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
Email Address: Johannes@Geneseo.edu
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 software from software.geneseo.edu
(login and select the category Academic)
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.
Reading and Tutorials
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.
Grading
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.
Academic Dishonesty
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