| 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 |
2025-FALL |
| Course Description |
Mathematics is a field of study about numbers, structures(Algebra), changes(Analysis), shapes(Geometry). 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, in Geometry such as Affine Varieties. 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 taste of the beauty of Mathematics. 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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| Course Content and Homework/Schedule/Tests Schedule |
| Week |
Course Content |
| Week 1 |
Basic English, Sets, Logic |
| Week 2 |
Basic Relations, Orders, Functions (I) |
| Week 3 |
Basic Relations, Orders, Functions (II) |
| Week 4 |
Basic Groups, Rings, Fields |
| Week 5 |
The set of Real numbers (I) |
| Week 6 |
The set of Real numbers (II) |
| Week 7 |
Midterm exam |
| Week 8 |
Metric spaces (I) |
| Week 9 |
Metric spaces (II) |
| Week 10 |
Continuous functions (I) |
| Week 11 |
Continuous functions (II) |
| Week 12 |
Sequences of real numbers (I) |
| Week 13 |
Final exam |
| Week 14 |
Sequences of real numbers (II) |
| Week 15 |
Affine spaces and Affine Varieties (I) |
| Week 16 |
Affine spaces and Affine Varieties (II) |
self-directed
learning |
02.Viewing multimedia materials related to industry and academia.
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| Evaluation |
Participation and in-class quizzes or homework exercises 56%:
If you attend the class, you take the in-class quizzes to obtain 4 points for the week.
Otherwise, you hand in homework exercises to obtain 4 points for the week. The homework assignment will be posted on I-learning. The assignment for each week is due on the Wednesday 6:00pm of the next week. There is no meeting for the final week. Free 4 points will be given
Midterm exam 22%: Cover materials from Week 2 to Week 6
Final exam 22%: Cover materials from Week 8 to Week 12
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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
3. Introduction to Analysis by William R. Wade, Fourth Edition
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| Teaching Aids & Teacher's Website |
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| Office Hours |
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| Sustainable Development Goals, SDGs(Link URL) |
| include experience courses：N |
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