基礎數論
Elementary Number Theory
學期
111-1
學分
3
學分
當期課號
910129
永久課號
SESE10016
開課單位
系統工程與科技學士學位學程
授課教師
張仁煦
類別
選修
上課時間表
| 節 | 週三 |
|---|---|
5 13:20–14:10 | 基礎數論 3 節連堂 |
6 14:20–15:10 | |
7 15:30–16:20 |
* 根據陽明交大上課時間表所列
概述
介紹基礎數論知識及研究方法 This course delivers an introduction for Number Theory.
先修科目
高中數學 The mathematics of senior high school
評分方式
1.期中考:50% 2.期末考:50% 1. Mid-term : 50 % 2. Final Exam: 50 %
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | 1 最大公因數與唯一分解 2 模數算數 3 線性同餘方程式 4 中國剩餘定理 5 費碼定理及尤拉定理 6 歐幾里德輾轉相除法及反元素 7 平方殘餘(Quadratic Residues)及尤拉準則 8 RSA 密碼簡介 9 期中考 10 指數運算 11 原根及其應用 12 解離散對數方程式(I) 13 解離散對數方程式(II) 14 模多項式 15 不可化約多項式 16 有限體 17 歐幾里德輾轉相除法及反元素 18 期末考 week1: G.C.D and unique factorization week2: Modular Arithmetic week3: Linear Modular Equations week4: Chinese Remainder Theorem week5: Fermat Theorem and Euler Theorem week6: Eucleadian Algorithm and Inverse Element week7: Quadratic Residues and Euler Criteria week8: RSA Crypto-system week9: Mid-term week10: Exponential Operation week11: Primitive Root and its application week12: Discrete Logarithm (I) week13: Discrete Logarithm (II) and El-Gamal Crypto-system week14: Polynomials over Z_p week15: Irreducible polynomials week16: Finite Field week17: Eucleadian Algorithm and Inverse element of a finite field week18: Final Exam |
教科書
教科書 A Computational Introduction to Number Theory and Algebra (2nd Edition) Victor Schup Cambridge Univ. Press 2009 0521516447