Math 22 Spring 2009 Schedule (Syllabus)

Prof. Tanya Leise   MWF 1pm Mudd205 plus Tues 1pm Mudd014

Text: A First Course in Linear Algebra by Robert A. Beezer

(Scroll down to "Lastest Version" and choose the 2nd option, "For electronic viewing [PDF]")

This text includes most of the solutions to the assigned exercises, so please try them on your own first in order to learn the material. Do use the solutions to check your answers and to help you when you get stuck. Reading the solution to a similar exercise may also be very helpful when you're not sure how to do a problem. You may use Mathematica on numerical exercises (indicate what command you used, what answer Mathematica gave, and how you used that to answer the question).
Date
Topic
Assigned Work and Links
Due Date
1/26-1/30


 
M Systems of linear equations (SSLE) Read Section WILA p2-6  
T

Lab #1 in Mudd014

Mathematica Help Sheet

 
W
Reduced row-echelon form (RREF) SSLE.C34,C50,M40,M70 Mon 2/2
F
Row operations Read proof techniques (PT) p769-779  
2/2-2/6
     
M
Types of solution sets (TSS) RREF.C10,C12,C14,T10,T11 Mon 2/9
T
Lab #2 Solving linear systems    
W
Free variables TSS.C21,C22,C24,C25,M51,M52,M53,M57 Wed 2/11
F
Homogeneous systems (HSE) HSE.C21,C22,C25,C31,M50,M51 Wed 2/11
2/9-2/13
     
M
Nonsingular matrices (NM) NM.M51,M52,T10,T30 Mon 2/16
T
Lab #3 Vandermonde matrices    
W
Vector operations (VO)
Linear combinations (LC)
VO.C15,T5,T18
LC.M10,M11
Mon 2/16
F
Spanning sets (SS) SS.C23,C41,C42,C60,T20 Wed 2/18
2/16-2/20
     
M

Linear independence (LI)
Linear dependence and spans (LDS)

LI.C20,C32,T10,T12,T20
LDS.T40
Fri 2/20
T
Lab #4 Concrete mixes    
W
Orthogonality (O) Handout: Gram-Schmidt Wed 2/25
F
Review    
2/23-2/27
     
M
Exam 1    
T
Lab #5 Gram-Schmidt    
W
Matrix operations (MO)
Matrix multiplication (MM)

MO.C14,M21,M24,M25
MM.C30,C32,T40,T41
Mon 3/2
F
Matrix inverses (MISLE, MINM) MISLE.C16,C23,C42,T10
MINM.T10,T11
Wed 3/4
3/2-3/6
     
M Column and row spaces (CRS) CRS.C20a,C31,T40,T41 Fri 3/6
T
Lab #6 Pipes
Pipes diagram
   
W
Four subsets (FS) FS.C61,M50 Mon 3/9
F
Vector spaces (VS)
Subspaces (S)

VS.M12,M15,M20
S.C16,C20,C21,M20
Fri 3/13
3/9-3/13
     
M
Linear independence and spanning sets (LISS)
Bases (B)
LISS.C25,C26,C40,C41
B.C11,C12,C13,C14
Fri 3/13
T
Lab #7 Portfolio analysis    
W

Dimension (D)
Properties of dimension (PD)

D.C21,C22,C23,C35,C36,M20
PD.T15,T20
Mon 3/23
F
Determinants (DM, PDM)
DM.C23,M15
PDM.M30,T20
Wed 3/25
3/14-3/22
Spring Recess    
3/23-3/27      
M
Determinants applications
Cramer's rule
Determinants HW Fri 3/27
T
Lab #8 Geometry and determinants    
W
Trace Rank Theorem and Trace HW Fri 4/3
F
Review Solutions to Rank Theorem Homework  
3/30-4/3
     
M
Exam 2    
T
No class    
W
Eigenvalues (EE) EE.C19,C22,C23,C24,T10 (do first 3 problems by hand) Wed 4/8
F
Properties of eigenvalues (PEE) PEE.T10,T22 (hint: think about <Uv,Uv> where v is an eigenvector of U) Wed 4/8
4/6-4/10
     
M
Similarity and diagonalization (SD) SD.C21,C22,T15,T16 Fri 4/10
T
Lab #9 Method of powers
   
W
Finish SD    
F

Projection into a subspace

 
4/13-4/17
     
M
Least squares
Worksheet Fri 4/17
T
Lab #10 Least squares    
W
Linear transformations (LT)
Injective linear transformations (ILT)

LT.C16,C26,C30,C41,C43
ILT.C20,C25,C28,C30

Mon 4/20
F
Surjective linear transformations (SLT)
Invertible linear transformations (IVLT)
SLT.C23,C25,C28,C29,T15
IVLT.C20,C21,C25(abc for 2,3,5), C50,M30,T15,T16
Fri 4/24
4/20-4/24
     
M
Representations (VR, MR) VR.C10
MR.C20,C21,C30,C40,C50,C51
Wed 4/29
T
Lab #11 Discrete dynamical systems    
W
Change of basis (CB) CB.C30,C40,T15 Fri 5/1
F
Review    
4/27-5/1
     
M
Exam 3    
T
Lab #12 Hill cipher Lester Hill's 1929 article on his cipher  
W
Change of basis    
F
Jordan canonical form Worksheet Wed 5/6
5/4-5/8
     
M
Intro to Google

Google handout
#5,7,8,9,10,15

Google exercises due Fri 5/8
T

Lab #13 Google

   
W Google and Markov chain theory    
F Review for the final exam 2008 2007 2006 final exams (note that W-perp is the set of all vectors that are orthogonal to W)  
       
Final exam

Wednesday, May 13

Mudd 206 2-5pm