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Course Information

Instructor Info:Geremias Polanco Encarnacion
Term: 2013F
Meeting Info: Tuesday Thursday
10:30 AM - 11:50 AM Cole Science Center 316
10:30 AM - 11:50 AM Cole Science Center 316
Description:

Number theory is the branch of mathematics that deals with the properties of whole numbers. This is an area in which simplicity and complexity meet in an astonishing way. Therefore, in this course you will be presented with problems that, in most cases, are very easy to state, but whose degrees of difficulty range from very easy to incredibly difficult. We will focus on learning the tools and techniques that are used to attack problems in the field and beyond. By following an inquisitive approach in this exploration of the theory of numbers, we will help sharpen problem solving skills, the basic weapon of a professional mathematician. You will also learn and apply basic principles used in mathematical research. Topics include divisibility, primes and factorization, congruency, arithmetical functions, quadratic reciprocity, primitive roots, Dirichlet's series, and other topics at our discretion and as time permits.

Course Objectives:

There are five main objective in this course:

  • To develop a conceptual understanding of the Elementary Theory of Numbers.
  • Learning how to write professional mathematical arguments.
  • Learning how to produce simple mathematical documents using latex.
  • Learning how to use computer experiments to make mathematical conjectures and proving them if possible.
  • Apply the theory learned to other disciplines to solve problems.

 

Evaluation Criteria:

The privious five objective will be evaluated as follows

Developing conceptual understanding of Number Theory, through

  • Homework problems and projects.
  • Classwork
  • Portfolio

Learning how to write professional arguments

  • In-class and homework xercises that require proof writing
  • Portfolio

Producing latex documents

  • Through problems and assignments that require latex
  • Portfolio

Using computer experiments to make conjectures

  • There will be specific assignments througout the course

Applying the theory to other disciplines

  • Homework sets and projects

 

Students who complete the following are guaranteed to receive an evaluation:

  • Attend all classes (misssing no more than three classes).
  • Do all hw sets (missing no more than two hw sets).
  • Do all experiments.
  • Complete portfolio and hand it on December 10, 2013
Additional Info:

Textbook: Elementary Number Theory, Seventh Ed, by David M. Burton, McGraw Hill

Portfolio: Every student is required to create a portfolio to be handed on Tuesday December 10. The portfolio will be a collection of items comprised of: all graded homework (including latex-typed exercises), graded quizzes, conjectures, proofs and/or observations from experiments, as well as any projects assigned in class. 

Non-classroom work-load Expectation: You are expected to work 6 to 10 hours per week outside class. If you find yourself putting more than 10 hours of work per week, let me know please. 

Syllabus: Please, read the attached syllabus below to better understand the description of each aspect of the course.