New Room: CUE 316
This course syllabus
contains important information not otherwise supplied on this website.
Getting good help can sometimes be frustrating. I am trying to make my self available by choosing varied office hours and being available by email. My email response time varies a lot so asking questions early is your best strategy. Sometimes you may have a complex question that would benefit by including a picture in email. This is fine, but please use reduced-size photos -- typically a 250kB picture is sufficient, while a 5MB picture can really bog down email.
Please note that all materials supplied by the instructor are under copyright restrictions and should not be disseminated or copied in written or electronic form except for your personal use in this course. Please keep this in mind when using the Course Textbook
. Chapter 25
. Chapter 26
- [Mon Aug 27] Finish reading Chapter 3.
- [Wed Aug 29] Chapter 4.
- [Fri Aug 31] Chapter 5.
- [Wed Sep 05] Chapter 6.
- [Fri Sep 07] Chapter 7.
- [Mon Sep 17] Chapter 8.
- [Wed Sep 19] Chapter 9.
- [Mon Sep 24] Chapter 10.
- [Wed Sep 26] Chapter 11 and Appendix A.
- [Mon Oct 01] Chapter 12.
- [Fri Oct 05] Chapters 13,14,Appendix B.
- [Mon Oct 08] Chapter 15.
- [Mon Oct 15] Chapter 16.
- [Mon Oct 22] Chapter 17.
- [Wed Nov 07] Through Chapter 21.
- [Mon Nov 26] Through Chapter 25.
- [Mon Dec 02] Through Chapter 26.
- Proof Techniques
- Vector Space Activity, Here are our in-class results.
- Quiz #1 Solution.
- Class Notes from Wednesday, September 5.
- Class Notes from Wednesday, September 12.
- Class Notes from Friday, September 21.
- Class Notes from Monday, September 24.
- Computing Radiographs, September 26.
- Transformations, September 28.
- Class Notes from Wednesday, October 10.
- Some Solutions to the Quiz of Friday, October 19.
- Some Solutions to the In-Class Assignment of Friday, October 19.
- Worksheet on Left-Inverse Tomography, and necessary code: tomomap.m, Lab5Radiographs.mat (33MB), Lab5Reconstructions.mat (30MB), ShowSlices.m.
- Activity on Heat State Evolution.
Here are some sample exercise solutions
from chapters 6 and 7. Keep in mind that lengthy answers are not necessarily better answers. Consider the brevity of my solutions and their focus on the current linear algebra concepts. And here are two more example proofs
. And, here are two examples
of how to show if a transformation is linear or not.
- [Due Date] Assignment
- [Fri Aug 24] Chapter 1, Exercises 1-7.
- [Mon Aug 27] Chapter 2, Exercises 1-6,10,12
- [Wed Aug 29] Chapter 3, Exercises 1-4,8
- [Fri Aug 31] Chapter 3, Exercises 10-14 and Vector Space Activity
- [Wed Sep 05] Chapter 4, Exercises 9,13,17
- [Fri Sep 07] Chapter 5, Exercises 2,4,8,12,13,16
- [Mon Sep 10] Chapter 5, Exercises 21-28
- [Wed Sep 12] Chapter 6, Exercises 16,24,25,31,36,39,42,43,49,50.
- [Fri Sep 14] Chapter 7, Exercises 11,13,14,15,24,27 (Also, know how to answer 5-8,21,23, but do not turn these in as homework.)
- [Fri Sep 21] Chapter 8, Exercises 1(a,b,c,g,h),2(a,b),3,11,14.
- [Wed Sep 26] Chapter 9, Exercises 15-19,33-35.
- [Fri Sep 28] Chapter 10, Exercises 1,2,4,5,8.
- [Wed Oct 03] Chapter 11, Exercises 1-4,7-10. Necessary code: tomomap.m
- [Fri Oct 05] Chapter 12, Exercises 1,3,5,7,8.
- [Mon Oct 08] Chapter 12, Exercises 10,13,15.
- [Wed Oct 10] Chapter 13, Exercises 1-8
- [Mon Oct 15] Chapter 14, Exercises 1,3,5,9,19; Chapter 15, Exercises 1-10 for Scenario B.
- [Fri Oct 19] Chapter 16, Exercises 1,3,8,11,12,13,14,25,26.
- [Mon Oct 22] Chapter 16, Exercises 27,28,29,46,47,48; and the Friday in-class activity.
- [Wed Oct 24] Chapter 17, Exercises 2,16.
- [Fri Oct 26] Chapter 17, Exercises 31,32,39,42.
- [Mon Oct 29] Chapter 17, Exercises 63, 67. Some Help.
- [Wed Oct 31] No Homework Due.
- [Fri Nov 02] In-Class Exercise on Left Inverse Tomography (modified 8AM Thursday Nov 1).
- [Mon Nov 05] In-Class Exercise on Heat State Evolution.
- [Mon Nov 05] Take-Home Quiz.
- [Wed Nov 07] Chapter 20, Exercises 10,11,13-17,21.
- [Mon Nov 26] Chapter 24, Exercises 2,6a,6b,12,15,20c,21a,22b,23c.
- [Fri Nov 30] Chapter 25, Exercises 1,3,5,6. Practice problems (not to turn in): 14-23.
- [Mon Dec 03] Chapter 26, Exercises TBD.
Midterm #1 Exam Details
Date: Friday September 14
Time: In-Class, 12:10-1:00
Material: Chapters 1-7.
Info: Closed-Book, Closed-Notes. Any necessary definitions and theorems will be provided. Emphasis will be on conceptual understanding, some mechanics, and ability to construct a clear, accurate and concise proof.
You should examine the cover sheet
for the exam as soon as possible.
(Optional) Midterm #1A Exam Details
Date: Friday October 12
Time: In-Class, 12:10-1:00
Material: Chapters 1-12.
Info: Closed-Book, Closed-Notes. You are expected to know relevant defintions and essential results of theorems. Emphasis will be on conceptual understanding, some mechanics, and ability to construct a clear, accurate and concise proof. This Midterm Exam is optional, and is being provided as an opportunity to improve your Midterm #1 score. If your score on Midterm #1A is better than your score on Midterm #1, then your Midterm #1 score will be replaced by the average of your scores on Midterm #1A and Midterm #1.
If you choose to take this optional Midterm Exam, you must confirm by email to me before noon on Tuesday, October 9. If you do not confirm on time, you cannot take the exam. In consideration of my time and planning, please confirm only if you fully expect to take the exam.
Midterm #2 Exam Details
Date: Wednesday November 14
Time: In-Class, 12:10-1:00
Study and Preparation Guide
Final Exam Details
I will supply these
materials for you to use during the exam. It is simply a copy of most of the definitions, lemmas, theorems and corollaries from the textbook.
Date: Friday, December 14.
Time: 1:00-3:00 pm
Skills for the final exam:
- Demonstrate correct use of linear algebra and mathematical language.
- Justify linear algebra steps taken to demonstrate/determine/prove/compute.
- Demonstrate writing a sound formal proof.
- Determine whether or not a subset of a vector space is a subspace.
- Understand when a transformation (and matrix) is diagonalizable, and be able to find a diagonalization.
- Understand when a transfomration (and matrix) is invertible, and be able to find the inverse.
- Find a basis for a subspace (e.g. range or null space, and other subspaces) and be able to transform vectors (and transforamtion matrices) into the coordinate representation relative to your basis.
- Use inner product spaces to answer questions about comparing vectors.
- Understand and implement the Gram Schmidt Method.
- Understand concepts of pseudo-inverse transformations.
- Understand and verify properties of projections.
- Understand and verify properties of symmetric matrices and orthogonal matrices.
- Determine long-term behavior of a dynamical system.
- Understand and verigy properties of orthogonal spaces.
- Relate any concept to the applications of tomography, heat diffusion, etc.
Some Exam Particulars:
- This exam is closed-book and closed-notes. All relevant definitions and theorems will be provided.
- Expect to construct at least one formal proof.
- Expect to construct a few different logical arguments to show/verify statements.
- Expect questions that cover ideas from eigenvalues through SVD.
- Expect questions that ask you to relate linear algebra and application concepts.
- Expect some computational tasks (e.g. projection, norm, inner product, orthogonality, coordinates, etc.)