Professor: Jeff
Johannes
Section 1 MWF 10:30-11:20a Sturges 103
Office:
South 326A
Telephone: 5403 (245-5403)
Office Hours: Monday 1:30 - 2:20p, Tuesday 8:00 - 9:00p, Wednesday 4:00 - 5:00p,
Thursday 4:00 - 5:00p, Friday 3:00 - 4:00p (may cancel occasionally)
and by
appointment or visit
Email Address: Johannes@Geneseo.edu
IM: JohannesOhrs
Web-page: http://www.geneseo.edu/~johannes
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), 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 February.
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). 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 January 30 of plans to observe the holiday.
Schedule (subject to change)
Date
Topic
January 18 Introduction
20 1.1
23 1.2
25 1.3A
27
2.1
30
2.2
February 1 2.3
3 2.4
6 2.5 PS 1 due
8
3.1
10
Q1 / 3.2
13 3.2
15
3.3
17 3.5
20
3.6
22 review PS2 due
24 XM1
27
4.1
29
4.2
March 2 4.3
5 4.4
7
5.1
9
5.2 PS3 due
19
5.3
21 Q3 / 5.4
23 5.4
26
5.5
28 5.7
30
review PS4 due
April 2 XM2
4 6.1
6
6.2
9
6.3
11 7.1
13
16
7.2 PS5 due
18
7.5
20 Q5 / 8.1
23
8.2
25
8.3
27 8.4
30
review PS6 due
Tueday, May 8 final exam 8-11a
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