Advanced Topics in Mathematics
LINKS TO

The ADVANCED TOPICS IN MATHEMATICS Course at Concord-Carlisle High School
2007-2008

image of new GPS satellites

(hold your cursor over any image to learn more)


ATM CLASS RESOURCES AND HANDOUTS


About Advanced Topics in Mathematics at CCHS:

What should be the goals of a course entitled Advanced Topics in Mathematics that is taught to seniors?

Answer:
  • It should expose students to what mathematics outside of a high school classroom setting really looks like.
  • It should give to students something memorable about mathematics while engaging them in a meaningful way and showing them a different face of the diverse mathematical world.
I have developed five main themes for this course. Here they are:




What is there in mathematics that one could teach/discuss/explore that would begin to address the above goals? Read on...

The topics below are those that are selected from each year:
(click on each title - or the menu at the top - to learn more)


TOPICS:

    Maxicode 2D Symbology barcode
- The theory of prime numbers
- Mersenne primes
- Abundant/deficient/perfect numbers
- Proof
- Pythagorean Triples
- Patterns in number theory
- Modulus Arithmetic
- Cryptography
- Bar Codes/2D Matrix Codes/Error Checking
- Assorted topics in number theory


    satellite orbit around earth
- Linear Programming and its applications
- The mathematics of the Global Positioning System
- Structure of the GPS
- Systems of lines/circles/spheres
- Projections
- Satellite signals and technology
- Geography
- The shape of space
- Fermi Problems


/Chaos Theory and Applications

    the Menger Sponge, a deterministic fractal
- Fractals defined
- Fractal dimension
- Expansion/Removal/Space-Filling fractals
- Fractals in nature
- Using Fractree software
- Chaos Theory
- Sensitive Dependence On Initial Conditions
- Iteration, seeds, orbits, fates
- The logistic equation
- Population Biology
- Chaos in nature
- Chaos in the Double Pendulum System - Complex numbers/the complex plane
- The Mandelbrot Set
- Using Fractint software


    a Moebius strip
- Topological equivalence
- Faces/edges/vertices/EulerŐs Formula
- Traversability
- 3-D topology
- Polyhedra
- Trees/Rooted Trees
- Kruskal's Algorithm
- Knot invariants
- Applications of Knot theory - Biometrics


At the bottom of each of my web pages I have included suggestions for books on each subject that I have found useful and entertaining. Here are some that are general to mathematics:
Recommended Readings:


Class Resources and Handouts:



Contact: abeckwith@colonial.net
This Page Last Updated: 6/1/08
Concord-Carlisle High School
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