基礎數學

Mathematical Logic and Reasoning

學期

109-1

學分

0 學分

當期課號

0802

永久課號

DAM1202

開課單位

自主學習課程

授課教師

王國仲

類別

選修

概述

這門課主要的目的是提供學生在修習數學課程上必備的基礎、邏輯、證明的訓練。

先修科目

高中數學

備註

無備註

教學方式

教師未提供此項資料

評分方式

第一次考試時間:2020/4/18,範圍:第一、二章,比重30%。第二次考試時間:2020/6/6,範圍:第三章,比重20%。第三次考試時間:2020/10/3,範圍:第四章,比重20%。第四次考試時間:2020/12/26,範圍:第五、六章,比重30%。

課程大綱

1. Logic and Proofs

1-1 Propositions ans Connectives 1-2 Conditionals and Biconditionals 1-3 Quantified Statements 1-4 Basic Proof Methods (I) 1-5 Basic Proof Methods (II) 1-6 Proofs Involving Quantifiers 1-8 Proofs from Number Theory
2. Sets and Induction

2-1 Basic Concepts of Set Theory 2-2 Set Operations 2-3 Indexed Families of Sets 2-4 Mathematical Induction 2-5 Equivalent Forms of Induction 2-6 Principles of Counting
3. Relations and Partitions

3-1 Relations 3-2 Equivalence Relations 3-3 Partitions 3-4 Modular Arithmetic 3-5 Ordering Relations
4. Functions

4-1 Functions as Relations 4-2 Constructions of Functions 4-3 Functions That Are Onto; One-to-One Functions 4-4 Inverse Functions 4-5 Set Images 4-6 Sequences 4-7 Limits and Continuity of Real Functions
5. Cardinality

5-1 Equivalent Sets; Finite Sets 5-2 Infinite Sets 5-3 Countable Sets 5-4 The Ordering of Cardinal Numbers 5-5 Axiom of Choice
6. Completeness and Real Number System

週次計畫

週次	主題
第 18 週	1. Logic and Proofs 2. Sets and Induction 3. Relations and Partitions 4. Functions 5. Cardinality 6. Completeness and Real Number System

教科書

書名: A transition to advanced mathematics, eighth edition. 作者: Douglas D. Smith, Maurice Eggen, Richard St. Ander

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