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, students’understanding of mathematical concepts learned in previous courses.
Course Objectives
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. 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.
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) and some knowledge of differential equations would be helpful.
Instructor
Jeremy Johnson
Office: 206 Korman Center
phone: (215) 895-2893
e-mail: jjohnson @ cs.drexel.edu
office hours: TBA. Additional hours by appointment.
TA
Servesh Tiwari
Office: Univ. Crossings 147 (CS Student Resource Center)
e-mail: st86@drexel.edu
office hours: R 2:00-4:00.
Meeting Time
TR 12:30-2:00 in Univ. Crossings
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
Every student must have access to Maple version 10.  Maple is available in the CS labs as well as Drexel labs.  Course notes will be provided on the web page as Maple worksheets that can not be read without Maple. Additional resources are listed below.  Students will be provided with a copy of the student edition of Maple 10 (either for free or at a reduced price - this is being set up).

  1. Maple Getting Started Guide.
  2. Maple User Manual.
  3. Maple Introductory Programming Guide.
  4. Maple Advanced Programming Guide.
  5. The text will be supplemented by several journal articles and readings from texts available in the library.

Topics

  1. Introduction to symbolic mathematics systems in general and Maple in particular.
  2. Effective use of Maple.
  3. Scientific programming in Maple.
  4. Cryptography and Number Theoretic Algorithms.
  5. Integer and polynomial arithmetic and the FFT
  6. Code generation (e.g. finite diferences schemes, automatic differentiation)
  7. Solution of systems of polynomial equations (introduction to Groebner Bases).
  8. Applications of Groebner Bases

Grading

  1. Homework assignments (55%)
  2. Midterm (25%)
  3. Final Exam (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.

Resources

Reference Books
  1. Maple Getting Started Guide.
  2. Maple Users Manual.
  3. Maple Introductory Programming Guide.
  4. Maple Advanced Programming Guide.
  5. Cox, D., Little, J., and O'Shea, D. Ideals, Varieties, and Algorithms, Second Edition. Springer-Verlag, 1997.
Web Pages
  1. Waterloo Maple
  2. Maple Student Center
  3. Maple Essentials
  4. Maple Programming
  5. Maple Application Center
  6. SymbolicNet -- Symbolic Mathematical Computation Information Center

Look Here for Important Announcements

Announcements ()

Lectures

This list is subject to change.
  1. Week 1
    1. Sept. 27, 2005 (Course Introduction and Introduction to Maple)
    2. Sept. 29, 2005 (Experimenting with Maple)
  2. Week 2
    1. Oct. 4, 2005 (Sequences, Recurrences and Growth Rates)
    2. Oct. 6, 2005 (A Fast Algorithm to Compute Fibonacci Numbers)
  3. Week 3
    1. Oct. 11, 2005 (The Euclidean Algorithm)
    2. Oct. 13, 2005 (Modular Arithmetic and Fast Powering)
  4. Week 4
    1. Oct. 18, 2005 (Modular Algorithms)
    2. Oct. 20, 2005 (Fast Integer Arithmetic)
  5. Week 5
    1. Oct. 25, 2005 (No Class)
    2. Oct. 27, 2005 (Modular Algorithm for Integral Polynomial Multiplication)
  6. Week 6
    1. Nov. 1, 2005 (Review Midterm Exam)
    2. Nov. 3, 2005 (Review Midterm Exam)
  7. Week 7
    1. Nov. 8, 2005 (Fast Fourier Transform)
    2. Nov, 10, 2005 (FFT Based Polynomial and Integer Multiplication)
  8. Week 8
    1. Nov. 15, 2005 (Numeric Solution of Univariate Equations)
    2. Nov. 17, 2005 (Polynomial System Solving)
  9. Week 9
    1. Nov. 22, 2005 (Multi-Dimensional Newton's Method)
    2. Nov. 24, 2005 (Univ. Holiday - NO Class)
  10. Week 10
    1. Nov. 29, 2005 (Rings and Algorithms)
    2. Dec. 1, 2005 (The Division Algorithm)
  11. Week 11
    1. Dec. 6, 2004 (Groebner Bases)
    2. Dec. 8, 2004 (Polynomial System Solving)

Programs and Worksheets

Assignments

Solutions

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