BackgroundBackground.docThis page of the web site makes available a one-semester course on Elementary Number Theory designed for high school students who love mathematics. The course is ideal for a student who has completed the usual high school curriculum of algebra, geometry, trigonometry, pre-calculus and calculus and is looking for new challenges. However, it could also be taken as a summer course or as an independent study in the midst of the traditional math sequence.
The course consists of 13 chapters. The first five chapters are relatively short and relatively easy and could form the basis for a short introduction to the topic. Beginning with Chapter 6, the material becomes significantly more challenging, but is within the grasp of many high school students. It is possible to cover all 13 chapters in one semester, but that will depend on the abilities of the students.
Unlike a conventional high school math course, where the important material is laid out in the text and the problems are either peripheral or numerical exercises, in this course as much as possible has been left to the student to discover and prove. Some proofs are left entirely to the student, others are started or outlined in the text, with pieces left as exercises. Only a few complex proofs are spelled out in full.
Because it is important for each student to complete every problem that is part of a proof of an important result, many of the harder problems come with hints. Students are encouraged to make a significant effort at every problem before resorting to the hints.
This web site contains links to a Table of Contents for this course, Chapter 1, Chapter 1 Solutions, Chapter 2, and Chapter 2 Solutions. The complete course, including pdf versions of all 13 chapters, solutions to all of the problems, and Microsoft Excel Workbooks designed to be used with some of the later modules, can be obtained from the author by sending an e-mail request to firstname.lastname@example.org.
Best of luck with the material. I hope your students (or you, if you are the student) find the subject challenging, rewarding and fun.
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For more information on the author click here. About_the_Author For more information on how this course came to be, click here. Background
Questions or comments about the course? Send an e-mail to email@example.com.