# Applied Symbolic Computation (CS 300)

Announcments  Lectures  Programs  Course Resources   Assignments and Solutions  Grading Policy
Course Description
This course covers the fundamentals of symbolic mathematical methods as embodied in symbolic mathematics software systems, including: fundamental techniques, simplification of expressions, solution of applications problems, intermediate expressions swell, basic economics of symbolic manipulation, efficient solution methods for large problems, hybrid symbolic/numeric techniques.
Course Goals
To provide students with the skills, judgement, and spirit necessary to effectively use a symbolic mathematics system such as Maple. To learn the features and limitations of Maple and related systems. To see how Maple can be used to solve a wide range of computational and mathematical problems. To see how computational tools can be applied to various application domains such as cryptography, signal processing, robotics, algorithm design and analysis, code generation, algebra and number theory, and scientific problems. To reinforce, through computational examples, understanding of mathematical concepts learned in previous courses.
This term will focus on number theoretic algorithms, integer factorization, primality testing, and cryptography.
Course Objectives
• To be able to use Maple (or similar system) to solve computational and mathematical problems.
• To be able to write Maple scripts to perform and analyze a series of computations, and to extend the features of Maple to solve a problem of interest
• To use Maple to explore a mathematical theorem, example, or concept or other scientific or engineering problems.
• To appreciate the limitations and features (symbolic, numeric, mathematical, visual, programming) of a symbolic mathematics system such as Maple.
• To use and understand some fundamental algebraic computations and algorithms (e.g. Euclidean algorithm, modular arithmetic and the Chinese Remainder theorem, fast Fourier transform, Groebner bases).
• To understand the mathematics behind and be able to implement and analyze a variety of number theoretic and cryptographic algorithms.
Audience
Undergraduate computer science, mathematics, engineering, and science students interested in learning about and applying computer algebra systems, such as MAPLE, to various application areas (in particular number theory and cryptography). The course is appropriate for students interested in scientific programming and an introduction to the algorithms underlying systems like MAPLE. For computer science students, the course counts towards the numeric and symbolic computing track, and due to the emphasis on cryptography, the computer and network security track.
Prerequisites
Undergraduate data structures course (CS 260)
Courses in calculus (MATH 200 or equivalent), linear algebra (MATH 201 or equivalent), discrete mathematics (MATH 221 or equivalent).
Instructor
Jeremy Johnson
Office: 206 Korman Center
phone: (215) 895-2669
e-mail: jjohnson AT cs DOT drexel DOT edu
office hours: TBA. Additional hours by appointment.
TA
Aliaksei Sandryhaila
Office: Univ. Crossings 147 (CS Student Resource Center)
e-mail: aus23 AT drexel DOT edu
office hours: M 3:00-5:00.
Meeting Time
TR 12:30-2:00 in Univ. Crossings 153
Course Mailing List
cs300@cs.drexel.edu

Please use this list for questions and discussions related to the course. If you know the answer to someone's question, please feel free to jump in, as long as well it is not an answer to a homework problem. I will moderate the list so that frivolous mail and spam is not forwarded.
Textbook
1. David M. Bressoud, Factorization and Primality Testing, Springer, 1989.
2. Every student must have access to Maple version 10. Course notes will be provided on the web page as Maple worksheets that can not be read without Maple. Maple is available in the CS labs as well as Drexel labs, and the student edition is available at a reduced price.
3. Additional resources are listed below.

### Topics

1. Introduction to symbolic mathematics systems in general and Maple in particular.
2. Effective use of Maple.
3. Programming in Maple.
4. Integer and polynomial arithmetic and the FFT
5. Cryptography and Number Theoretic Algorithms.
• Euclidean algorithm, continued fractions, and fast exponentiation
• Modular Arithmetic
• RSA public-key cryptosystem
• Primality testing
• Algorithms for integer factorization

1. Class Participation (15%)
2. Three Homework assignments (45%)
3. Two Quizes (40%)
Assignments and exams will be returned on a regular basis to provide feedback to students. All students must do their own work. Any violation of this will result in a zero grade for the assignment. A second violation will lead to an F for the course.

Grades are based on a curve with the mean normalized to a B provided the mean performance shows competency of the material.

### Resources

Reference Books
1. Maple Getting Started Guide.
2. Maple Users Manual.
3. Maple Introductory Programming Guide.
Web Pages

Announcements ()

### Lectures

This list is subject to change.

### Programs and Worksheets

• line.mw - worksheet for lecture containing intro to Maple and problems with linear equations.
• euclid.mws - Worksheet on the Euclidean Algorithm
• power.mws - Worksheet on fast powering
• mod.mws - Worksheet introducing modular arithmetic, the Chinese Remainder algorithm (CRA), and modular algorithms
• imult.mws - Worksheet on integer multiplication
• karatsuba.mws - Worksheet on Karatsuba's integer multiplication algorithm

### Assignments and Exams

• Assignment 1 - Assignment 1 (15%) - Due May 5
• Assignment 2 - assign2.mw (15 %) - Due May 26
• Assignment 3 - Assignment 3 (20 %) - Due June 8 by 5pm
• Exam 1 - Studyguide 1 (20%) - in class on Thur. April 27
• Exam 1 (Extra problem) - See webct for exam instructions. Due Tue. May 16 at 11:55 pm.

### Solutions

• None yet.

Created: 9/26/05 (revised) by jjohnson@cs.drexel.edu