| Course Name |
(中) 數學導論(1232) |
| (Eng.) Introduction to Mathematics |
| Offering Dept |
Department of Applied Mathematics |
| Course Type |
Required |
Credits |
3 |
Teacher |
TSAI YA LUN |
| Department |
Department of Applied Mathematics/Undergraduate |
Language |
English |
Semester |
2026-FALL |
| Course Description |
Mathematics is a field of study about infinity(numbers), structures(Algebra), shapes(Geometry), uncertainty(Probability), estimations(Analysis), and changes(Dynamics). Modern study in mathematics follows the axiomatic approach based on the Set theory and Logic. In this course, we will present some basic introduction from the set theory to different fields in Mathematics, particularly in Analysis such as continuous functions and sequences of real numbers, in Algebra such as Fields. All materials covered will be the very basic ones. |
| Prerequisites |
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self-directed learning in the course |
Y |
| Relevance of Course Objectives and Core Learning Outcomes(%) |
Teaching and Assessment Methods for Course Objectives |
| Course Objectives |
Competency Indicators |
Ratio(%) |
Teaching Methods |
Assessment Methods |
The main goal of this course is to prepare freshman majoring in mathematics with some tastes of the beauty of mathematics, understanding of reasons why mathematical truth is always true, and probably the acknowledgment of why mathematics can be good. The other objective is to prepare them the ability to read mathematical literature written in English and, moreover, the ability to write proofs in English.
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| 1.Basic Knowledge in Mathematical Sciences |
| 2.Professional Knowledge in Mathematical Analysis |
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| Attendance |
| Assignment |
| Quiz |
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| Course Content and Homework/Schedule/Tests Schedule |
| Week |
Course Content |
| Week 1 |
Basic English, Sets, Logic (I) |
| Week 2 |
Basic English, Sets, Logic (II) |
| Week 3 |
Basic Relations, Orders, Functions (I) |
| Week 4 |
Basic Relations, Orders, Functions (II) |
| Week 5 |
Basic Relations, Orders, Functions (III) |
| Week 6 |
Basic Groups, Rings, Fields (I) |
| Week 7 |
Basic Groups, Rings, Fields (II)
Midterm exam (I) 10/22 |
| Week 8 |
Midterm exam (II) 10/29 |
| Week 9 |
The set of Real numbers (I) |
| Week 10 |
The set of Real numbers (II) |
| Week 11 |
The set of Real numbers (III) |
| Week 12 |
Metric spaces (I) |
| Week 13 |
Metric spaces (II) |
| Week 14 |
Continuous functions (I) |
| Week 15 |
Continuous functions (II) |
| Week 16 |
Final exam (I) 12/21
Final exam (II) 12/24 |
self-directed
learning |
02.Viewing multimedia materials related to industry and academia.
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| Evaluation |
(1) In-class quizzes or homework exercises 39%+(1%~6%):
In-class participation points are 1~6: Every obtains 1 free point and at most 5 more points besides the free one. Moreover, if you attend the class, you take the in-class quizzes to obtain points from quizzes. Otherwise, you hand in homework exercises to obtain 1 point for each hour you miss class. You can miss the classes for at most 13 hours. The homework assignment will be posted on I-learning. The assignment for each homework is due on the Monday/Thursday 5:00pm of the next week.
(2) Midterm exams 12%+12%:
Midterm (I) is on 10/22 and Midterm exam (II) is on 10/29. Cover materials from Week 1 to Week 7 (Open books, open notes)
(3) Final exams 24%+12%:
Final (I) is on 12/21 and Final exam (II) is on 12/24. Cover materials from Week 9 to Week 15 (Open books, open notes)
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| Textbook & other References |
No required textbook, but here are some suggested references:
1. Hangout for each week will be uploaded on I-Learning.
2. Foundations of Higher Mathematics by Peter Fletcher, C. Wayne Patty, Third Edition
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| Teaching Aids & Teacher's Website |
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| Office Hours |
| 預約 |
| Sustainable Development Goals, SDGs(Link URL) |
| include experience courses：N |
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