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YongTao Chen
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    14/06/2014
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ENT Elementary Number Theory

  • Mr. Chen YongTao
    Teacher
Course subject : Math: Elementary theory of numbers
Language : English (US)
Elementary Number Theory is such a charming subject of mathematics that many great mathematicians devoted to it because of its wealth of easily accessible and fascinating questions, and its intellectual appeal. Gauss once remarked that "mathematics is the queen of the sciences and arithmetic the queen of mathematics".

There have been quite many good textbooks on Elementary Number Theory. My intent on developing this 3-week long course is to try imparting the primary coverage of the subject during as short a time as possible, which might make the learning easier, and pave the way to further study of more advanced courses. The efforts into writing present lecture notes of this course are focused on three aspects: self-containnedness, conciseness, as well as logic coherence. The examples given in the course are carefully selected.

The lecture notes is the fruit of many years' experience in teaching. So the participants are expected to read the notes seriously first. Then they are encouraged to try doing the relevant exercises, most of which are more or less directly related to corresponding definition, example, or proposition. The homework assignment for each lecture consists of more challenging problems. It is my hope that taking part in this compact course could be felt like making a fun excursion.

The course consists of 6 lectures, each of which contains two periods of lessons. In the spirit of teachings in reality, in each week are delivered two lectures, and the lecturing on the entire course is thus completed in 3 weeks.

Elementary Number Theory is the study of the basic structure and properties of integers. Learning Number Theory helps improving one's ability of mathematical thinking. Successful completion of this course will enable you to:

  1. Prove results involving divisibility and greatest common divisors;
  2. Solve systems of linear congruences;
  3. Find integral solutions to specified linear Diophantine Equations;
  4. Apply Euler-Fermat’s Theorem to prove relations involving prime numbers;
  5. Apply the Wilson’s theorem;
  6. Use the Euler's Criteria to solve relevant problems.

This self-contained course on Elementary Number Theory imparts the primary coverage of the subject. Topics include: Divisibility, Division algorithm, Primes and Composites, Greatest Common Divisors, Least Common Multiples, Fundamental Theorem of Arithmetic, Linear Diophantine Equations, Congruences, the Chinese Remainder Theorem, Euler-Fermat's Theorem, Wilson's Theorem, and Euler's Criteria.

A set of review problems at medium level of difficulty is provided at the end of the course, which is intended to test your understanding of what you have learned from the entire course.

This course assumes no specific background knowledge other than the patience to work about 6 hours each week. Anyone who wants a taste of the glamour of mathematics is welcomed to enrol in this course.