We will learn ...
This course provides an overview of some fundamental areas in mathematics, including calculus, linear algebra, discrete mathematics, and probability. We will explore key definitions from these subjects and learn how to prove or disprove whether an example satisfies a given definition. We will then advance to more proof writing by exploring properties of numbers, sets, functions, and relations. By the end of the course, you will know how to explore and manipulate new mathematical objects.
Definition
exploring definitions by examples, and thinking about its motivations
Property
exploring the properties of given definitions by proof writing
Research
exploring fun topics in mathematics by research
You need to do ...
HW0: Tell me your email before September 12 to get extra 2pt — this is a required work. Important information will be announced through email.
Definition
Midterm 1 (20%):
Property
Midterm 2 (20%):
Research
Presentation (20%):
Homework (40%):
A few tips for learning mathematics ...
Mistakes Make You Smarter: Everyone learns through experiences and mistakes. For each new concept you learn, generate as many examples as possible to train your brain to distinguish between right and wrong.
Ask Questions: Beyond knowledge, mathematics is fundamentally about logic. Question everything you encounter—why it is defined this way, why an assumption is required, why a proof needs a particular step, and so on.
Think Carefully: Sound arguments should hold true in any circumstance. Verify the examples you generate to ensure they align with your argument.
Help Each Other: Learning together can make the process easier. Teaching others is also an effective way to reinforce your own understanding.
Course Info
- Term: Sep 8, 2025 – Dec 26, 2025
- Meeting time: Wednesday, 11:10 am – 12:00 noon @ SC0014
- Meeting time: Friday, 9:10 am – 11:00 am @ SC0014
- Recitation: Friday, 11:10 am – 12:00 noon @ SC0014
- Instructor: Jephian Lin | 林晉宏
- Email: chlin [at] math.nsysu.edu.tw
- Office: SC2002-5
- Office Hours: Tuesday, 3:10 pm – 5:00 pm
- Office Hours: Thursday, 3:10 pm – 5:00 pm
Textbook
Introduction to Proofs
Jim HefferonCourse website
Tentative Schedule
Policies/Ethics
Accessibility
Students with diverse learning styles and needs are welcome in this course. In particular, if you have a disability/health consideration that may require accommodations, please feel free to approach me.
Grading
Percentage scores will be converted to letter grades according to the university-wide standard table.
Attendance
You are expected to attend the classes.
Missing work
If you miss some course components due to illness, accident, family affliction, or religious observances, please talk to me and provide the documentation. In such cases, the course component is excused, and your course score will be calculated by distributing the weight of the missed item(s) across the other course components. Missing components are limited to at most 20%.
Academic integrity
Do not copy others' work, including others' homework, the textbook, online materials, and others' answers in an exam; if it is really necessary, add proper citations to your references. It makes no point (and gives you no point) if the work is not yours since you learned nothing.