Penn Math Math 312: Linear Algebra Spring 2014

Faculty: Jerry L. Kazdan
    Telephone: (215) 898-5109
    email: kazdan AT
    Office Hours: Wed. 10:30-11:30   (and also by appointment) in DRL 4E15
Grader: Christodoulos Savva
    Telephone: (215) 746-3201
    email: csavva AT
    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 Bretscher Linear Algebra with Applications, 5th edition, Pearson (2012).
*NOTE:* This text 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 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 Exams

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.

Course and Homework Grading

Some References: books, articles, web pages

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 R2 to R3 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-Saddles
Markov 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 Determinants
Ordinary Differential Equations:
    The kernel of Lu := u"+4u
    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]
   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 a unitary matrix 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:

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