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課程簡介 Course Introduction
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開課年度學期 Year / Term
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113 學年度 第 2 學期
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開課班級 Department
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應用數學系 應數一
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授課方式 Instructional Method
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課堂教學 、 中英文雙語授課
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課程電腦代號 Course Reference Number
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150048
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課程名稱(中文) Course Title(Chinese)
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數論
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課程名稱(英文) Course Title(English)
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Number Theory
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學分數/時數 Credit Hours
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3 /
3
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必(選)修 Requirement / Elective Course
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選修
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授課老師 Instructor
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孫新民
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助教 Teaching Assistant
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上課時間 Meeting Time
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星期四，節次3、4、5
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上課教室 Classroom
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JB103
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Office Hours
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孫新民：4444/789A
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| 獲獎及補助情形 Awards and Grants |
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| 聯合國永續發展目標 (SDGs跨域類別) Sustainable Development Goals, SDGs |
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SDGs 04.
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優質教育：確保有教無類、公平以及高品質的教育，及提倡終身學習
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課程目標 Learning Objectives
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數論為數學學習者及應用數學者所應具備的基本知識. 本課程為對數論之相關內容作一概略介紹.
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先修 ( 前置 ) 課程 Prerequisite
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| 彈性教學規劃 Flexible Teaching/Planning Schedules |
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課程大綱 Course Syllabus
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| 週次 Week |
課程單元大綱 Unit |
教學方式 Instructional Method/Style/Teaching Style |
參考資料或相關作業 References or Related Materials |
評量方式 Grading |
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1
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Divisibility
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2
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Prime Numbers
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3
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Factorization
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4
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Congruences I
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5
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Congruences II
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6
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Arithmetic Functions
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7
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放假
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8
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Euler’s theorem and Fermat’s little theorem
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9
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期中考
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10
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Primitive Roots I
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11
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Primitive Roots II
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12
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Quadratic Residues
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13
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Quadratic Reciprocity Law
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14
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Sums of Squares
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15
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The distribution of primes
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16
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An Introduction to Cryptography , 繳交期末報告
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17
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討論期末報告
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18
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討論期末報告
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單一課程對應校能力指標程度 The Degree to Which Single Course Corresponds to School Competence
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| 編號 No. |
校核心能力 School Core Competencies |
符合程度 Degree of conformity |
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1
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公民力 (Citizen)
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3
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2
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自學力 (Self-learning)
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4
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3
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資訊力 (Information)
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4
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4
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創造力 (Creativity)
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4
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5
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溝通力 (Communication)
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5
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6
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就業力(Employability)
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5
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單一課程對應系能力指標程度 The Degree to Which Single Course Corresponds to Department Competence
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| 編號 No. |
類別 Category |
系核心能力 Department Core Competencies |
符合程度 Degree of conformity |
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01
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系所
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學生具備數學思考與推理能力
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5
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02
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系所
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學生擁有數學應用與解決問題能力
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4
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03
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系所
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學生具備代數、離散、統計及科學計算能力
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3
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04
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系所
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學生具有小學數學之專業教學能力
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3
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05
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系所
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學生具有跨領域之科學知識
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4
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06
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系所
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學生擁有閱讀討論與發表之專業能力
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4
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單一課程對應院能力指標程度 The Degree to Which Single Course Corresponds to College Competence
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| 編號 No. |
院核心能力 College Core Competencies |
符合程度 Degree of conformity |
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1
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語文能力
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4
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2
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溝通與合作能力
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4
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3
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創新與實踐能力
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4
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4
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專業知能
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5
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教科書或參考用書 Textbooks or Reference Books
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館藏書名 Library Books
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備註 Remarks
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教材
[Crisman] K.-D. Crisman, Number Theory: In Context and Interactive, 2024.
https://math.gordon.edu/ntic/
https://math.gordon.edu/ntic/ntic/chapter-prologue.html
[Raji] W. Raji, An Introductory Course in Elementary Number Theory.
https://www.saylor.org/2013/05/blog-qa-with-dr-wissam-raji-author-of/
https://www.saylor.org/2013/05/blog-free-elementary-number-theory-open-textbook-released-under-cc-by/
https://www.math.usm.edu/perry/old_classes/mat421sp17/An-Introductory-Course-in-Elementary-Number-Theory.pdf
[Moser1957] L. Moser, An Introduction to the Theory of Numbers, 1957.
http://www.trillia.com/moser-number.html
[Carmichael1914] R.D. Carmichael, The Theory of Numbers, John Wiley & Sons, Inc., 1914. (Gutenberg Release 2013)
[Nathanson2000] M.B. Nathanson, Elementary Methods in Number Theory, 2000. 電子書, 不能印書
[Schroeder2009] M.R. Schroeder, Number Theory in Science and Communication, Springer-Verlag,
5th ed., 2009. (1986. 512.7 S381) 電子書, 不能印書 (應用)
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參考用書 I.
[HW2008] G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers, 6th ed., Clarendon Press, 2008. 512.7 H269 (入門經典書)
[NZM1991] I. Niven, H.S. Zuckerman, and H.L. Montgomery, An Introduction to The Theory of Numbers, 5th ed., John Wiley & Sons, Inc., 1991. 512.7 N734 (傳統教科書)
[Guy1994] R.K. Guy, Unsolved Problems in Number Theory, 2nd ed., Springer-Verlag, 1994. 512.7 G986
[Dickson1919] L.E. Dickson, History of the Theory of Numbers, Vol. I Divisibility and Primality, Vol. II Diophantine Analysis, Vol. III Quadratic and Higher Forms, Chelsea Publishing Co., 1919. (Reprinted by the American Mathematical Society, 1999) 512.709 D554
https://archive.org/details/historyoftheoryo01dick
https://archive.org/details/historyoftheoryo02dick
https://archive.org/details/historyoftheoryo03dick
[Carmichael1915] R.D. Carmichael, Diophantine Analysis, John Wiley & Sons, Inc., 1915. (Gutenberg Release 2006)
[Poritz2014] J.A. Poritz, Yet Another Introductory Number Theory Textbook, 2014.
[Dickson1929] L.E. Dickson, An Introduction to the Theory of Numbers, 1929.
https://archive.org/details/in.ernet.dli.2015.466075/page/n11/mode/2up
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參考用書 II. (需要代數及分析基礎)
[Shoup2008] V. Shoup, A Computational Introduction to Number Theory and Algebra, 2008.
https://shoup.net/ntb/
[Stein2017] W. Stein, Elementary Number Theory: Primes, Congruences, and Secrets, 2017.
https://wstein.org/ent/
[Rademacher] H. Rademacher, Lectures on Analytic Number Theory, 1954-1955.
http://www.math.tifr.res.in/~publ/ln/tifr02.pdf
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※請尊重智慧財產權，不得非法影印教科書※
※ Please respect intellectual property rights and do not illegally photocopy textbooks. ※
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教學方法 Teaching Method
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教學方法 Teaching Method
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百分比 Percentage
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講述
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60 %
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問題導向學習
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20 %
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討論
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20 %
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| 總和 Total |
100 % |
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成績評量方式 Grading
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| 評量方式 Grading |
百分比 Percentage |
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平時成績
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30 %
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期中考
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30 %
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期末報告
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40 %
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| 總和 Total |
100 % |
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成績評量方式補充說明
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平時成績(作業撰寫,其他報告,課堂參與,含習題及點名)(30%)、期中考(30%)、期末報告(40%)
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課程大綱補充資料 Supplementary Material of Course Syllabus
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