**DEPARTMENT OF MATHEMATICS**

**Number Theory Syllabus (Fall 2022)**

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**Professor: **Yoonjin Lee

**Office: ** Science Complex Building B, 313 (Tel: extension 6653)

**E-mail: ** yoonjinl@ewha.ac.kr

**Homepage: ** http://math.ewha.ac.kr/~yoonjinl/

**Text Book: ***Elementary Number Theory and its applications, *6th edition,
by Kenneth H. Rosen.

**Course requirements: ** Linear Algebra I

**References:***Elementary Number Theory*
by D. Burton

**Course Description:**

Number Theory was studied for its long and rich history, its wealth of easily accessible and fascinating questions, and its intellectual appeal. But, in recent years Number Theory has been studied for both for the traditional reasons and for the compelling reason that number theory has become essential for Cryptology.

Topics include the integers, divisibility, prime numbers, primality testing, factorization methods, congruences, Diophantine problems, arithmetical functions, Fermat's little theorem, primitive roots, quadratic reciprocity, Diophantine equations, Fermats's last theorem, arithmetical functions and so forth. Applications will be drawn from Cryptology, and Coding theory.

**Course Outline:**

- Chapter 1: The Integers. 1.1, 1.2, 1.5

Chapter 3: Primes and Greatest Common Divisors. 3.1 to 3.5, 3.7

Chapter 4: Congruences. 4.1 to 4.3

Chapter 6: Some Special Congruences. 6.1 to 6.3.

Chapter 7: Multiplicative Functions. 7.1 to 7.2

Chapter 9: Primitive Roots. 9.1 to 9.2, 9.5

Chapter 11: Quadratic Residues. 11.1 to 11.2

Chapter 8: Cryptology. 8.1, 8.3, 8.4, 8.6

Chapter 13: Some Nonlinear Diophantine Equations. 13.1 to 13.2 (if time permits)

**Grades:**

You will be evaluated throughout the whole semester by means of one midterm exam, one research project, a comprehensive final exam, two quizzes and Homework. No make-up exams will be given.

**Test Schedules: **

**Grading Policy:**

Homework and Quizzes | 20 % (= 10 + 10) | |

Project | 10 % | |

Mid-term Exam | 35 % | |

Final Exam | 35 % |

**Projects:**
The project includes a 8-10 page expository *original* paper and a class presentation.
Suggested project topics and detailed guidelines will be provided in class.

**Homework and Quizzes:**

"NO" late homework will be accepted.

You have to spend enough time for reviewing the material on a regular basis. The best way to learn the material is to spend some time thinking about the homework problems virtually every day as our class progresses. You are strongly encouraged to do the practice problems as well, but you do not need to hand in the practice problem sets. In addition, you are encouraged to discuss the homework assignments with others, but you must write up your own solutions and turn them in individually. Some selected homework problems may be presented by students in class.

**Other class expectations:**

The student must attend all the lectures if possible. Your participation in discussion during class will be significantly important for this course.