MA2330: Introduction to Linear Algebra

Course descritpion

An introduction to linear algebra and how it can be used, including basic mathematical proofs. Topics include systems of equations, vectors, matrices, orthogonality, subspaces, and the eigenvalue problem. Not open to students with credit in MA2320 or MA2321. Course prerequisite is any math class numbered MA1090 or higher.

Credits: 3.0

Lec-Rec-Lab: (0-3-0)

Semesters Offered: Fall, Spring

Pre-Requisite(s): MA 1160 or MA 1161

Text

R.A. Beezer, A First Course in Linear Algebra, (Version 2.22)

This is a free electronic book available from Rob Beezer's website: http://linear.ups.edu/adoption.html .

It is huge, comprehensive and somewhat unusual in the way it is written but it contains all that we need and the price is right!

I suggest you download the PDF file labeled "For electronic viewing" with file name fcla-electric-2.22.pdf and keep it on your computers just occasionally printing out small portions as you need.

This download is: http://linear.ups.edu/download/fcla-electric-2.22.pdf.

There are also other formats available for example for, Kindle and sony reader. See: http://linear.ups.edu/download.html .

If you like this free electronic book please consider donating to R.A. Beezer's project: http://linear.ups.edu/donate.html .

Tentative Schedule.

Solving systems of linear equations.

Date

Topic

Homework

Due

Aug 30

SSLE Solving Systems of Linear Equations

Read section WILA:

What is Linear Algebra?

Read section SET: Sets

Sep 01

Reduced Row-Echelon Form (RREF)

SSLE.C34,C50,M40,M70

Sep 08

Sep 03

Types of Solution Sets (TSS)

RREF.C10,C12,C14,T10,T11

Sep 08

Sep 06

Labor Day Recess

Sep 08

Free variables (FV)

TSS.C21,C22,C24,C25,

M51,M52,M53,M57

Sep 13

Sep 10

K-Day Recess

Sep 13

Homogeneous Systems of Equations (HSE)

HSE.C21,C22,C25,C31,M50,M51

Sep 15

Nonsingular Matrices (NM)

NM.M51,M52,T10,T30

Sep 17

Review

Sep 20

Exam 1

Vectors, Matrices, Orthogonality and Data fitting.

Date

Topic

Homework

Due

Sep 22

Vector Operations (VO)

Linear Combinations (LC)

VO.C15,T5,T18

LC.M10,M11

Sep 24

Spanning Sets (SS)

SS.C23,C41,C42,C60,T20

Sep 27

Linear Independence (LI)

LI.C20,C32,T10,T12,T20

Sep 29

Orthogonality (O)

Handout t.b.a.

Oct 4

Oct 01

(O) continued

Oct 04

Matrix Operations (MO)

Matrix Multiplication (MM)

MO.C14,M21,M24,M25

MM.C30,C32,T40,T41

OCt 06

Oct 06

Matrix Inverses (MISLE,MINM)

MISLE.C16,C23,C42,T10

MINM.T10,T11

OCt 08

Oct 08

Data Fitting: Least Squares

and Orthogonal Projections

Handout t.b.a.

Oct 13

Oct 11

Data Fitting continued

Oct 13

Review

Oct 15

Exam 2

Vector spaces and dimension.

Date

Topic

Homework

Due

Oct 18

Column and Row Spaces (CRS)

CRS.C20a,C31,T40,T41

Oct 20

Four Subsets (FS)

FS.C61,M50

Oct 22

Vector Spaces and Subspaces (VS,S)

VS.M12,M15,M20

S.C16,C20,C21,M20

Oct 27

Oct 25

(VS,S) continued

Oct 27

Linear Independence

and Spanning Sets

(LISS)

LISS.C25,C26,C40,C41

Oct 29

Bases (B)

LISS.C25,C26,C40,C41

B.C11,C12,C13,C14

Nov 01

Dimension (D)

D.C21,C22,C23,C35,C36,M20

Nov 03

Finish (D) and Start (PD)

Nov 05

Properties of Dimension (PD)

PD.T15,T20

Nov 08

Review

Nov 10

Exam 3

Eigenvalues and diagonalization

Date

Topic

Homework

Due

Nov 12

Determinants (DM,PDM)

DM.C23,M15

PDM.M30,T20

Nov 15

Determinants (DM,PDM)

DM.C23,M15

PDM.M30,T20

Nov 18

Eigenvalues and Eigenvectors (EE)

EE.C19,C22,C23,C24,T10s

(do first 3 problems by hand)

Nov 20

Properties of Eigenvalues

and Eigenvectors

(PEE)

PEE.T10,T22

(Hint: think about 〈Uv,Uv 〉,

where v is an eigenvector of U)

Nov 29

Thanksgiving Recess Nov 22 to Nov 26

Nov 29

Similarity and Diagonalization (SD)

SD.C21,C22,T15,T16

Dec 01

Application 1: Difference equations

handout t.b.a.

Dec 02

Application 2: Differential equations

handout t.b.a.

Dec 05

Review

Dec 08

Exam 4

Finale.

Dec 10

Final Review

Dec 15

Final Exam 3:00pm to 5:00pm

You are responsible for all of the material in these sections even if it is not presented in class.

Grading

Your grade will be based on 3 out of 4 in class examinations (15% each, lowest exam score dropped) a 2 hour final (45%) and homework exercises (10%).

Some advice

This course in Linear Algebra will likely be your first introduction to abstract axiomatic mathematics. This approach may seem very unfamiliar at first and your performance will depend heavily on how much effort you put into understanding the concepts. At a minimum you should

Attend all lectures.
Review each lecture afterwards - aiming for understanding.
Attempt all exercises by yourself.
Work through exercise solutions with other students in the class.
Read the course related material.

File translated from T_EX by T_TH, version 3.87.
On 30 Aug 2010, 08:54.