Math 4822A, A Classical Introduction to Modern Number theory

Math 4822A: A Classical Introduction to Modern Number theory

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Instructor:: Maosheng Xiong : mamsxiong AT ust DOT hk
Office: 3475 Tel: 2358-7456; Office hours: please feel free to stop by my office anytime during weekdays or make an appointment.

Lecture:: Monday: 15:00--16:20, Rm 4503;; Friday: 10:30--11:50, Rm 4503.

Course Description:: 4 credit units. Prerequisite: Math 3121 and Math 4141.; This is a continuation of MATH 4141 on number theory at undergraduate level. We will follow the book "A classical introduction to modern number theory" by Ireland and Rosen, and the main topics are Gauss sums, Jacobi sums, cubic and biquadratic reciprocity, equations over finite fields, elliptic curves, the zeta function and basic algebraic number theory. We shall try to follow the text book as closely as possible.

Textbook:: K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Graduate Texts in Mathematics 84, Second Edition, Springer-Verlag, 2003.

Reference books:: J.H. Silverman, A friendly introduction to number theory, 3rd edition.; I. Niven, H.S. Zuckerman, H.L. Montgomery, An introduction to the theory of numbers, 5th edition, John Wiley & Sons, Inc, 1991.; G.H. Hardy, E.M. Wright, The theory of numbers, Oxford University Press, 1960.; Hua Loo-Keng, Introduction to number theory, Springer.

Homework: Homework will be assigned every two weeks and will be announced in advance.

Assessment Scheme: no extra credit.: Homework: 30%; Take-home Midterm Exam: 30%; (Possible) Final project: 40%

Intended Learning Outcomes:: The School of Science Intended Learning Outcomes and the Math Department Intended Learning Outcomes are distributed separately along with this syllabus. Upon the end of the course, you should have opportunities to and be able to
ILO A. recognize the power of abstraction and generalization, and apply logical reasoning to investigate mathematical work with independent judgement (cf Science ILO 1, Math ILO 3P)

ILO B. collaborate effectively in team work (cf Science ILO 2, Math ILO 5)

ILO C. communicate effectively about math to peer and teaching staffs using available equipments or presentation softwares (cf Science ILO 4, Math ILO 4)

ILO D. apply rigorous deductive reasoning in conjunction with quantative methods to analyze and solve problems related to math profession (cf Science ILO 6, Math ILO 2)

Teaching Approach:: The lectures by the instructor on course materials will focus on proofs and computation. By understanding proofs and doing assignments, you will gradually attain the ability for ILO A.
For ILOB, Students will form a group of two to work on final projects.
For ILOC, at the end, students will give oral presentations on the final project that they have finished, by using transparencies, WORD documents, power-point presentations or any math softwares.
For ILO D, there will be written assignments every two weeks and a take-home exam.

Academic Integrity:: The University places a strong emphasis on academic integrity. No cheating or plagiarism will be tolerated. Please visit the website at http://www.ust.hk/provost/integrity for details.

Learning Environment:: Attendance is expected. Please arrive on time and avoid leaving early. Mobile phones should be turned off during the class. Please feel free to ask questions in class.