MATHEMATICS 5101: Linear Mathematics in Finite Dimensions
Information for the section at 4:10 of AU 2013
Instructor: Dr. Rodica D. Costin
Office: 436 Math Tower
Office hours: Wed 12-1p.m., (new time!)
Fri: 1:30-2:30 p.m.,
or by appointment
Here are lecture notes for the first few lectures:
Wed Aug 21 We start by giving the
abstract definition of a vector space, Sec. 1.1 and 1.2 in the
lecture notes Vector Spaces.
Fri Aug 23 We continued and followed
up to Theorem 15.
Mon Aug 26 We went up to Theorem 20.
Here is the revised chapter on
Vector Spaces (typos corrected etc.)
Wed Aug 28 We finished the first
chapter, and started to talk about Linear Transformations; here
are the notes.
Homework 1 is due next Friday,
(The grader will grade a subset of these problems and give points for turning in solutions for the others.)
Fri Aug 30 Lecture
notes (with revised p.1-5).
Mon Sept 2
Wed Sept 4 Lecture notes (with
revised pages, starting with p.8)
Homework 2 due Friday Sept 13. A few first steps to help
you do calculations using Maple.
Fri Sept 6 Lecture notes (with corrections
and a change in notation)
Mon Sept 9 Lecture notes (we went
through pages 16-21)
Wed Sept 11 We continue from the
notes posted on Monday: left and right inverse and start talking
about the Dual Space
(see revised notes below).
Homework 3 due Friday Sept 20
Fri Sept 20 ...continued
Mon Sept 23 Lecture notes (pages 13-15 only, disregard pages 16-20)
Wed Sept 25 Lecture notes (with pages 16 and up revised)
Homework 5 due
Friday Oct 4
Fri Sept 27 Lecture notes (with p 20,
Friday Oct. 11
Mon Sept 30... we
continued (see the lecture note of Friday Sept 27, Sec. 3.1,
due Wednesday Oct. 9th! (OK, you can turn it in on Friday Oct 11 if need be, but it is better to have it done before, in preparation for the midterm exam. Look on the rest of the problems of 5.2 also.)
Wed Oct 2 Lecture notes
Fri Oct 4
Mon Oct 7
Eigenvectors - full chapter
Wed Oct 9
Fri Oct 11 Midterm exam
Homework 7: (due Friday Oct
18) From the hand out of Oct 11, solve 5.3.3, 5.3.4, 5.3.7, 5.3.8,
and 5.3.17-Typo here: the element (2,2) is not 5, but
0.5!!! (For this last problem you are supposed to check the
formula of .16, that (I-A)(I+A+A^2+...)=I, valid when all
eigenvalues of A have absolute value less than 1, as it is the
case for A=number).
Inner product spaces
Mon Oct 14 Definition of inner product spaces Notes (disregard page 6 here)
Wed Oct 16 Notes (with p 6 revised) (disregard page 10 and up here)
Homework 8 CORRECTION: in Problem 1,
<x,y>=1/4 times the sum
Wed Oct 23 Notes
Here is the full chapter on Inner Product Spaces.
Fri Oct 25 We started the chapter
on Spectral Properties of Self-Adjoint Matrices Notes
Mon Oct 28
Wed Oct 30 Notes
Fri Nov 8 Notes please
disregard p. 34 here, see it revised with the next
Mon Nov 11 Veterans day (no classes)
Wed Nov 13 SDV
Application of SVD: image compression
Mon Nov 18 ...Functional
Wed Nov 20 Normed Spaces
Fri Nov 22 ...continued. More on Lower Rank Approximations
Mon Nov 25 An
introduction to linear mathematics in infinite dimensions. Some
Mon Dec 2
Final exam information
Pick your the final exam in my office MW 436 on Monday Dec 9
between 2-3 p.m. in my office MW 436.
According to the official schedule the final exam is to be turned in on Tuesday Dec 10 between 4:00pm-5:45pm, in my office.