MATHEMATICS 5101: Linear Mathematics in Finite Dimensions
Information for the section at 9:10 of AU 2017, Enarson Classroom Bldg 358
Instructor: Dr. Rodica
Office: 436 Math Tower
Office hours: MW 10:20-11:15 AM or by appointment
I will post here lecture notes, as well as homework assignments and other announcements.
Wed Aug 23 We went over
Sec.1.1 and 1.2 in the lecture notes 1.Vector Spaces.
Fri Aug 25 We continued from the notes above: Sec. 1.3
Mon Aug 28 You are responsible for reviewing complex numbers (operations, polar form, geometric interpretation, the n'th roots of 1)
Exercise: (you do not need to turn it in, but we will use these facts)
1. Show that any n'th root of 1 (that is, a number z so that z^n=1) has the form exp(2 pi k i/n) for k integer.
2. Denote a=exp(2 pi i/n). Show that 1, a, a^2,..., a^(n-1) are all the roots of 1 (that is, there are n of them, and no more).
3. Show that the number a above satisfies 1+a+a^2+...+a^(n-1)=0
4. Plot, on separate planes, the roots of 1 for n=2. Then for n=3, then n=4. Then n=5. What do you see?
Wed Aug 30
We started Sec. 2.2.
HW 1 due Wed Sept 6
Fri Sept 1st We finished the chapter on Vector Spaces.
Wed Sept 6 We start talking about determinants. Here are the lecture notes: 2. Determinants (new file)
Here is a Maple example on how to solve systems and produce latex output.
HW 2 due Wed Sept 13.
Fri Sept 8 We continued determinants (Sec. 2.4 and 2.5) with a brief break for a fire alarm.
Mon Sept 11 We finished determinants and started 3.
Wed Sept 13 We did Sec. 2.2 and 2.3 (of Linear Transformations).
Here is HW3 due Wed Sept 20.
Fri Sept 14 Null space and range. Here is the edited chapter on linear transformations, with changes in Sec. 3.5.
Mon Sept 18 We did Sec. 3.6, 3.7.
Wed Sept 20
We did Sec. 3.8, 3.9.1. Here is HW4
Fri Sept 22 We continued...
Mon Sept 25 and continued... with Sec. 3.11
Wed Sept 27 Here is a handout and HW 5 .
We will soon start the chapter on 4.Eigenvalues and Eigenvectors.
Fri Sept 29 We finished Ch. 3 and started Ch.4, on Eigenvalues and Eigenvectors, Sec. 4.3
Mon Oct 2 We continued with Sec. 4.2, 4.4...up to 4.12.
Wed Oct 4 We continued with 4.1.13, 4.1.14 (but did not go over Remark 1. points 3. and 4.) HW6 and its corresponding handout.
Here is the chapter on Eigenvalues and Eigenvectors with revised proof of Theorem 6 and of sections 4.13, 4.14 (I expect more revisions along the way)
Fri Oct 6 Sec 14.14, 15
Mon Oct 9 We proved that similar matrices have the same characteristic polynomial and we did a review.
MIDTERM: Wednesday Oct. 11. You are allowed to bring a cheat sheet (regular size paper with your own notes, written on both sides, if you wish). Required material: everything!
Topics not to be missed when you review: examples of vector spaces that we often encountered, linear transformations (definition, null space, range, theorems and other facts, inverse, right and left inverse, important examples). Eigenvectors and eigenvalues (definition, calculation, theorems and other facts, application to differential equations).
Wednesday Oct. 11 Midterm!
Have a Nice Break!
Mon Oct 16 We showed that det(AB)=det A det B, here are the notes. And 4.14. 1...3.
Wed Oct 18 Here is HW7. We did 14.6.: 3, 4, 14.7, 5.1, 5.2
Fri Oct 20 We covered 5.3
Mon Oct 23 We covered 5.4, 5.6
Wed Oct 25 HW8 We covered 5.6.1 and 2, also 5.8
Fri Oct 27 plan: 5.9, 5.10-12, 6.2.7, 6.3 then Inner Product Spaces
Mon Oct 30 we continued...
Wed Nov 1 and continued up to page 10. Here is HW 9.
Fri Nov 3 and continued
Mon Nov 6 and continued up to Sec. 8.1
Mon Nov 13 and continued with Sec. 11.2-3, 11.5-6Wed Nov 15 Sec 11.7, 11.9-11, 12.1.1. And here is next HW, due Wed Nov 29, HW 11
Final exam: Monday Dec 11 10:00am-11:45am according to the university schedule (please check!)