction to Symbolic Computation

When and Where

Semester: Spring 2009
Meeting time: M W F 9:00 - 9:50 am               
Meeting place: SCE 408

Instructor

Name: Alexey Ovchinnikov
E-mail address:
URL: http://www.math.uic.edu/~aiovchin
Office location: SEO 608
Office hours: M W F 10:00 - 10:50 am or by appointment
Office telephone number: (312) 996-8612

Course Objectives

This course introduces students to symbolic computation. This includes introduction to computer algebra systems (such as Maple), symbolic computation, and the mathematical algorithms employed in such computation, with examples and applications to topics in undergraduate mathematics.

Prerequisite

Grading

The grade will be given on the basis of quizzes (10%) given in class without prior announcement, two projects (15% per each), two written tests during the semester (15% per each), and written final exam (30%).

Text

Introduction to Maple by Andre Heck, 3rd Edition, Springer-Verlag, 2003. This book is only recommended and NOT required.

You are expected to do the homework given at the end of lecture notes for each class and read the lecture notes before the corresponding classroom discussion.

Part I: First Steps with Maple

• L-1: Introduction to Computer Algebra; Maple worksheet.
• L-2: Getting Started and Getting Help; Maple worksheet.
• L-3: Exact and Floating-Point Numbers; Maple worksheet.
• L-4: Algebraic and Complex Numbers; Maple worksheet.
• L-5: Assignment and Unassignment; Maple worksheet.
• L-6: Evaluation and Names of Variables Maple worksheet.
• L-7: Types, Attributes, Properties, and Units Maple worksheet.
• L-8: I/O Formats and Files Maple worksheet, the files mysum (Maple procedure) and mydata.txt .
• L-9: Code Generation and Connectivity Maple worksheet, and the file hello.dll (for Windows).

Part II: Polynomials and Rational Expressions

• L-10: univariate and multivariate polynomials; Maple worksheet.
• L-11: rational expressions; Maple worksheet.
• L-12: representations of expressions; Maple worksheet.
• L-13: substitution, expansion, and factorization; Maple worksheet.
• L-14: normalizing, collecting, and sorting ; Maple worksheet.