先修课程、其它学习要求
Pre-requisites or Other
Academic Requirements
数学分析 II(MA102a)或高等数学 A 下(MA102B), 线性代数 II (MA104b)
Mathematical Analysis II (MA102a) or Advanced Mathematics A II( MA102B), Linear
Algebra II (MA104b)
后续课程、其它学习规划
Courses for which this course
is a pre-requisite
其它要求修读本课程的学系
Cross-listing Dept.
课程主要讲述整除理论,素数,同余方程,典型的丢番图方程,指数与原根,二次剩余与二次互反律,积性数论函数、
Dirichlet 级数、格点和 Minkowski 定理等基础数论知识,以及这些理论的一些实际应用。学生通过本课程学习可以打下良
好的数论知识基础,体会该学科的魅力,了解数论的应用,为后续更高级课程的学习做好知识准备。
Main topics of the course include:basic theories about divisibility, primes, congruences, special Diophantine equations,
index and primitive roots, quadratic residues and reciprocity, multiplicative arithmetic functions, Dirichlet series, latticen
and Minkowski’s theorem, as well as some important applications of number theory. Students are expected to lay down a
solid background in number theory, have a feeling of the beauty of the subject, learn about its applications, and get well
prepared for subsequent, more advanced courses.
通过对本课程的学习,学生能够理解和掌握初等数论的基本理论和一些重要应用。同时,学生应当理解现代数学(包括代
数和分析等)在经典的数论问题中的应用,加深对现代数论前沿研究内容和研究方法的理解。
An adequate training through this course should help the students to understand the basic methods and techniques in
elementary number theory as well as some important applications. Also, students are expected to have a good
understanding of the roles of modern mathematics - including algebra and analysis - in the applications of classical
number theoretic questions, thus enhancing their comprehensions of advanced research topics and methods in the
frontiers of modern number theory.
课程内容及教学日历 (如授课语言以英文为主,则课程内容介绍可以用英文;如团队教学或模块教学,教学日历须注明
主讲人)
Course Contents (in Parts/Chapters/Sections/Weeks. Please notify name of instructor for course section(s), if
this is a team teaching or module course.)