Type of Credit: Elective
Credit(s)
Number of Students
This course is an introduction to the main topics of number theory at the undergraduate level and also covers theorems at the graduate level, like Prime Number theorem, but an elementary proof for it without techniques from complex analysis. I will also bring in concept of theorems and hopefully can help students understand how a proof comes.
能力項目說明
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
|---|---|---|
In-class Hours: 3; Outside-of-class Hours: 5.
Week 1: Divisibility. (Chapter 2 in textbook 1)
Week 2: Greatest common divisor and the Euclidean algorithm. (Section 3.1 and Section 3.2 in textbook 1.)
Week 3: Primes and the fundamental theorem of arithmetic. (Section 4.1 and Section 4.2 in textbook 1.)
Week 4: Congruence and the Chinese remainder theorem. (Chapter 5 in textbook 1.)
Week 5: Congruence and the Chinese remainder theorem. (Chapter 5 in textbook 1.)
Week 6: Primitive roots. (Chapter 7 in textbook 1.)
Week 7: Primitive roots. (Chapter 7 in textbook 1.)
Week 8: Finite fields.
Week 9: Midterm Exam
Week 10: Quadratic residues. (Chapter 9 in textbook 1.)
Week 11: Quadratic reciprocity. (Chapter 9 in textbook 1.)
Week 12: Arithmetic functions and Mobius inversion formula. (Section 2.1 to Section 2.5 in textbook 2.)
Week 13: Arithmetic functions and Mobius inversion formula. (Section 2.6 to Section 2.8 in textbook 2.)
Week 14: Average of arithmetic functions. (Section 3.1 to Section 3.4 in textbook 2.)
Week 15: Average of arithmetic functions and some elementary theorems on the distribution of prime numbers. (Section 3.11 , Section 4.1 and 4.2. to Section 4.4 in textbook 2.)
Week 16: Some elementary theorems on the distribution of prime numbers and the prime number theorem (Section 4.3 to Section 4.5 in textbook 2).
Week 17: The prime number theorem (Section 4.5, Section 4.9 and Section 4.10 in textbook 2).
Week 18: Final Exam
The instructor may change the schedule above depending on how the lectures will be going.
Homework: 40%
Midterm: 30%
Final exam : 30%
Note that late homework will not be collected but the lowest two homework grades will be dropped. Homework will be given weekly on Moodle and be collected biweekly on Moodle.
Textbook 1: Introduction to Number Theory by Marty Erickson, Anthony Vazzana, and David Garth, ISBN 978-1-4987-1749-6 (Hardback).
Textbook 2: Introduction to Analytic Number Theory by Tom M. Apostol, ISBN 978-1-4419-2805-4, ISBN 978-1-4757-5579-4 (eBook).
| 書名 Book Title | 作者 Author | 出版年 Publish Year | 出版者 Publisher | ISBN | 館藏來源* | 備註 Note |
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