Type of Credit: Required
Credit(s)
Number of Students
1. The Fundations: Logics and Proofs
2. Basic Structures: Sets, Funtions, Sequences, Sums and Matices
3. Algorithms
4. Number Theory and Cryptography
5. Induction and Recursion
能力項目說明
1. 學生須熟練數學基礎之數，集合、函數、無窮，矩陣，演算法等常用符號和原理。
2. 學生須學會基本數學邏輯的推導及思考模式，以順利修習大學數學課程。
3. 數學證明方法之訓練，讓學生備妥基本之數學語言和知識，奠定各數學領域所需之專業基礎知識。
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
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本課程同時使用中英雙語教學
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周次 |
課程主題 |
TA課規劃 |
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1 |
The Foundations: Logic and Proofs Propositions Logic and Application of Propositional Logic |
上課模式說明及設定office hour |
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2 |
Propositional Equivalences and Predicates and Quantifiers |
1.1, 1.2習題解答與觀念講解回答問題，小考評量。 |
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3 |
Nested Quantifiers and Rules of Inference |
1.3, 1.4習題解答與觀念講解回答問題，小考評量。 |
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4 |
Normal Forms and Introduction to Proofs |
1.4, 1.5習題解答與觀念講解回答問題，小考評量。 |
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5 |
Proof Methods and Strategy |
1.6, 1.7習題解答與觀念講解回答問題，小考評量。 |
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6 |
Basic Structures: Sets, Functions, Sequences, Sums, and Matrices Sets and Set Operations |
1.8, 1.9習題解答與觀念講解回答問題，小考評量。 |
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7 |
Functions |
2.1, 2.2習題解答與觀念講解回答問題，小考評量。 |
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8 |
Sequences and Summations |
2.3習題解答與觀念講解回答問題，小考評量。 |
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9 |
期中考 |
檢討考卷 |
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10 |
Cardinality of Sets and Matrices |
2.5, 2.6習題解答與觀念講解回答問題，小考評量。 |
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11 |
Algorithms, The Growth of Functions |
3.1, 3.2習題解答與觀念講解回答問題，小考評量。 |
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12 |
Complexity of Algorithms |
3.3習題解答與觀念講解回答問題，小考評量。 |
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13 |
Divisibility and Modular Arithmetic, Integer Representation and Algorithms |
4.1, 4.2習題解答與觀念講解回答問題，小考評量。 |
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14 |
Primes and Greatest Common divisors, Solving Congruences |
4.3, 4.4習題解答與觀念講解回答問題，小考評量。 |
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15 |
Applications of Congruences and Cryptography |
4.5, 4.6習題解答與觀念講解回答問題，小考評量。 |
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16 |
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5.1, 5.2習題解答與觀念講解回答問題，小考評量。 |
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17 |
Recursive Definitions and Structural Induction, Recursive Algorithms and Program Correctness |
5.3, 5.4, 5.5習題解答與觀念講解回答問題，小考評量。 |
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18 |
期末考 |
檢討考卷 |
學生學習投入時間:
每週課堂教學 2小時
每週預習/複習 4-5小時
本課程無涉及 AI 使用。
小考:20% 期中: 40% 期末: 40%
Discrete Mathematics and Its Applications: Rosen