Theory of Numbers

In Spring 2023 I will teach Number Theory, MATH 5234(G) A. I shall use the following course design, and use the book: Elementary Number Theory by Jones and Jones.

It is an interesting supplement to one's pure mathematical mind, and many renown mathematicians devoted a great deal of their career in the area of number theory; Euler, Gauss, Jacobi, Weierstrass, Riemann, Dirichlet, Hilbert, Hardy.
The following is a quote from the Wikipedia website, and you may further read about it here.
- - The number-theorist Leonard Dickson (1874–1954) said "Thank God that number theory is unsullied by any application". Such a view is no longer applicable to number theory. In 1974, Donald Knuth said "...virtually every theorem in elementary number theory arises in a natural, motivated way in connection with the problem of making computers do high-speed numerical calculations". Elementary number theory is taught in discrete mathematics courses for computer scientists; and, on the other hand, number theory also has applications to the continuous in numerical analysis. As well as the well-known applications to cryptography, there are also applications to many other areas of mathematics.

Prerequisite: MATH 2332 Mathematical Structures (Logic and Proofs) in 2018-2019 Catalog, or equivalent courses.
There are four sessions, and the final exam.
20% of a session grade is from Homework Quiz, 10% is from Group Work and Quiz, and 70% is from Session Test.
50% of the course grade is from session grades, and 50% is from the final exam.
Good work ethic and study habit are required throughout the semester.
Georgia Southern Credit Hour Policy: For each 50 min lecture, a minimum of two hours of out of class work is required.

- Homework Quiz will be assigned after each class meeting, and they are collected and graded for reasonable efforts.
- Homework Quiz provides students with opportunities to review concepts, practice standard problems, and challenge themselves with advanced problems which require independent and critical thinking.

- There will be eight class periods throughout the semester during which students will help each other on improving their skills and concepts on standard materials, and take individual quizzes.

- There will be four 50-minute long tests, and the final exam.
- Sample tests will be available before each test and the final exam.

- There will be one term project that is required for the course.
- A preliminary report and a final report on students' progress will be assessed.

- The required topics to cover in this course are: Chp 1 Divisibility; Chp 2 Prime Numbers; Chp 3 Congruences; Chp 4 Congruences with a Prime-Power Modulus; Chp 5 Euler's Function; Chp 6 Group of Units; Chp 7 Quadratic Residues.
- Additional topics to cover among the following are yet to be determined: Arithmetic Functions, The Riemann Zeta Functions, Sums of Squares, or Modular Forms.