Mathematica Across the Curriculum

A case study in use throughout the mathematics major

Dr. Chris Lee
Associate Professor of Mathematics
Roanoke College

Some Background

Roanoke College

Liberal arts college in the Blue Ridge Mountains of SW Virginia

Approx. 2000 students

Department of Mathematics, Computer Science, and Physics

20 tenure track faculty

10-12 mathematics majors per year

Workload split between major and support courses

Mathematics Curriculum

Technology

Long standing committment to technology in the classroom

Not a question of if, but what.

Revision / Goals

As we revisited our mathematics curriculum over the last few years we identified the important goal of continuity between courses.

Question : Why aren't we applying this approach to our use of technology?

Pre-2008

Texas Instruments TI-89

Used throughout calculus series and random other courses     ← best crutch ever invented!

Mathematica

Used in "advanced" courses  ← when warranted?  misses some of the best features.

Other M_________ software

Used by random faculty, legacy of experiences at other colleges?  ← at a minimum this is
                                                                                                             confusing to students.

Solution:

Incorporate Mathematica throughout the curriculum

Students ability to use the software grows with the complexity of the problems

Ditch the innoculation model

proficiency with Mathematica only comes through repeated and frequent use.

difficult to learn Mathematica if your only goal is to learn Mathematica.

clear applications facilitate learning.

Calculus

Weekly labs

90 minutes  (in addition to three 60 minute class sessions)

students work through a Mathematica notebook

examples

lessons

problems

Calculus I Lab Example

Parametric equations - breaking the sound barrier

Discussion Question: What's going on at the extremes of the slider?  At values of the speed for which the circles no longer intersect would there still be a sonic boom?  Do we need to change something in the plot?

Calculus II Lab Example

Projectile Motion - Golf Drive

Questions: If the fairway is sloping down at 6 degrees, what is the furthest the golfer can hit the ball?   If the fairway is sloping down at 10 degrees and the pin is 2100 feet away, at what angle should the golfer hit the ball to go for a hole-in-one?

Calculus II Lab Example                  "Lab Example Notebook"

Projectile Motion - Free Throw

Questions:  If the shot is released from an initial height of 6 feet with initial speed 25 ft/sec and angle 47 degrees above horizontal, is it good? Verify all calculations.

Student's Homework

Find the center of mass of a solid, with constant ρ, first quadrant, bounded by 
                       z = (Sqrt[x^2+y^2]) and z=(Sqrt[4-x^2-y^2])

Plot3D[{(Sqrt[x^2 + y^2]), (Sqrt[4 - x^2 -y^2])}, {x,-(Sqrt[2]),(Sqrt[2])},{y,-(Sqrt[2]),(Sqrt[2])}, AxesLabel -> {x, z, y}, Filling ->{1}, AspectRatio -> 1]

Differential Equations

Fourier sine series solutions to heat equation p.d.e' s.

(Subscript[u, k_])[x_,t_]:=(∑_(n=1)^k)-((40 (-1+Cos[n π]))/(n π))(e^((-(n^2)(π^2)t)/2500))Sin[((n π x)/50)

How is it working?

... frequency, repetition

       Any guesses as to the attention span and retention of a modern day college freshman?

Add daily homework assignments using Mathematica

Mathematica and a tablet PC

Seamless Integration

Run live during class.

Frequent cut/paste back and forth between Mathematica and a Bluebeam pdf annontator.

Class notes and Mathematica files posted after class.

Final Considerations

Student Access

Labs

Personal PC's

Institutional Support

Curriculum Development

Faculty Participation

Wolfram Support

Flexible licensing

Screencasts / Other Training