Math 312: Linear Algebra |
Spring 2014 |
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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: Christodoulos Savva

Telephone: (215) 746-3201

email:csavva AT sas.upenn.edu

Office Hours: Tues 1:30-2:30 & Wed. 3-4 (and by appointment) in DRL 3W1.Linear Algebra is at the heart of many diverse current applications of mathematics. Notable contemporary examples involve understanding large data sets such 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 text 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 Canvas site has been arranged for the course. You may find it useful for communication.

Step one is to sign-up.

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 recently have taught this course several times: Math 312 Fall 2012 Math 312 Spring 2013.

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:

Homework and Exams from Dr. Jauregui's Section of Math 312, Fall 2012.

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.

kernel and image

Some Maple Examples, Volcano

Span, Basis, etc.

A large collection of Linear Algebra Problems [ compressed version]Inner Products and Orthogonality

Inner Products & Least Squares,

Least Squares -- weighted [Large],

Examples Using Orthogonal Vectors [Large]

Examples and Fourier Series for f(x)=x

Quadratic polynomials Max-Min-SaddlesMarkov Chains and Positive Matrices

Markov-Google: Dr. Jauregui's slides (Oct.25, 2012)

2002 Ivy League Basketball ranking, Searching the Web with Eigenvectors

Properties of DeterminantsOrdinary Differential Equations:

The kernel of Lu := u"+4u

Lu=-D^{2}u

ODE-Matrix

Eigenvalues and ODE's

ODE Systems

ODE: Complex Eigenvalues [Large]

Tri-Diagonal Matrix

Example of a poor solution

Change of variable in a multiple integral [Large]SVD:

Notes on Singular Value Decomposition [Large]

Tutorial on Principal Component Analysis

Principal Component Analysis: Example

Application to Image Compression using Matlab: Melancholia Melancholia-Square SVD: Matlab (p. 29)

Patterns in Supreme Court Decisions A 2003 analysis using singular value decomposition.

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 [Large]Linear Programming;

An Example, figure More Examples,

Linear Programming From Linear Algebra and its Applications by Gilbert Strang.pdf [Canvas]

Homework Assignments:

- Set 1 Due: Thurs. Jan 23 in class [Late papers will be accepted until 1:00 PM Friday.] Solutions
- Set 2 Due: Thurs. Jan 30 in class [Late papers will be accepted until 1:00 PM Friday.] Solutions
- Set 3 Due: Thurs. Feb. 6 in class [Late papers will be accepted until 1:00 PM Friday.] Solutions
- Set 4 Due: Thurs. Feb. 13 in class [Late papers will be accepted until 1:00 PM Friday.] Solutions
- Set 5 Due: Thurs. Feb. 27 in class [Late papers will be accepted until 1:00 PM Friday.] Solutions
- Set 6 Due: Thurs. Mar. 6 in class [Late papers will be accepted until 1:00 PM Friday.] Solutions
- Set 7 Due: Thurs. Mar. 20 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 8 Due: Thurs. Mar. 28 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 9 Due: Thurs. April 10 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 10 Due: Thurs. April 17 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 11 Due: Thurs. April 24 in class [Late papers will be accepted until 1:00 PM Friday.]

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. 18, 2014: Original, Condensed, Solutions.
- Exam 2: Tues. Apr. 1, 2014: Original, Condensed, Solutions.
- Final Exam: Monday, May 5, 2014: Original, Condensed, Solutions.
- List of Exam Scores