AMS10A, Fall 2012, Section 01: Lectures

Week

Date

Section in the book (Lay)

Topic

 

Week 1

Fri Sept 28th

Mon Oct 1st

Wed Oct 3rd

Fri Oct 5th

 

Supp Notes

Intro

Algebraic theory of complex numbers

Geometric theory of complex numbers

Polar forms of complex numbers

Complex polynomials and roots

Week 2

Mon Oct 8th

Wed Oct 10th

Fri Oct 12th

Ch 1.1

Ch 1.2

Ch 4.6

Linear systems of equations

Echelon forms and ranks

 

Week 3

Mon Oct 15th

Wed Oct 17th

Fri Oct 19th

Ch 1.6 & Ch 1.10

Ch 2.1 & Ch 2.4

Ch 2.2-2.3

Applications of linear systems

Matrix algebra

Inverses

Week 4

Mon Oct 22nd

Wed Oct 24th

Fri Oct 26th

Ch 2.5

Ch 2.6-2.7

Ch 1.3-1.4

Ch 4.1

LU factorization

Applications

Spaces of vectors

 

Week 5

Mon Oct 28th

Wed Oct 31st

Fri Nov 2nd

Ch 1.5 & Ch 1.7

Ch 4.3-4.7

(Ch 2.8 2.9)

Span, Linear independence

Bases, dimension, co-ordinate systems, change of basis

Mid-term

Week 6

Mon Nov 5th

Wed Nov 7th

Fri Nov 9th

Ch 2.8, 2.9

Ch 4.2. (4.3, 4.5. 4.6 again)

Ch 1.8-1.9

Subspaces: Null space, column space, row space

Linear transformations in Rn

Week 7

Mon Nov 12th

Wed Nov 14th

Fri Nov 16th

Ch 3

Ch 6.1

Determinants

Dot products, norms of vectors

Week 8

Mon Nov 19th

Wed Nov 21st

Fri Nov 23h

Ch 6.2-6.3

Orthogonality

Orthogonal subspaces, projections, bases

THANKSGIVING

Week 9

Mon Nov 26th

Wed Nov 28th

Fri Nov 30th

Ch 6.4-6.6

Ch 5.1-5.2

Ch 5.3

Ch 5.6-5.8

(Ch 4.8-4.9)

Gram-Schmidt; Applications - Best approximation

Eigenvalues

Diagonalization

Applications

 

Week 10

Mon Dec 3rd

Wed Dec 5th

Fri Dec 7th

(Ch 4)

General vector spaces

Review

Finals exam

Monday

Dec 10th

12:00pm-03:00pm

DONE!