Prerequisite: 116 or the equivalent
Distribution: Mathematical Modeling. Majors can fulfill the major presentation requirement in this course in 2005-06.
Number theory is the study of relationships between natural numbers. Gauss called it the "Queen of Mathematics" because of the simplicity of its questions and the beauty of its results. The subject is interesting to mathematicians partly because questions can be easy to state but very difficult to solve completely. For example, how many primes are there that are less than a given number? Though Gauss, one of the greatest mathematical minds of all times, was able to formulate a good guess at an answer to this question, it was almost a hundred years before his guess was proven to be correct.
Thus, we'll consider topics in this course as diverse as: how to tell if a large number is prime; how to measure 1 qt. of a liquid using only a 12 qt. and a 5 qt. container; how to construct effective cryptic codes; and finite systems that arise from the natural numbers by using simple ideas about divisibility. The structures we'll study will also be a good introduction to some of the more abstract topics covered in courses like Math 305 and 306.
There will be
an emphasis on writing proofs, and Math 223 provides one way to meet
the "proofs prerequisite" for Math 302 and Math 305. Math 223 counts
toward the mathematics major/minor as an elective.
Prerequisite: 116 or the equivalent
Distribution: Mathematical Modeling. Majors can fulfill the major
presentation requirement in this course in 2005-06.
