Course Elements
This course consists of the following components:
Lectures (recorded)
They serve as the main learning materials for this course.
- Recorded videos of the lectures will be uploaded to Canvas for students to access at their convenience.
- Mandatory quizzes will be integrated into the lectures to assess understanding and encourage active learning.
- Quizzes will be graded either by completion or with unlimited attempts.
Supplementary Materials
Along with the recorded lectures, additional materials relevant to each lecture will be provided.
- These materials include historical notes, terminology explanations, online resources, and additional content that may not be fully covered in the lecture.
- You are encouraged to explore these materials and use them as references in your assignments, exams, and essays.
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 as well.
- Submit your glossary as a PDF file to Gradescope before the Final week.
- The glossary can be used as an index to resources for solving exam problems.
Exercises
Attached to each lecture and some supplementary notes, there will be short questions named exercises for practice and self-assessment.
- Exercises are not mandatory: they will not be collected or graded.
- However, they are highly recommended as they help reinforce understanding of lecture topics and practice important methods.
- The difficulty of exercises is between quizzes and homework problems.
Homework
There will be a total of four weekly homework assignments.
- Collaborative discussions with peers are encouraged. However, you must write the solutions in your own words and acknowledge collaborators.
- Homework is expected to be typed using $\LaTeX$.
- Pay close attention to clear and well-reasoned writing.
- References used in homework answers should be listed (either manually or using BibTeX). Immediate problem-solving resources should be avoided.
- Submissions should be compiled into a PDF file and uploaded to Gradescope.
- The specific grading policy will be determined by the TA.
Exam
There will be one take-home final exam.
- The final exam will consist of approximately 6-8 problems and is estimated to take around 3-4 hours to complete.
- It will be released at the beginning of the last week and due at the end of the session.
- Only results (theorems/lemmas/propositions/examples) provided during the lectures or in the homework are allowed for reference.
- Solutions should be handwritten on the exam paper. You can upload either a scanned copy or an annotated PDF file.
- Before submitting the final exam, ensure that your solutions are well-reasoned, and your writing is clear and legible.
- If you have any questions, please reach out to me or the TA for assistance.
Essay
The ability to present mathematical reasoning in a clear and organized manner through mathematical writing is a skill that requires training. This is also one of the objectives of this course.
- In the middle of the course, you will be provided with a sample essay. Your task is to complete it by filling in the missing steps or details.
- Afterward, you need to choose a topic related to number theory and write your own essay, following the format of the provided sample.
- Essays are expected to be typed using $\LaTeX$.
- The purpose of the essay is to practice mathematical writing. While originality is not a requirement, it is essential to adhere to academic integrity, write clearly, and acknowledge collaboration and references.
Discussion Sections
Discussion sections will provide students with an opportunity to ask questions, review challenging concepts, and engage in collaborative problem-solving.
- These sessions will be conducted by the TA.
- For further details, please consult with the TA.
Communication
Feel free to contact me if you have any questions or concerns.
- Please reach out to me primarily through Canvas messages. If you prefer to email me, please start the subject line with “Math110”.
- Provide as much information as possible regarding the topic you wish to discuss.
- I will respond within 24 hours on weekdays, but please note that weekend delays may occur. Also, remember to check Canvas for any updates.
- Don’t hesitate to reach out.
LaTeX
- $\LaTeX$ is widely used for mathematical writing. You will need 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, Overleaf knowledge base, and $\LaTeX$ wikibook.
- I will provide solution shells for each homework. Upload them to an online $\LaTeX$ IDE such as Overleaf and start typing your solutions.
- Or you can import them into a local $\LaTeX$ IDE. To know more about getting LaTeX locally on your laptops, see The TUG beginning page. (Note that as of 2022, proTeXt has been retired permanently. You can use TeX Live on Windows instead.)
- If you need help getting started, please contact me (Guidelines for Communication).
Note that: to edit and compile the .tex file, you need to download it and upload it to an online or local IDE.