## 授課老師

 【經歷】 國立清華大學81、90、96校傑出教學獎 【網站】 http://www.ee.nthu.edu.tw/ccc 【授課】 通訊系統、錯誤更正碼、線性代數、離散數學 【專長】 數位通訊、錯誤更正碼、訊息理論、無線網路

## 課程大綱

This course gives an introduction to the essentials of discrete and combinatorial mathematics.

【先修課程】
Prerequisites
 ♠ High-school mathematics, Calculus (preferred).

【課程說明】
Course Description
 ♠ This course gives an introduction to the essentials of discrete and combinatorial mathematics.

【指定用書】
Textbook
 ♠ R. P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction, 5th ed. Boston: Pearson Addison Wesley, 2004.

【參考書籍】
References
 ♠ R. J. McEliece, R. B. Ash, and C. Ash, Introduction to Discrete Mathematics. ﻿New York: Random House, 1989. ♠ N. L. Biggs, Discrete Mathematics, 2nd ed. New York: Oxford University Press, 2002. ♠ C. L. Liu, Elements of Discrete Mathematics, 2nd ed. New York: McGraw-Hill, 1985. ♠ C. L. Liu, Introduction to Combinatorial Mathematics. New York: McGraw-Hill, 1968. ♠ K. H. Rosen, Discrete Mathematics and Its Applications, 8th ed. New York: McGraw-Hill, 2019. ♠ R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley, 1994.

【課程內容】
Course Contents
 Fundamentals ﻿♠﻿  Logic ♠ ﻿ Set theory ﻿﻿♠  Mathematical induction ﻿﻿♠﻿  Functions: definitions, pigeonhole principle ♠  Relations: definitions and properties, equivalence relations, partial orders﻿ Enumeration﻿﻿ ♠ Principles of counting ♠ Principle of inclusion and exclusion ♠ Recurrence relations: homogeneous recurrence    relations, nonhomogeneous recurrence relations ♠ Generating functions: generating functions for solving    recurrence relations, generating functions for partitions of integers ♠ Complexity of algorithms Graph Theory ♠ Introduction: definitions and properties, graph isomorphism, Euler trails and circuits, planar graphs ♠ Trees: definitions and properties, rooted trees, spanning trees, trees and sorting ♠ Optimization and matching: shortest-path problem, minimal spanning trees, matching problem, maximum flow problem

【 2023/4/7- 5/19 Calendar】期中成績預警開始(至5月19日止)Academic Warning System Starts Sending out Alert (4/7-5/19)   ♠   【 2023/4/22 Calendar】校慶環校路跑Cross Country Long Distance Running   ♠   【2023/6/30 Calendar】教師送繳非應屆畢業生111學年度第2學期成績截止Deadline for 2023 Spring Semester Grade Submission   ♠   【2023/4/23 Calendar】校慶活動日University Foundation Anniversary Celebration   ♠   【2023/7/3 Calendar】112學年度暑碩專班上課開始、註冊日、休退學及畢業生免繳學雜費截止2023 Summer In-service Master Program Begins, Registration   ♠   【2023/7/3 Calendar】暑期班選課及繳費開始(至7日止)Course Selection and Fee Paying Begins for Summer Session (7/3-7/7)   ♠   【2023/4/29 Calendar】校慶日University Foundation Day   ♠   【2023/7/31 Calendar】111學年度第2學期研究生論文口試結束Thesis Defense Ends   ♠   【2023/7/31 Calendar】111學年度第2學期結束2023 Spring Semester Ends   ♠   【 2023/1/16 Calendar】寒假開始Winter Break Begins!   ♠   【2023/8/1 Calendar】112學年度第1學期開始2023 Fall Semester Begins   ♠   【2023/8/14 Calendar】新生申請112學年度第1學期學雜費減免(至25日止)   ♠   【2023/6/31 Calendar】教師升等資料、教師進修及休假研究申請案送人事室截止Deadline for Submission of Faculty Promotion Application and Sabbatical Leave Application   ♠   【2023/8/21 Calendar】112學年度入學各級新生、轉學生選課(至24日止)Course Selection for New Students/Transfer Students in Fall 2023 (8/21-8/24)   ♠   【2023/8/21 Calendar】112學年度入學各級新生、轉學生選課(至24日止)Course Selection for New Students/Transfer Students in Fall 2023 (8/21-8/24)   ♠   【 2023/6/10 Calendar】畢業典禮Commencement   ♠   【 2023/6 /12 - 6/16 Calendar】期末考開始   ♠   【2023/8/29 Calendar】112學年度第1學期第3次選課開始(至31日止)3rd Course Selection Period (8/29-8/31)   ♠   【 2023/6/15 - 6/19 Calendar】112學年度第1學期第2次選課開始(至19日止)2nd Course Selection Period for 2023 Fall Semester (6/15-6/19)   ♠   【2023/9/4-9/6 Calendar】新生領航營(至6日止)   ♠   【 2023/6/19 Calendar】暑假開始Summer Vacation Begins   ♠   【2023/2023/9/11 Calendar】全校各級學生上課開始、註冊日Class Begin, Registration!受理軍公教遺族就學減免申請(至15日止)!弱勢助學金申請(至10月6日止)!   ♠   【 2023/6/22- 6/23 Calendar】端午節Dragon Boat Festival   ♠   【2023/9/29 Calendar】中秋節Mid-Autumn Festival (no class)   ♠   【2023/10/9 Calendar】國慶日彈性放假，課程由教師自行擇期補課Holiday-Double Tenth Day (no class: make-up classes will be scheduled)   ♠   【 2023/6/30 Calendar】教師送繳非應屆畢業生111學年度第2學期成績截止Deadline for 2023 Spring Semester Grade Submission   ♠   【2023/10/9-12/3 Calendar】期中教學意見反映(至12月3日止) Mid-term Feedback on Teaching (10/9-12/3)   ♠   【2023/10/10 Calendar】國慶日Double Tenth Day (no class)   ♠   【2023/10/30 Calendar】112學年度第1學期申請課程停修開始(至11月24日止)Course Withdrawal Begins (10/30-11/24)   ♠   【2023/11/15 Calendar】校務會議University Council Meeting   ♠   【2023/12/8 Calendar】教學意見調查開始(至113年1月7日止)Online Course Evaluation (12/8-1/7)   ♠   【2024/1/1 Calendar】開國紀念日New Year's Day (no class)   ♠   【2024/1/8 Calendar】期末考試開始(至12日止，彈性學期週數16或17週課程依公告之課程大綱辦理)Final Exams (1/8-1/12)   ♠   【2024/1/15 Calendar】寒假開始Winter Break Begins!   ♠   【2024/2/8 Calendar】春節彈性放假Holiday-Chinese New Year   ♠   【2024/2/9 Calendar】除夕Chinese New Year’s Eve   ♠   【2024/2/10-2/14 Calendar】春節及春節彈性放假(至14日止)Chinese New Year   ♠   【2024/2/19 Calendar】全校各級學生上課開始、註冊日Classes Begin, Registration   ♠   【2024/2/28 Calendar】和平紀念日228 Peace Memorial Day (No Class)   ♠   【2024/3/1-3/3 Calendar】梅竹賽(1日至3日，1日下午停課，由教師自行擇期補課；若停賽則正常上課)(暫訂) [Tentative] Mei-Chu Game (3/1-3/3)   ♠