Math 411, Fall 2003

Syllabus & Homework

On this page you will find a short syllabus for Math 411 indicating the topics and sections of the text we will cover. You should check this page frequently to obtain your homework assignments.

Course Syllabus

Math 411 is a second course in Linear Algebra; the first course, Math 311, is a prerequisite. The difference between these courses is both the level of sophistication and the perspective: whereas Math 311 concerns matrices, Math 411 concerns linear transformations.

I hope to cover the entirety of Axler's book, Linear Algebra Done Right, and to discuss a few additional topics. In detail:

vector spaces

basis and dimension
subspaces, quotient spaces and direct sums
dual spaces

linear transformations

kernel and range
transpose
rank-nullity theorem
eigenvalues and eigenvectors
structure theorems and canonical forms

inner product spaces
operators on inner product spaces

self-adjoint operators
normal operators
positive operators
orthogonal and unitary operators
the spectral theorem: diagonalization

quadratic and bilinear forms

rank
signature
classical groups

Detailed Syllabus & Homework Assignments

An example of how to read the table.

On Tuesday, 26 Aug we covered pages 1-12 of Chapter 1 in class.
For Thursday, 28 Aug your assignment is to
- Do problems 1,2,4 on page 19
- Read pages 1-12 thoroughly.
- Do a first reading of pages 13-18.

Date Sections Homework Assignment Reading
Tue, 26 Aug Ch. 1, p1-12 1,2,4 on p19 Ch. 1, p1-18.
Thu, 28 Aug Ch. 1, p13-18 5,7,8,14,15 on p 19 and extra problem Ch. 1, p13-18 and Ch. 2, p22-23
Tue, 2 Sep Ch. 2, p22-24 1,2,4 on p35 Ch. 2, p22-27
Thu, 4 Sep Ch. 2, p25-30 5,8,9 on p35 Ch. 2, p25-34
Tue, 9 Sep Ch. 2, p30-32 7,11,12,14,16,17 on p35 Ch. 2, p30-34 esp. 2.18 - 2.2.19
Thu, 11 Sep Ch. 3, p37-45 3-5,7 on p59 Ch. 3, p37-45, p53-55
Tue, 16 Sep Ch. 3, p45 8,10,11,14,16,24 on p59 Ch. 3, p48-58
Thu, 18 Sep Ch. 3, p53-58 nothing new nothing new
Tue, 23 Sep Ch. 3, p48-53 20-23 on p59 nothing new
Thu, 25 Sep Ch. 3, p48-53 nothing new review
Tue, 30 Oct Problems nothing new review
Thu, 2 Oct Ch. 4, p63-68 homework sheet Ch. 4, p63-72
Tue, 7 Oct Ch. 4, p69-72, Ch. 5, p75-78 3,5,6 on p94 Ch. 5, p75-84
Thu, 9 Oct Ch. 5, p79-84 8,10,11,15,16 on p94 Ch. 5, p79-87
Tue, 14 Oct Ch. 5, p84-90 nothing new Ch. 5, 87-93
Thu, 16 Oct Ch. 5, p91-93 20,22 on p94 nothing new
Tue, 21 Oct Mostly problems nothing new Ch. 8, p163-167
Thu, 23 Oct Problems & exam review nothing new nothing new
Tue, 28 Oct Exam Exam covers Ch. 1 - 5 Exam
Thu, 30 Oct Ch. 8, p163-167, 173-174 homework sheet, 1,3,10-12 on p188 Ch. 8, p163-176
Tue, 4 Nov Ch. 8, p175-176, 183-187 5,19 on p188 Ch. 8, p177-187
Thu, 6 Nov Ch. 8, p168-169 nothing new nothing new
Thu, 13 Nov Ch. 8, p172-173, 179-182 21-23,25-27 on p188 nothing new
Tue, 18 Nov Ch. 6, p97-102 3,9 on p122 Ch. 6, 97-111
Thu, 20 Nov Ch. 6, p103-108 5,6,8,10 on p122 Ch. 8, 108-116
Tue, 25 Nov Ch. 6, p108-116 homework sheet, 13,19-21 on p122 Ch. 6, p117-121, Ch. 7, p127-132
Tue, 2 Dec Ch. 6, p117-121, Ch. 7, 127-132 26-29 on p122 & 1,2,16 on p158 Ch. 7, p133-137
Thu, 4 Dec Ch. 7, p133-137 12,13 on p158 Ch. 7, p144-150
Tue, 9 Dec Ch. 7, p144-150 19,20,21 on p158 Ch. 7, p152-157
Thu, 11 Dec Ch. 7, p152-157 homework sheet, 23 on p158 done!

Date	Sections	Homework Assignment	Reading
Tue, 26 Aug	Ch. 1, p1-12	1,2,4 on p19	Ch. 1, p1-18.
Thu, 28 Aug	Ch. 1, p13-18	5,7,8,14,15 on p 19 and extra problem	Ch. 1, p13-18 and Ch. 2, p22-23
Tue, 2 Sep	Ch. 2, p22-24	1,2,4 on p35	Ch. 2, p22-27
Thu, 4 Sep	Ch. 2, p25-30	5,8,9 on p35	Ch. 2, p25-34
Tue, 9 Sep	Ch. 2, p30-32	7,11,12,14,16,17 on p35	Ch. 2, p30-34 esp. 2.18 - 2.2.19
Thu, 11 Sep	Ch. 3, p37-45	3-5,7 on p59	Ch. 3, p37-45, p53-55
Tue, 16 Sep	Ch. 3, p45	8,10,11,14,16,24 on p59	Ch. 3, p48-58
Thu, 18 Sep	Ch. 3, p53-58	nothing new	nothing new
Tue, 23 Sep	Ch. 3, p48-53	20-23 on p59	nothing new
Thu, 25 Sep	Ch. 3, p48-53	nothing new	review
Tue, 30 Oct	Problems	nothing new	review
Thu, 2 Oct	Ch. 4, p63-68	homework sheet	Ch. 4, p63-72
Tue, 7 Oct	Ch. 4, p69-72, Ch. 5, p75-78	3,5,6 on p94	Ch. 5, p75-84
Thu, 9 Oct	Ch. 5, p79-84	8,10,11,15,16 on p94	Ch. 5, p79-87
Tue, 14 Oct	Ch. 5, p84-90	nothing new	Ch. 5, 87-93
Thu, 16 Oct	Ch. 5, p91-93	20,22 on p94	nothing new
Tue, 21 Oct	Mostly problems	nothing new	Ch. 8, p163-167
Thu, 23 Oct	Problems & exam review	nothing new	nothing new
Tue, 28 Oct	Exam	Exam covers Ch. 1 - 5	Exam
Thu, 30 Oct	Ch. 8, p163-167, 173-174	homework sheet, 1,3,10-12 on p188	Ch. 8, p163-176
Tue, 4 Nov	Ch. 8, p175-176, 183-187	5,19 on p188	Ch. 8, p177-187
Thu, 6 Nov	Ch. 8, p168-169	nothing new	nothing new
Thu, 13 Nov	Ch. 8, p172-173, 179-182	21-23,25-27 on p188	nothing new
Tue, 18 Nov	Ch. 6, p97-102	3,9 on p122	Ch. 6, 97-111
Thu, 20 Nov	Ch. 6, p103-108	5,6,8,10 on p122	Ch. 8, 108-116
Tue, 25 Nov	Ch. 6, p108-116	homework sheet, 13,19-21 on p122	Ch. 6, p117-121, Ch. 7, p127-132
Tue, 2 Dec	Ch. 6, p117-121, Ch. 7, 127-132	26-29 on p122 & 1,2,16 on p158	Ch. 7, p133-137
Thu, 4 Dec	Ch. 7, p133-137	12,13 on p158	Ch. 7, p144-150
Tue, 9 Dec	Ch. 7, p144-150	19,20,21 on p158	Ch. 7, p152-157
Thu, 11 Dec	Ch. 7, p152-157	homework sheet, 23 on p158	done!