MATH 110: Introduction to Number Theory

Fall 2022 • MWF 2:40 PM - 3:45 PM at Soc Sci 2 071 (in-person)

• Course Information
• Learning Outcomes
• Grade
• Guidelines
  • Quizzes
  • Glossary
  • Homework
  • Midterm
  • Final
  • Guidelines for Communication
  • $\LaTeX$

Course Information

Syllabus on Github

• Instructor.  Xu Gao (xgao26@ucsc.edu), McHenry Library 1292

• Office Hours.  MW 4:30 – 5:30 PM, or by appointment. (This is when you come and talk to me if you have any questions, or otherwise.)

• Textbook.  An Illustrated Theory of Numbers by Martin H Weissman.

• TA.  Yuk Shing Lam (ylam14@ucsc.edu), Mchenry 1261. 

• TA’s Office Hours.  Tuesday and Friday 11:00 AM – 12:00 PM

• Discussion Sections.

  Cowell 216	Tu 09:20AM-10:25AM
  McHenry 1270	F 09:20AM-10:25AM

Lecture notes can be found here.

Learning Outcomes

• Familiarize Ideas and problems in number theory that play essential roles in modern mathematics.
• Understand the roles of theorems, proofs, and counterexamples.
• Develop problem-solving skills.
• Practice clear, concise, and precise mathematical writing.

Grade

The grade will be based on: Quizzes (10%), Glossary (10%), Homework (30%), Midterm (20%), and Final (30%). We will use the following grading scheme (but curve may apply).

Total scores	Grade
$\geqslant 98$	A$+$
$90$ – $97$	A
$88$ – $89$	A$-$
$85$ – $87$	B$+$
$78$ – $84$	B
$75$ – $77$	B$-$
$70$ – $74$	C$+$
$60$ – $69$	C
$55$ – $59$	C$-$
$40$ – $54$	D
$< 40$	F

To pass the course, your grade should be at least C.

Guidelines

Quizzes

• Prepare a draft paper at the beginning of each meeting and write down your name and student ID.
• There may or may not be a quiz near the end of the meeting. If there is, you are expected to finish it in at most 5 minutes, and I will show you the answer after that.
• The quizzes will be collected when the meeting ends. Even if there is no quiz in one meeting, I will still collect the draft paper with your name and student ID as a participation record.
• If you cannot attend a meeting, please contact me.

Glossary

• Throughout the course, you will maintain a glossary of terms and results that you find difficult to digest or wish to remember. Add your thoughts on them, and whenever possible, include examples.
• The glossary can be typed or handwritten, long or short, but it cannot be empty. The point is it is about your learning experience.
• You are asked to share your glossary every two or three weeks. To do this, navigate to the Glossary page and upload a PDF file to Gradescope. Be aware of the due date.

Homework

• There will be homework every week. Please turn in the homework on the due date. (If you need an extension, please ask before the due date.)
• You are encouraged to discuss the problems with your peers. However, you must write the homework by yourself using your words and acknowledge your collaborators.
• The homework is expected to be typed using $\LaTeX$. There will be a tex shell for each homework, and you can start with it.
• Pay close attention to the presentation and the clarity of your reasoning. This course is writing-intensive.
• List the references you have used in your answer.
• To submit the homework, navigate to the Homework page and upload the compiled PDF file to Gradescope.

Midterm

• The Midterm is on Oct 24 Monday and will be given during the lecture times.
• Please prepare draft papers before the exam.
• You can use your notes and textbook during the exam. But you cannot discuss the problems with others.
• The only results (theorems/lemmas/propositions) you’re allowed to use are either provided during the lectures or in the homework.

Final

• According to the registrar, the final will be on Tuesday, Dec. 6, from 4:00 PM to 7:00 PM.
• You can look up your notes, homework, and textbook during the exam. But you cannot discuss the problems with others.
• No digital devices are allowed during the exam.
• The only results (theorems/lemmas/propositions) you’re allowed to use are either provided during the lectures or in the homework.
• If you have any questions, ask me or the TA.

Guidelines for Communication

• You are welcome to ask me any questions during class and the office hours.
• Besides those times, please contact me primarily via Canvas. I will reply within 24 hours during the weekdays.
• Contact me via email (xgao26@ucsc.edu) if and only if you haven’t received any response for a long time.
• When you contact me, please provide as much information as possible on the subject you intend to discuss.
• Never hesitate to reach out.

$\LaTeX$

• $\LaTeX$ is widely used for mathematical writing. You will need to learn basic $\LaTeX$ for this course.
• To start, look at the .tex files I provide you. Google anything beyond the files, and use online resources such as Tex Stack Exchange Links to an external site., Overleaf knowledge base Links to an external site., and $\LaTeX$ wikibook Links to an external site..
• I will provide solution shells for each homework. Upload them to online $\LaTeX$ IDEs such as Overleaf Links to an external site.and start typing your solutions.
• Or you can import them into a local TeX IDE. To know more about getting $\LaTeX$ locally on your laptops, see The TUG beginning page Links to an external site.. (Note that as of 2022, proTeXt has been retired permanently. You can use TeX Live on Windows Links to an external site.instead.)
• If you need help getting started, please contact me (Guidelines for Communication).