|Instructor Info:||Geremias Polanco Encarnacion|
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.
There are five main objective in this course:
The privious five objective will be evaluated as follows
Developing conceptual understanding of Number Theory, through
Learning how to write professional arguments
Producing latex documents
Using computer experiments to make conjectures
Applying the theory to other disciplines
Students who complete the following are guaranteed to receive an evaluation:
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.
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