# Notes for 2025F Math107A Introduction to Mathematics I [Course website](https://www-math.nsysu.edu.tw/~chlin/2025FMath107A/2025FMath107A.html) * [Week 1: Introduction and Limit](https://hackmd.io/@jephianlin/H17u7YB5gx) * Week 2: continued * Week 3: continued * [Week 4: Linear Combination](https://hackmd.io/@jephianlin/H15W0dSogl) * Week 5: Discussion on Wednesday, No class on Friday * Week 6: + Discussion on Wednesday: [How to write a good proof?](https://hackmd.io/@jephianlin/good-proof) + Midterm 1 on Friday :::info The midterm 2 covers everything from the textbook [Introduction to Proofs](https://hefferon.net/proofs/). There are only a few pages, so you are encouraged to print it out. In this period, the lessons are **completely through discussions**, without lectures from Jephian. - On Fridays, we will go through definitions together. Each group pick **6 questions** as homework to answer, with at least 1 question from each page. - On Wednesday, we call random people to present your answers. ::: * Week 7: + Discussion on Wednesday: [Common English usage in Mathematics](https://hackmd.io/@jephianlin/eng-in-math) + No class on Friday * Week 8: + Discussion on Wednesday: [Logic connectors](https://hackmd.io/@jephianlin/eng-in-math) and [logic flow](https://www-math.nsysu.edu.tw/~chlin/math-runway/proof-puzzles.pdf) + Chapter 1 Numbers in [Introduction to Proofs](https://hefferon.net/proofs/) * Week 9: + Discussion on Wednesday + Chapter 2 Sets in [Introduction to Proofs](https://hefferon.net/proofs/) * Week 10: + Discussion on Wednesday + Chapter 3 Functions and Relations in [Introduction to Proofs](https://hefferon.net/proofs/) * Week 11: + Discussion on Wednesday + Complete everything in [Introduction to Proofs](https://hefferon.net/proofs/) * Week 12 + Discussion on Wednesday + Midterm 2 on Friday :::info There will be the Poster Exhibition on **Wednesday (12/24) 10:00 ~ 12:00** on the **first floor of College of Science**. You may find [some photos of past events](https://photos.google.com/share/AF1QipM-Dg0KYIqmUGkJFi_b-X4eohXFRbyFucUFwGrKgg7TAqj1yc8r8Kx8NjLjoL6-GQ?key=b0VlNUNrQWhjX20zd2pqYVdmNy03cnRCM1otaEV3) through the link. The goal of the last period of this semester is to equip you with the presentation skills and offer you experiences at international conferences. You need to join a group and give a poster presentation (within 5 minutes). **Resources:** - [Projects for newbie math lovers](https://hackmd.io/@jephianlin/projects-newbie): List of potential projects for students who loves mathematics yet are new to college mathematics. - [Padlet](https://padlet.com/jephianlin/introduction-to-mathematics-i-preparation-for-poster-exhibit-autj21p3q8pe4z8i): Submit your group topic, members, any progresses, and poster PDF file. - [Overleaf](https://overleaf.com/): Online LaTeX platform for building your poster PDF. Learn how to type math formulas [here](https://sagelabtw.github.io/LA-Tea/style.html). Create your own project and use the [template](https://www.overleaf.com/read/rxfwfcgjcvxz#39dbf2). **Grading scale:** - 0: Not prepared. - 5: You don't really understand the content. - 10: You understand the content. - 15: You understand the content and the presentation is smooth. - 20 or more: You suprised me! ::: * Week 13: Research + Group working time on Wednesday: Decide your topic and your group member. Any changes after this day requires approval from the instructor. + Group working time on Friday: Explore your topics following the steps in [Projects for newbie math lovers](https://hackmd.io/@jephianlin/projects-newbie). * Week 14: Research + Please work on your poster and practice your presentation. + Submit your current draft through Padlet by **Wednesday (12/10) 23:59**. + No class this week. * Week 15: Research + Submit your poster PDF through Padlet by **Wednesday (12/17) 23:59**. + Group working time on Wednesday. + **Digital poster on Friday**: Each group needs to bring a computer to demonstrate the poster. * Week 16: Presentation + Poster Exhibition on **Wednesday (12/24) 10:00 ~ 12:00** on the **first floor of College of Science**. + People who cannot attend the Poster Exhibition should present their work individually at the regular class time **Wednesday (12/24) 13:00 ~ 14:00** on the **first floor of College of Science**. --- Other content: Graph Isomorphism, Open Set and Closed Set ### Homework Each group should work together to finish the "Practices" part in the note of each week. Please turn in your homework to the TA during the recitation class on **Friday 11:10 ~ 12:00** at SC4014. Before you turn in your work, please check the following. - [ ] Name and student ID are included for each group member. - [ ] Each sentence is complete. - [ ] Take a photo of your work so that you may prepare for the presentation on next Wednesday. ### Discussion After you turned in the homework on Friday, please take the next few days to think carefully about your answers. On **next Wednesday**, I will can some people to present their work. You are welcome to present some problems in "Challenges" as well.