MATH 309: Computing in Mathematics

Prerequisites & Bulletin Description

Course Objectives

Students will learn to use Mathematica for interactive calculations, graphing and programming. Declarative programming style is emphasized. Methods covered will include:

  1. Algebraic simplification and expansion
  2. Graphing expressions in one and two variables 
  3. Differentiation and integration (numerical and symbolic)
  4. List construction and manipulation
  5. Graphing lists
  6. Structured programming with all standard control structures
  7. Use of text paragraphs to annotate notebooks

Students will be able to choose appropriately from these techniques to solve problems from calculus, and students will present their solutions as completely documented Mathematica notebooks.

Evaluation of Students

Students will be required to submit Mathematica notebooks throughout the semester demonstrating their mastery of increasingly complex techniques and documentation standards. Notebook problems will demonstrate student ability to select and use appropriate methods from Mathematica to solve mathematics problems and present their solutions clearly. Homework may be assigned as group projects; however student evaluation by notebooks done as homework will be supplemented by proctored examinations covering Mathematica methods.

Course Outline

Topics & Length
Topics Number of Weeks
Expressions including transcendental functions, text paragraphs 2
Graphing in one and two variables 2
Differentiation and integration (numerical and symbolic) 2
Lists 2
Structured programming 3
Solving problems using all the above. Some ideas from numerical analysis, statistics, etc. may be introduced here to illustrate uses of Mathematica 4

Textbooks & Software

There are many books on Mathematica, but the instructor should choose carefully. The majority are either too simple and omit programming or are too advanced for beginners. Some instructors have found the following satisfactory if a bit on the advanced side:

Ruskeep, Heikki, Mathematica Navigator, Academic Press, San Diego CA, 1999

The writers of Mathematica have prepared an inexpensive, encyclopedic volume that does not present the material in the order it is usually taught:

Wolfram,, The Mathematica Book, Wolfram Research, Champagne IL, 2002

Some students will want to use Mathematica at home. Students will not be required to purchase Mathematica, but a student version is usually available at the SF State Bookstore.

Submitted by: David Meredith 
Date: December 2, 2002