Math 312: Linear Algebra |
Spring 2013 |
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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 4E15Grader: [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 BretscherLinear Algebra with Applications, 5th edition, Pearson (2012).

*NOTE:*This is a new edition (Dec. 2012). It is also available in abinder--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 ExamsSyllabus

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.

Some References:books, articles, web pages

Notes:

Some Applications Using Linear Algebra

Matrices as Maps and Symmetries

The Letter F

Linear maps from R^{2}to R^{3}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=-D^{2}u

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 aunitarymatrix 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:

- Set 0 (This will not be collected.)
- Set 1 Due: Thurs., Thurs. Jan 17 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 2 Due: Thurs., Thurs. Jan 24 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 3 Due: Thurs., Thurs. Jan 31 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 4 Due: Thurs., Thurs. Feb. 7 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 5 Due: Thurs., Thurs. Feb. 21 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 6 Due: Thurs., Thurs. Mar. 14 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 7 Due: Thurs., Thurs. Mar. 28 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 8 Due: Thurs., Thurs. Apr. 4 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 9 Due: Thurs., Thurs. Apr. 11 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 10 Due: Thurs., Tues. Apr. 23 in class [Late papers will be accepted until 1:00 PM Wednesday.]

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

- Exam 1: Tues. Feb. 12, 2013: Original, Compressed
- Exam 2: Thurs. March 21, 9:00-10:20 Original, Compressed
- Final Exam: Wed. May 1, 2013: Original, Compressed, Solutions
- List of Exam Scores