Penn Math Math 312: Linear Algebra Spring 2013

Faculty: Jerry L. Kazdan
    Telephone: (215) 898-5109
    email: kazdan AT math.upenn.edu
    Office Hours: Wed. 10:30-11:30   (and also by appointment) in DRL 4E15
Grader: [Your last name M-Z] Yuanpei Cao
    email: yuanpeic AT sas.upenn.edu
    Office Hours: Wed. 12:30-2:30 (and by appointment) in DRL 1N1.
Grader: [Your last name A-L] Ying (Anna) Pun
    Telephone: (215) 898-6218
    email: punying AT math.upenn.edu
    Office Hours: Wed. 3-4, Thurs. 4-5 (and by appointment) in DRL 3C17.

Linear Algebra is at the heart of many diverse current applications of mathematics. Notable contemporary examples involve understanding large data setssuch as the idea behind Google searches and the structure of DNA.
Our goal is to present both the major ideas and give you technical skills.
To be successful in this course, you should be present for all class meetings and plan to take good notes.

Text: Otto Bretscher Linear Algebra with Applications, 5th edition, Pearson (2012).
*NOTE:* This is a new edition (Dec. 2012). It is also available in a binder--ready version, which is the same book but is three-hole punched and is less expensive.
The ISBN for the binder-ready version is: 0321796942 The hardbound ISBN is: 0321796977
Penn's Bookstore (and probably online sources) should have both versions.

Note that a Blackboard site has been arranged for the course. You may find it useful for communication.

Prerequisites & Review Material: Math 240 or equivalent.
To remove rust from your backgroung I suggest doing the linear algebra problems from recent Math 240 Final Exams

Syllabus
I taught this course last semester: Math 312 Fall 2012.
Based on that experience, the version this semester will be a bit different. In particular, in order to do more applications of linear algebra to real-life problems we will cover the material in Chapters 1-3 of the text more quickly. It is largely a review of material in Math 240.

Course and Homework Grading

Some References: books, articles, web pages

Notes:
Some Applications Using Linear Algebra
Matrices as Maps and Symmetries
The Letter F
Linear maps from R2 to R3 are just linear equations.
Homework and Exams from Dr. Jauregui's Section of Math 312, Fall 2012.
Some Maple Examples
Span, Basis, etc.
A large collection of Linear Algebra Problems
inner products & least squares,
Orthogonal Projection
Least Squares -- weighted
Summary Fourier: f(x)=x
The kernel of Lu := u"+4u
Lu=-D2u
Eigenvalues and ODE's
Properties of Determinants
Quadratic polynomials   Max-Min-Saddles
Every square matrix A is similar to an upper triangular matrix T (Schur) . Moreover A=U*TU, where U is a unitary matrix and T is upper triangular.
Change of variable in a multiple integral *
SVD Picture example: Melancholia   Melancholia-Square   SVD: Matlab (p. 29)
SVD Supreme Court Example: Patterns in Supreme Court Decisions A 2003 analysis using singular value decomposition.
Linear Programming An Example,   figure   More Examples,  References

Homework Assignments:

Exams: There will be two in-class exams and a Final Exam. You may always use one 3"×5" card with handwritten notes on both sides