For my masters I need to do a capstone project this term. I pick a subject and then develop a series of lectures that are intended to be an ‘enrichment topic’, and likely targetted at upper year HS students.

Here’s the outline:

Students create a mini-course on a single mathematical enrichment topic. The course created

will be roughly three one-hour lessons that include both teaching and mathematical problem

solving.

• An “enrichment topic” means a topic that is outside of the union of the curriculum documents

(including courses that are not mathematics) for a generic jurisdiction. For example, teaching

calculus to Grade 10 students would not count as an enrichment topic.

• The mini-course can be aimed at any level from Grade 9 to Grade 12 (or college for college

teachers).

• The mini-course can be approached from a number of different angles, including an historical

angle, a contest preparation angle, etc.

And here’s some possible ideas:

## Summary

- Applications of … (eg. Logarithmic Functions,

Complex Numbers, etc.) - Approximating Functions
- Arithmetic, Geometric and Harmonic Means
- Binary Numbers
- Cauchy-Schwarz Inequality
- Ceva’s Theorem
- Circle Geometry
- Chinese Remainder Theorem
- Compass and Straightedge Constructions
- Congruence Classes
- Conic Sections
- Continued Fractions
- Cryptography
- Cubic Equations and Polynomials of Higher

Degree - Diophantine Equations
- Euclidean Algorithm
- Euler Phi Function
- Euler’s Formula
- Factoring Polynomials
- Fermat’s Last Theorem
- Fermat’s Little Theorem
- Game Theory
- Generating Functions
- Geometric Inequalities
- Graph Theory
- Graphing Polar Curves
- Group Theory
- History of … (eg. Trigonometry,

Indian Mathematics, Fibonacci) - Infinite Series
- Invariants
- Inversion
- Limits of Sequences
- Linear Programming
- Magic Squares
- Markov Chains
- Mathematical Logic
- Mathematics of Gambling
- Matrix Theory
- Mersenne and Fermat Numbers
- Nine Point Circle
- Open Problems (eg. Goldbach’s Conjecture,

Do any odd perfect numbers exist?) - Partitions
- Pell’s Equation
- Pencils of Planes
- Pick’s Theorem
- Platonic Solids and Polyhedra
- Polar Coordinates
- Primality Testing
- Properties of the Pedal Triangle
- Ptolemy’s Inequality
- Pythagorean Triples
- Quadratic Residues
- Random Walks
- Regular Expressions
- Set Theory
- Spherical Trigonometry
- Tessellations

So I have it narrowed down to two ideas.

- Golden Ratio

Pros: I think it’s a cool enrichment topic and I’m personally interested in it.

Cons: I don’t know squat about the golden ratio. So in addition to developing the course, I have to learn and understand something about it. Like right now I couldn’t even do an outline of what I’d be teaching. And I’m concerned that the math behind it may be too much for a HS enrichment course. So basically, unsure if this is too much for me to handle over the summer. - Mathematics of loans

Pros: Easy for me to do, zero learning, The opposite of 1), I’d likely be done this early since I’d be just drafting an outline, screwing around in latex and spending some time building out some interesting exercises like ‘calculate PV/FV’ and ‘build an amortization schedule’.

Cons: Less certain this is a viable ‘enrichment’ topic.

Looking for your opinion on which way I should go. And if you choose 1) would welcome guidance on what area of the golden triangle I should focus on (I did some reading on this over the weekend, and holy crap that ratio is everywhere).

## Summary

I suppose I could do #28 on the list, graphing polar curves. I plan on getting a tattoo once I’m done the degree and was thinking of getting a unit circle, which would tie in nicely. But, a golden ratio tattoo opens up some interesting possibilities as well.