# 2049: Majors' Seminar

Students will work on FOUR projects with different due dates. Each project weights 4 points. The goals are to help you refresh some important topics in Math or learn something interesting from the speakers' talks then know how to type up the reports in LaTex. Check the syllabus for the grading scheme of MATH 2049.

**Instructions**:

• You can work with your classmates to understand the projects but you need to type up the reports on your own. You can also ask for some minor assistance from faculty in the math department or at the library.

• You must cite your work properly. Please refer to this link for instructions on citation.

• You must turn in both LaTex and pdf files of your projects on Dropbox on the due dates. Late project submissions will not be accepted. For reference, check out the projects in the past.

*** Projects which do not relate to talks presented in the seminar:

**Project #1** (due date: 2:10 pm on Tuesday, 2/10)

• State the Mean Value Theorem.

• Illustrate the geometric meaning of the theorem.

**Project #2** (due date: 2:10 pm on Tuesday, 3/3)

• What is Gaussian elimination in Linear Algebra?

• Explain the importance of this method in different applications.

**Project #3** (due date: 2:10 pm on Tuesday, 3/31)

• What is Newton's method?

• Illustrate the geometric meaning of Newton's method in approximating roots of a function.

**Project #4** (due date: 2:10 pm on Tuesday, 4/28)

• Define linear regression. Clearly state and explain the assumptions of simple linear regression.