Mathematics 233 :  Linear Algebra I
Fall 2012

Introduction

Professor:          Jeff Johannes                                 Section 2    MWF  11:30a-12:20p    Sturges 113
Office:               South 326A
Telephone:         5403 (245-5403)
Office Hours:     Monday 3-4p, Wednesday 4-5p, Thursday 12N-1p, 8-9p, Friday 1-2p, and by appointment or visit
IM:                     JohannesOhrs
Web-page:          http://www.geneseo.edu/~johannes
Course Assitant: Iwona Drapala

Course Materials
Visual Linear Algebra with Maple and Mathematica Tutorials, by Eugene Herman & Michael Pepe
Maple
Maple tutorials from outboxes (can be accessed via your browser here after logging in)

Purposes
• to explore any and all algebraic consequences of lineness
• to see how lines, planes, and their higher dimensional analogues interact geometrically
• to develop fluency with matrices, the notation of linear algebra, and the associated vocabulary of linear algebra
Overview
Linear algebra is the algebra of anything resembling straight lines.  And since lines were the first algebraic objects you studied, this can't be bad, right?  Well, yes and no.  Linear algebra is based on the most basic of algebraic fundamentals.  And then planes are like lines.  And lines in three dimensions are like lines in two dimensions.  But they're a little more complicated.  And away we go.  Linear algebra is about the simplest geometry (linear) of higher dimensions.  We will rely upon visualisation in order to extend familiar concepts to unfamiliar territory.  Along the way we will also study vectors and matrices as valuable notation for working in different dimensions.

In many ways our class experience will be defined by our exceptionally unique book.  If you look at the edge of the book - all of those blue-tinged pages are computer driven tutorials.  Why computers?  Calculators don't have the capacity to clearly implement the visualisations, and computers allow you to see what is happening more easily than hand-made graphs.  And they are more interactive than the mere textbook.  As a side benefit, you will learn to use Maple for any future uses you may have.  Real-world linear algebra isn't done by hand - it's done by computers in systems with vast dimensions.   The tutorials are designed to walk you through them -- you are definitely not programming in maple (though you could).
In addition to planning time to do homework, please take time to carefully follow the tutorials and read the sections in the book (the authors say about an hour for each section).  Notice use of the words “time” and “carefully”.  Read the sections slowly.  Read actively.  If you do not understand some statement reread it, think of some potential meanings and see if they are consistent, and if all else fails, ask me.  If you do not believe a statement, check it with your own examples - the maple environment should be friendly for modifying and exploring the consequences.  Finally, if you understand and believe the statements, consider how you would convince someone else that they are true, in other words, how would you prove them?
Because the much of your learning will happen when you work through tutorials in your own time and at your own pace, we will structure classtime more as an interactive discussion of the reading than lecture.  For each class day there is an assigned reading/tutorial.  Read the section before coming to class and complete the tutorial if appropriate.  In addition to the reading, consider the problems following the reading.  If there are no questions from the reading we will discuss problems not a part of the problem sets during the class discussion.

Learning Outcomes
Students will be able to:
I.    Solve systems of linear equations;
II.    Know the geometry and algebra of vectors in Rn;
III.    Recognize the concepts of the terms span, linear independence, basis, and dimension, and apply these concepts to various vector spaces and their canonical subspaces;
IV.    Know matrix algebra and the relation of matrices to linear transformations;
V.    Compute and use determinants;
VI.    Compute and use eigenvectors and eigenvalues;
VII.    Determine and use orthogonality;
VIII.    Develop the ability to apply linear algebra to significant applied and/or theoretical problems.

Your grade in this course will be based upon your performance on homework, quizzes and three exams.  The weight assigned to each is designated below:
Homework (6)                5% each
Quizzes (3)                     5% each
Colloquium Report (1)   5%
In-class exams (2)        15% each
Final exam (1)             20%

Problem Sets
There will be problem sets assigned at the onset of each new chapter.  Problems will be both maple-based and hand-produced.  Maple-based problems must be computer printouts.  The hand-produced questions may be typed or handwritten.  Homework will be due shortly after each chapter ends.  You are encouraged to consult with me outside of class on any questions toward completing the homework.  You are also encouraged to work together on homework assignments, but 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)
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.  Homework will be returned on the following class day along with solutions to the problems.  Please feel free to discuss any homework with me outside of class or during review.

Quizzes
There will be short quizzes after the homework has been returned, covering the material in the chapter from the homework.  For chapters immediately preceding exams, there will be no quiz.  Quizzes will consist of short pencil-paper computations taken directly from your textbook (perhaps only part of a question, or a modified maple question [or a slightly modified question, in having taught this three times in 2 years, I'm running out of options]), and will have limited opportunity for partial credit. Because quizzes will consist of routine questions, they will be graded on a decile scale. There will be no makeup quizzes.

Colloquium Report
Attend one of the department colloquium talks.  Write a report.  In the report, describe the content of the talk (including a detailed discussion of the mathematics).  In addition to your description of the talk, also write how this talk added to your understanding of the nature of mathematics.  Papers are due within a classweek of the colloquium presentation.  I will gladly look at papers before they are due to provide comments.  If you have another interesting way you would like to satisfy this course component, I might be open to it.  I will not accept any proposals that I haven't been told about before the end of September.

Exams
There will be two exams during the semester and a final exam during finals week.  If you must miss an exam, it is necessary that you contact me before the exam begins.  Exam questions will be taken directly from your textbook (perhaps only part of a question, or a modified maple question [or a slightly modified question, in having taught this three times in 2 years, I'm running out of options]).  The final exam will be half an exam focused on the final three chapters, and half a cumulative exam.  Exams will be graded on a scale approximately (to be precisely determined by the content of each individual exam) given by
100 – 80%   A
79 – 60%    B
59 – 40%    C
39 – 20%    D
below 20%   E
For your interpretive convenience, I will also give you an exam grade converted into the decile scale.  The exams will be challenging and will require thought and creativity.  They will not include filler questions (hence the full usage of the grading scale).

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.

Social Psychology
Wrong answers are important.  We as individuals learn from mistakes, and as a class we learn from mistakes.  You may not enjoy being wrong, but it is valuable to the class as a whole - and to you personally.  We frequently will build correct answers through a sequence of mistakes.  I am more impressed with wrong answers in class than with correct answers on paper.  I may not say this often, but it is essential and true.  Think at all times - do things for reasons.  Your reasons are usually more interesting than your choices.  Be prepared to share your thoughts and ideas.  Perhaps most importantly "No, that's wrong." does not mean that your comment is not valuable or that you need to censor yourself.  Learn from the experience, and always try again.  Don't give up.

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 (Tabitha Buggie-Hunt, 105D Erwin, tbuggieh@geneseo.edu) 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 no later than September 10 of plans to observe the holiday.

Schedule (subject to change)

Date              Topic
August 27     Introduction
29          1.1
31          1.2

September 5          1.3A
7          2.1

10          2.2
12          2.3
14          2.4

17          2.5 PS 1 due
19          3.1
21          Q1 / 3.2

24          3.2
26          3.3
28          3.5

October 1      3.6
3            review PS2 due
5            XM1

10          4.1
12          4.2

15          4.3
17          4.4
19          5.1

22          5.2 PS3 due
24          5.3
26          Q3 / 5.4

29          5.4
31          5.5
November 2  5.7

5           review PS4 due
7           XM2
9           6.1

12         6.2
14         6.3
16         7.1

19         7.2 PS5 due

26          7.5
28          Q5 / 8.1
30          8.2

December 3 8.3
5          8.4
7          review PS6 due

10         review

Friday, December 14 final exam 12N-3p

Problem Sets:

1: §1.1 P 12, 21; §1.2 M 5, 7; §1.3A M 5, 6; §2.1 M 3 / P 15; §2.2 P 6, 11; §2.3 M 7 / P 6

2: §2.4 M 6, P 5; §2.5 P 7, 12; §3.1 M 7, P 8; §3.2 M 6 / P 9; §3.3 P 8; §3.5 M 2, 3; §3.6 P 4, 7

3: §4.1 P 5, 6; §4.2 M 8, P 7; §4.3 M 4, P 2; §4.4 1, 7

4: §5.1 P 16, 22; §5.2 M 5, P 21; §5.3 P 5, 8; §5.4 M 3, P 7; §5.5 P 12, 14; §5.7 P 10, 21

5: §6.1 P 5, 7; §6.2 M 6, P 10; §6.3 P 1, 2, 3, §7.1 M 8, P 8, 22 (include a geometric argument as well as the algebraic)

6: §7.2 M 8, P (16 and 17 scored as one question); §7.5 P 5, 7; §8.1 P 12, 15; §8.2 M 3, P 12; §8.3 M 3, P 3; §8.4 P 11