## Mathematics 333:  Linear Algebra II Fall 2019Introduction

Professor:        Jeff Johannes                                    Section 1    MWF    1:30-2:20p   Sturges 105
Office:             South 326A
Telephone:       245-5403
Office Hours:   Monday 2:30 - 3:30p, Tuesday 8:00 - 9:00p, Wednesday 12:00N - 1:20p, Thursday 4:00 - 5:00p, Friday 12:30 - 1:20p, and by appointment or visit.
Web-page:        http://www.geneseo.edu/~johannes

Textbook
Linear Algebra Done Right, third edition, by Sheldon Axler (errata here)
Extract from Linear Algebra Through Geometry by Banchoff & Wermer

Purposes
In Linear Algebra I you learned about matrices and systems of equations, invertibility, determinants, linear transformations, bases, and eigenvalues (and much more).   How will our Linear Algebra II be different?  There are many options for direction.  Our text avoids determinants.  I don't believe as strongly as the author that this is "right", but I do agree that it is convenient.  We will begin revisiting arbitrary vector spaces and spend most of our time thinking about linear transformations, with a rather minimal and occasional role played by the matrices which were so central to Linear Algebra I.

Background
Probably more so that any other course, we will be constantly navigating different backgrounds.  Linear Algebra I, especially taught at different institutions can be quite varied.  Because of this, each student's experience will be different.  I can promise there will be topics we discuss (mostly early) that everyone will have seen before.  I can promise there will be topics that are familiar to some and not to others (mostly in the middle).  And, unless someone has learned a significant amount of theory of linear algebra on their own, I'm pretty confident there will be topics that are new to all.  I have taken data from my colleagues who have taught Linear Algebra I here to know what was seen here, but please tell me if something is unfamiliar to you.

Learning Outcomes
Upon successful completion of Math 333 - Linear Algebra II, a student will be able to:
• Analyze finite and infinite dimensional vector spaces and subspaces over a field and their properties, including the basis structure of vector spaces,
• Use the definition and properties of linear transformations and matrices of linear transformations and change of basis, including kernel, range and isomorphism,
• Compute with the characteristic polynomial, eigenvectors, eigenvalues and eigenspaces, as well as the geometric and the algebraic multiplicities of an eigenvalue and apply the basic diagonalization result,
• Compute inner products and determine orthogonality on vector spaces, including Gram-Schmidt orthogonalization, and
• Identify self-adjoint transformations and apply the spectral theorem and orthogonal decomposition of inner product spaces, the Jordan canonical form to solving systems of ordinary differential equations.

Half of your grade will come from problem sets.  Another tenth will come from each of two midterm exams.  Your mandatory in-class problem presentation will contribute three percent, and your final project will contribute seven percent.  The final fifth will come from the final exam.

Problem Sets
There will be six problem sets due on indicated dates.  The problems will be mostly proofs.  I strongly recommend consulting with me as you work on these problem sets.  I also recommend working together on them, however I want to carefully emphasise that each must write up their own well-written solutions.  A good rule for this is it is encouraged to speak to each other about the problem, but you should not read each other's solutions.  A violation of this policy will result in a zero for the entire assignment and reporting to the Dean of Students for a violation of academic integrity.  Each question will be counted in the following manner:
0 missing or plagiarised question
1 question copied
2 partial question
3 completed question (with some solution)
3.5 completed question with only "fixable errors" - minor missteps or minor writing errors
4 completed question correctly and well-written
Each entire homework set will then be graded on a 90-80-70-60% (decile) scale.  Late items will not be accepted.

Solutions and Plagiarism
There are plenty of places that one can find all kinds of solutions to problems in this class.  Reading them and not referencing them in your work is plagiarism, and will be reported as an academic integrity violation.  Reading them and referencing them is not quite plagiarism, but does undermine the intent of the problems.  Therefore, if you reference solutions you will receive 0 points, but you will *not* be reported for an academic integrity.  Simply - please do not read any solutions for problems in this class.

Presentations
When discussing the new material for each section, each day will begin with an opportunity for student presentation.  Potential problems will be offered in class and maintained hereEach student must present at least one problem during the semester.  Presentations will be scored out of 7 points.

The class presentations will be graded roughly as follows:
7    excellent
6    very good - at most minor errors
5    some problems, but the main idea of the solution is clear
3    some correct things
1    attempted
0    no presentation

I will determine priority for presenting problems.  Each student who has not yet presented will have priority over students who have presented.  A second (or more) problem may be presented in order to replace a prior presentation.  Students may also earn one extra point for the corresponding problem set by presenting at the 7 point level.  I will have a priority list at all times for presentations.  Students may present more than once per problem set, but representations have lowest priority.  Students may earn no more than one point per problem set in this fashion.

Opening Meeting
Students will earn one extra point on the first problem set by visiting office hours during the first two weeks of classes, i.e. no later than 10 September.

Final Project
Your final project will constitute writing up a 1200-2000 word detailed explanation of a linear algebra topic beyond Linear Algebra I material selected by you and approved by me.  Projects may be completed individually or in pairs.  Project proposals must be submitted before fall break.  There will not be duplicate topics - first proposals will be given priority.  Selecting the topic by the deadline will be worth 10%, the draft will be worth 40%, and the final paper will be worth 50%.

Exams
The exams will consist of a few problems at a level between the presentation problems and the problem set problems.

Feedback
Occasionally you will be given anonymous feedback forms.  Please use them to share any thoughts or concerns for how the course is running.  Remember, the sooner you tell me your concerns, the more I can do about them.  I have also created a web-site which accepts anonymous comments.  If we have not yet discussed this in class, please encourage me to create a class code.  This site may also be accessed via our course page on a link entitled anonymous feedback.  Of course, you are always welcome to approach me outside of class to discuss these issues as well.

While working on homework with one another is encouraged, all write-ups of solutions must be your own. You are expected to be able to explain any solution you give me if asked. The Student Academic Dishonesty Policy and Procedures will be followed should incidents of academic dishonesty occur.

Disability Accommodations
SUNY Geneseo will make reasonable accommodations for persons with documented physical, emotional or learning disabilities.  Students should consult with the Director in the Office of Disability Services (105D Erwin) and their individual faculty regarding any needed accommodations as early as possible in the semester.

Religious Holidays
It is my policy to give students who miss class because of observance of religious holidays the opportunity to make up missed work.  You are responsible for notifying me by September 10 of plans to observe a holiday.

Schedule (loose and subject to variations)

August 26    Introduction
28    1A
30    1B

September 4 1C
6         2A

9        2B
11      2C
13      3A

16      PS1-2 due
18      3B
20      3C

23      3D
25      3E
27*    3F.1

30      3F.2
October 2    PS3 due
4        Review for exam

7        Exam 1 (Chapters 1-3)
9        Exam return, 4
11      5A  Deadline for selecting project topics

16      5B
18      5C

21      6A
23      PS4-5 due
25      6B

28      6C
30      7A
November 1 PS6 due

4        Review for Exam
6        Exam 2 (Chapters 4-6)
8        Exam return, 7B

11      7C    Project draft due
13      7D   (more material in ยง7.4.2 here)
15      8A

18      PS7 due
20      8B
22      8C

25      8D

2        2.8.1
4        2.8.2
6        Review, Final Project due

9        Review, PS8+ due

Wednesday, December 11 8:00-11:00a  Final Exam (half 7-8, 2.8, half 1-6) (maybe 8:30-11a? 8-10:30a? 8:30-11:30a?)