Project Topics

If your team is able to come up with a topic on your own, that's great! Send me an email and I'll make sure that you "reserve" your topic. Project topics will be assigned on a "first come, first served" basis, so make sure you email me with your topic request as soon as your team makes a decision. I'm very happy to talk with you about what kinds of things you might present for the topic that you select, so please don't be shy about asking me for help in deciding what topics would be reasonable to cover. Remember: this is supposed to be fun, so spend some time exploring and looking for neat stuff.

Chosen Topics

• Cryptography and Number Theory (Henry, Ryan, Steph)
• Goldbach's Conjecture (Brad, Jacqueline, Josh, Richie)
• Integers as sums of squares (Rachel, Angela, Carl)
• Continued Fractions (Aviva, Jeff, Nick)
• Number Theory in Pop Culture (Jen, Tom, Wael)
• Pythagorean Triples (Alli, Brittney, Ryan)
• Partitions (Dan, Sasha, Ted)
• The Riemann Zeta Function (Johanna, John, Kevin)
• Hensel's Lemma (Dennis, Katie, Kevin)
• Fermat's Last Theorem (Alex, Lance, Ob)

Suggested Topics

• Fermat's Last theorem
• Analytic Number Theory and the Riemann Zeta Function
• Average Orders of Arithmetic Functions (average order of $\phi$, average order of $\nu$,…)
• Primality Tests (Industrial Strength Primes,…)
• Factorization Techniques (Pollard's $\rho$ method, Fermat factorization,…)
• Cryptography and Number Theory
• Odd perfect numbers and/or amicable pairs
• Hensel's Lemma
• P vs. NP and integer factorization
• Covering Classes
• Pell's Equation
• Pythagorean Triples
• Fermat Primes
• Distribution of Primes (Chebyshev's Theorem, Bertrand's Postulate, …)
• Additive Number Theory
• Partitions
• Goldbach's Conjecture
• Integers as sums of squares (Fermat's two square theorem, Lagrange's four square theorem, Waring's Problem)
• Jacobi's four square theorem
• Gauss Circle Problem
• Merten's Conjecture
• Continued Fractions
• Problems from the "Concluding Remarks" section of any chapter in Strayer
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