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MTH 405: Research projects for high school students


Description

The idea is to introduce talented high school to research projects in mathematics.  We expect that the students are committed and passionate about mathematics.  The most advanced students will be mentored by Prof. Shaska  with the intention that students participate in nationwide competitions.  

Admission

To be accepted to the program the student must be passionate about mathematics, to have a letter of recommendation from a mathematics teacher, and to have a 15 minute interview with Prof. Shaska.  Homeschooled kids are also welcomed.  

The class will have a maximum capacity of 10 seats.  

The student can choose to get credit for the class if she/he so chooses and enroll in a special topics course for undergraduates.  However, in that case she/he will be responsible for paying tuition to Oakland University. 

Meeting times


Time:  To be arranged 

Software

We will use Sage/Python for some of the projects.  No prior knowledge of Sage or Python is required, but the kids must be willing to learn some basic programing routines as we progress in the program.


Contacts

Topics

  • Quadratics and symmetric matrices
  • Conics
  • Rational points on conics
  • Elliptic curves
  • Abelian Groups 
  • Points of finite order on an elliptic curve
  • Rational points on elliptic curves
  • Higher degree curves
  • Hyperelliptic curves
  • History of integrals
  • Abelian integrals
  • Abel and Jacobi
  • Riemann and the theta-function
  • Rational points on curves
  • Mordell-Weil theorem
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