Arithmetic Through Linear Algebra Using Maple

By Gary A. Harris
Department of Mathematics
Texas Tech University
Lubbock, Texas 79409
g.harris@ttu.edu

This workbook is the major portion of a junior level course required of all students seeking secondary teacher certification at Texas Tech University. It is first and foremost a mathematics course driven by the mathematics content. In it the students review and reinforce their understanding of mathematical concepts from arithmetic through linear algebra. Students become familiar with the general capabilities of a CAS, and obtain experience employing these capabilities to solve mathematical problems in the context of MAPLE. In order to communicate with the program students obviously have to use the appropriate syntax; however, learning MAPLE syntax is never considered to be the main objective. We view MAPLE as one example of a computer algebra system (CAS) and focus on the general capabilities of a CAS and how these relate to the mathematics at hand.

Justification: Computer algebra systems are having a profound impact on curriculum and instruction of mathematics at all levels from grade school through graduate school. Some argue that the very nature of mathematics is being altered by CAS. In any event it is clear that the current and future students of mathematics must be familiar with the capabilities of this technology and have experience with its use.

Prerequisites: It is assumed the students are familiar with the traditional lower division college level mathematics content including differential, integral, and multi variable calculus and linear algebra.

Contents:

 1. Getting Started With Basic CalculationPDF MWS
 2. Elementary Number TheoryPDF MWS
  MAPLE Programming SupplementPDF MWS
  Technical TextPDF MWS
 3. Binomial Theorem and Pascal's TrianglePDF MWS
 Quiz 1PDF
 4. Elementary AlgebraPDF MWS
 Quiz 2PDF
 5. Basic of GraphingPDF MWS
 Quiz 3PDF
 6. Limits in CalculusPDF MWS
 7. Derivatives in Calculus PDF MWS
 Quiz 4PDF
 8. Integration in Calculus via AreaPDF MWS
 Quiz 5PDF
 9. Integration in Calculus via Anti-DerivativesPDF MWS
 Quiz 6PDF
10. Sequences and SeriesPDF MWS
11. Elementary Matrix ManipulationPDF MWS
12. Matrices and Linear SystemsPDF MWS
 Quiz 7PDF
13. Matrices and Vector SpacesPDF MWS
 Quiz 8PDF
14. Eigenvalues and EigenvectorsPDF MWS
 Quiz 9PDF