2049: Majors' Seminar

Students will choose 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.

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, 2/18)

    •    State the two parts of the fundamental theorem of Calculus.
    •    Illustrate the geometric meaning of the second part.

Project #2 (due date: 2:10 pm on Tuesday, 3/4)

    •    Define an eigenvalue and its associated eigenvector of a square matrix.
    •    Explain the importance of eigenvalues in different applications.

Project #3 (due date: 2:10 pm on Tuesday, 3/18)

    •    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, 4/1)

Choose either one of these problems:

Problem 1

    •    Explain the Central Limit Theorem?
    •    Illustrate the Central Limit Theorem graphically.

Problem 2

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