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There are some things that you absolutely have to use computers for in mathematics.
2. Computers are used to extend the number of examples of graphs of different kinds of math equations available to students. This includes 2-D and 3-D graphs, both static and animated.
3. Certain kinds of equations cannot be solved using algebra - they have to be solved numerically using a computer. For instance, there is no algebraic way to solve a simple equation like x2 = sin(x), the solution must be approximated using numerical methods.
4. Small 2 x 2 or 3 x 3 systems of equations can be solved by hand, but large systems of equations require the use of a computer to be solved.
5. Determinants and inverses of Small 2 x 2 or 3 x 3 matrices can be solved by hand, but large matrices require the use of a computer.
6. Statistics rely heavily on computers. As a simple representative example, it is suggested that students be introduced to linear regression. More is covered on linear regression in the section on downloading and working with data.
7. For high school calculus classes, some kinds of integrals have no closed form and their solutions must be approximated using numerical methods on a computer. This skill is not presented here but is covered in the section on advanced applications.
1. Factoring and Prime Numbers
This is a simple lesson plan that shows how to factor numbers at the Linux command line using "factor" and "seq".
X Windows: Factoring Numbers
Server Based CGI: ICM, Polynomial Factoring Demo
server based CGI: WIMS, Factoring Numbers and
Prime Number Generator (Java applet)
2. Graphing Equations
console or X Windows: GNU Emacs Calc Mode
X Windows/SVGAlib: Basic Gnuplot Commands
X Windows/SVGAlib: Introduction to Gnuplot
X Windows: geg - A GTK+ Equation Grapher
Server Based CGI: ICM, Curve Plot Demo
Based CGI: WIMS, 2D plots - Tracs anims
emulation: Graphing Using a Spreadsheet
3. Solving Equations Numerically
Server Based CGI: ICM, Maxima Demo
solve(3*x+2=0); solve (x^2+3*x+2=0); solve (3*x*y+1 = x + y,y);
Server Based CGI: MathServ, Solving a Polynomial Equation
Server Based CGI: WIMS, Numerical Calculator
to solve sin(x) = cos(x) between x = -1 and x = 1,enter the following command in the Numerical Calculator window:
Server Based CGI: WIMS, Function Calculator
emulation: Solving Equations Numerically Using a Spreadsheet
4. Solving Systems of Equations
This is a lesson plan for solving systems using matrices in Lotus 123. Lotus 123 can be emulated with dosemu or wine. It can easily be adapted to a lesson plan for a Linux spreadsheet.
server: WIMS, Linear solver
5. Working with Matrices
Server Based CGI: ICM, Maxima Demo
A:matrix([1,2],[3,4]); # define A as a 2x2 matrix determinant(A); # compute the determinant of A transpose(A); # compute the transpose of A B:invert(A); # define B as the inverse of A A.B; # multiply A times B
X Windows: DrGenius
Server Based CGI: WIMS, Matrix multiplier
Server Based CGI: WIMS, Matrix calculator
6. Linear Regression
Gnuplot can be used for linear regression. Put the following x-y data pairs in a file called "test.dat".
1 1 2 2 4 3 5 6Run Gnuplot. At the Gnuplot prompt execute the following commands:
f(x) = a*x + b # define a linear function fit f(x) 'test.dat' via a,b # compute the regression coefficients a,bGnuplot will converge on the regression coefficients and you will see the output:
Final set of parameters ======================= a = 1.1 b = -0.3You can plot the polynomial and the data with the command:
plot f(x), 'test.data'
emulation: Linear Regression Using a Spreadsheet
Martindale's Reference Desk: Mathematics Calculators
Download Maxima from a GNU mirror
Interactive Demos of Mathematical Computations (ICM)
Spreadsheets for Linux at LinuxLinks.com
Chris Browne's Page on Spreadsheets
Spreadsheets, Mathematics, Science, and Statistics
Introduction to Math and Spreadsheets
Spreadsheet Lesson Plans Grades 6-8
World Wide Web Interactive Mathematics Server (WIMS)