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 enumeration,
	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

  

【成績考核】

        Grading

♠	Homework 20%, two midterm exams 50%, final exam 30%.

 

 

【參考網站】

            Web Page 

♠	https://www.ee.nthu.edu.tw/ccc/eecs2060.html

 



【課程板書與作業】

 

互聯網 (Internet) 除了將各種區域網路 (Local Area Networks)透過互聯網服務供應商(Internet Service Providers, ISPs) 連接起來外,也提供各式的終端設備連網,在龐大的 Internet 上有大量各式的路由器 或是交換機...
 

【課程概述】
      Course Description
       互聯網 (Internet) 除了將各種區域網路 (Local Area Networks)透過互聯網服務供應商(Internet Service Providers, ISPs) 連接起來外,也提供各式的終端設備連網,在龐大的 Internet 上有大量各式的路由器 或是交換機,但是因為各種網路的性質,速度,容量的不同,資料在網路上傳輸就可能發 生各種狀況,例如封包被延遲,被繞遠路,甚至被丟棄等等. 也可能引發網路阻塞, 造成服務中斷。
       本課程將介紹計算機網路的基本運作原理與標準的網路七層結構,由淺入深,可以讓我們對於計算機網路的運作有最基本的認識,本課程還會介紹全球建置最多的有線網路──IEEE 802.3 Ethernet 的基本運作原理, 還有全球建置最多的無線區域網路──IEEE 802.11 Wireless LAN 的基本運作原理,  想知道網路交換機(switches) 是如何運作的嗎 ? 想知道網際網路最重要也最關鍵的通訊協議 ── TCP/IP 是如何運作的嗎 ? 想知道網際網路最重要的路由器 (Routers) 是如何運作的嗎 ? 在本課程裡您都可以學到這些重要的基本知識。
       本課程採用最新之磨課師線上課程 (MOOCs,Massive Open Online Courses) 內容方式授課. 課程內容包含介紹 IEEE 802.3 乙太網路(Ethernet), IEEE 802.11 無線區域網路 (Wireless LAN),IEEE 802.1Q 虛擬區域網路 (Virtual LAN), 交換機的擴張樹演算法 (IEEE 802.1D Spanning Tree Algorithm), 區域網路的可靠傳輸技術──滑動視窗技術 (Reliable Transmission Technology-Sliding Windows),路由器運作原理以及網路互連技術 (Routers,Interneworking, IP protocol), 以及TCP(Transmission Control Protocol) 與網路阻塞偵測與控制技術 (TCP Congestion Control, AIMD,Slow Start)。  

【課程講義與練習題】

熱力學為探討能量的入門科目. Thermodynamic 本身的含義即為熱與功. 熱力學是在探討熱與功之間的轉換等....Thermodynamics is the basic subject to explore the concept of “energy”. The word “Thermodynamics” means heat and work – thus Thermodynamics discusses the transformation between heat and work…

課程說明
         Course Description 
熱力學為探討能量的入門科目. Thermodynamic 本身的含義即為熱與功. 熱力學是在探討熱與功之間的轉換. 由於熱與功之間的轉換需借助物質, 也就是說能量以物質為媒介才能轉換, 熱力學衍生為物質特性與能量間的關係. 本科目的重點在於介紹能量的觀念, 說明熱力學第零,第一,第二,第三定律與其應用; 如何決定物質的狀態(state) 以及所具有的能量, 用於熱力學第一與第二定律的分析; 以及推導Thermodynamic Relations,以及如何利用 Thermodynamic Relation 決定物質的 Property.

Thermodynamics is the basic subject to explore the concept of “energy”. The word “Thermodynamics” means heat and work – thus Thermodynamics discusses the transformation between heat and work. Since the transformation between heat and work requires matters (medium), Thermodynamics can also involve the relationship between matters’ properties and energy. This course will introduce: 

指定與參考用書
 Text Books / References 

教學方式
Teaching Method

教學進度
          Syllabus 

This course provides an overview of the current database management systems. The goals are 1) to get students familiar with how to use a database system to solve real problems; 2) the internals of a database and some state-of- the-art implementations (e.g., MySQL, PostgreSQL etc.).

介紹信號處理在音樂、語音、或其他日常生活中聽得到的聲訊中的應用：包含分析與合成兩大部分。學生修完本課程,應能對這個領域的核心技術、背景觀念有充分理解......This course introduces the application of signal processing, including analysis and synthesis, in music, audio or other sounds that can be heard in daily life. After completing this course, students should be able to fully understand the core technology and basic concepts in this field.

 影片需重新下載可參閱此:https://www.youtube.com/channel/UCuwrgeMCklTPnoN5PVaF5mg/videos

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Course Description
This is one of the core courses for the EE Department. The intent is to use rigorous mathematical expressions so that the students may appreciate experimentally observable phenomenom regarding static electric fields, steady electric current, static magnetic fields. The students will also learn the coupling between electric and magetic fields that leads to time-varying electro-magnetics. The derivation and physical insight behind the Maxwell’s Equations will be emphasized.
　　The course contents are pivotal for later course such as electromagnetic waves, introduction to optical engineering, photonics, high-frequency circuit design, solidstate devices.
　　Required background knowledege include: Calculus (I, II), vector analysis 
 ♠ This course requires your total devotion. Preview and review are essential in keeping up!

Engineering Mathematics in this class is to teach how to solve differential equations, which are models in many engineering problems. This post-calculus mathematics is needed and used by today's scientists and engineers....

1 	First order differential equations 
2	Second order differential equations 
3	Laplace transform 
4	Series solutions for differential equations 
5	Systems of differential equations 
6	Fourier series 
	【工程數學一題庫練習】