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, judgment, 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, students’ understanding of mathematical concepts learned in previous courses.

This term, the course will focus on applications to algorithm design, generation, and analysis.

Course Objectives
Undergraduate computer science, mathematics, engineering, and science students interested in learning about and applying computer algebra systems, such as MAPLE, to various application areas. The course is appropriate for students interested in scientific programming and an introduction to the algorithms underlying systems like MAPLE.  The course counts towards the numeric and symbolic computing track for computer science students.
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).
Jeremy Johnson
Office: University Crossings 100C
phone: (215) 895-2669
office hours: T,R 10-11 and W 5-6. Additional hours by appointment.
Michael Andrews
Office: University Crossings 147 (Cyber Resource Center)
office hours: TBD.
Meeting Time
TR 11:00-12:20 in UC 153
Course Mailing List

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.

Every student must have access to Maple version 10. Maple 10 is available in the CS and Drexel computing labs. Students may also obtain a copy through IRT. Course notes will be provided on the web page as Maple worksheets that can not be read without Maple. Additional resources are listed below.
  1. Maple 10.
  2. Maple Getting Started Guide.
  3. Maple User Manual.
  4. Maple Introductory Programming Guide.
  5. Maple Advanced Programming Guide.
  6. Maple 10 Quick Reference Card - Windows Version.
  7. Maple 10 Quick Reference Card - Mac OS X Version.
  8. Maple 10 Quick Reference Card - UNIX Version.
  9. The text will be supplemented by several journal articles and readings from texts available in the library.


  1. Introduction to symbolic mathematics systems in general and Maple in particular.
  2. Effective use of Maple.
  3. Programming in Maple.
  4. Combinatorics and Analysis of Algorithms
  5. Asymptotic Analysis
  6. Integer and polynomial arithmetic.
  7. Cryptography and Number Theoretic Algorithms.
  8. Algorithm and Code generation
  9. Theorem Proving and Combinatorial Identities
  10. Other applications based on student interests.


  1. Homework assignments (60% - 4 X 15%)
  2. Midterm - in class using Maple (20%)
  3. Final Exam - take home due during the scheduled time of the final (20%)
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 may 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.


Reference Books
  1. Marko Petkovsek, Herbert Wilf, and Doron Zeilberger, "A = B", A K Peters, Ltd, 1996..
  2. Herbert Wilf, "generatingfunctionology", 2nd Ed., A K Peters, Ltd, 1994.. (3rd Ed. is available for purchase, and 2nd edition is available for download)
  3. Robert Sedgewick and Philippe Flajolet, "An Introduction to the Analysis of Algorithms", Addison-Wesley, 1996.
  4. Ronald L. Graham, Donald E. Knuth, and Oren Patashnik, "Concrete Mathematics: A Foundation for Computer Science", 2nd Ed., Addison-Wesley, 1994.
Web Pages
  1. Waterloo Maple
  2. Maple Student Center
  3. Maple Essentials
  4. Maple Programming
  5. Maple Application Center
  6. The Online Encyclopedia of Integer Sequences
  7. SymbolicNet -- Symbolic Mathematical Computation Information Center
  8. ECCAD - East Coast Computer Algebra Day
  9. IMACS Conferences on Applications of Computer Algebra

Look Here for Important Announcements

Announcements ()


This list is subject to change.
  1. Week 1
    1. Sept. 26, 2006 (FindMax, Permutations, Harmonic and Stirling Numbers)
    2. Sept. 28, 2006 (Generating Permutations)
  2. Week 2
    1. Oct. 3, 2006 (Dominoes and Fibonacci Numbers)
    2. Oct. 5, 2004 (The Euclidean Algorithm)
  3. Week 3
    1. Oct. 10, 2006 (Fast Integer Multiplication and Interpolation)
    2. Oct. 12, 2006 (Fast Powering and Binary Divide and Conquer Recurrences)
  4. Week 4
    1. Oct. 17, 2006 (Review Assignment 1)
    2. Oct. 19, 2006 (Recursive Data Structures and Algorithm Exploration)
  5. Week 5
    1. Oct. 24, 2006 (Counting Binary Trees)
    2. Oct. 26, 2006 (Generating Functions)
  6. Week 6
    1. Oct. 31, 2006 (Generating Functios)
    2. Nov. 2, 2006 (Midterm)
  7. Week 7
    1. Nov. 7, 2006 (Analysis of Quicksort)
    2. Nov. 9, 2006 (The Symbolic Method)
  8. Week 8
    1. Nov. 14, 2006 (The Symbolic Method)
    2. Nov. 16, 2006 ()
  9. Week 9
    1. Nov. 21, 2006 (Makeup lecture - assist with assignment 3)
    2. Nov. 23, 2006 (No Class)
  10. Week 10
    1. Nov. 28, 2006 (Probability Generating Functions)
    2. Nov. 30, 2006 (Bivariate Generating Functions)
  11. Week 11
    1. Nov. 28, 2006 (Asymptotic Analysis of Linear Recurrences)
    2. Nov. 30, 2006 (Stirlings Identity)

Programs and Worksheets



Created: 9/15/06 (revised 9/25) by