Professor: Jeff Johannes Section 3 MWF 1:30-2:20p Sturges 105

Office: South 326A

Telephone: 5403 (245-5403)

Office Hours: Monday 2:30 - 3:20p, Tuesday 10:30 - 11:20a, 8:00 - 9:00p, Wednesday 12:30 - 1:20p, Thursday 8:00 - 9:00p, and by appointment or visit

Email Address: Johannes@Geneseo.edu

Web-page: http://www.geneseo.edu/~johannes

Course Materials

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

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. Along the way we will also study vectors and matrices as valuable notation for working in different dimensions.

Reading

For each class day there is an assigned reading. Read the section before coming to class. I feel the book is detailed, but I will naturally not always agree with their choices in presentation. It is best to play along with the reading - read with paper and pencil and follow along with the steps they take. We will spend class-time talking about questions from the reading and discussions of an alternative point of view on the topics. If you do not do the reading, attending class will be like listening to friends talk about a film you haven't seen.

Reading Quizzes

You are responsible for reading the sections before they are discussed in class. The schedule is given below. Occasionally - as I see it necessary - we will have short (two minute) reading quizzes to check that the reading is being done. As the class shows this is not necessary, they will become less frequent. Most will not be announced. The reading quizzes may be as straight forward as - "Write enough to convince me you did the reading." There will be no makeup reading quizzes.

Learning Outcomes

Students will be able to:

• Solve systems of linear equations,

• Analyze vectors in R^n geometrically and algebraically,

• Recognize the concepts of the terms span, linear independence, basis, and dimension, and apply these concepts to various vector spaces and subspaces,

• Use matrix algebra and the related matrices to linear transformations,

• Compute and use determinants,

• Compute and use eigenvectors and eigenvalues,

• Determine and use orthogonality, and

• Use technological tools such as computer algebra systems or graphing calculators for visualization and calculation of linear algebra concepts.

• Solve systems of linear equations,

• Analyze vectors in R^n geometrically and algebraically,

• Recognize the concepts of the terms span, linear independence, basis, and dimension, and apply these concepts to various vector spaces and subspaces,

• Use matrix algebra and the related matrices to linear transformations,

• Compute and use determinants,

• Compute and use eigenvectors and eigenvalues,

• Determine and use orthogonality, and

• Use technological tools such as computer algebra systems or graphing calculators for visualization and calculation of linear algebra concepts.

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:

Problem Sets (6) 5% each

Quizzes (3) 5% each

Reading Quizzes (?) 5%

In-class exams (2) 15% each

Final exam (1) 20%

Problem Sets

There will be problem sets assigned at the beginning of the course. Problem sets will be due shortly after each chapter ends. You are encouraged to consult with me outside of class on any questions toward completing the problem sets. 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 problem set will then be graded on a 90-80-70-60% (decile) scale. Late items will not be accepted, as solutions will be posted immediately. Homework will be returned on the following class day. Please feel free to discuss any homework with me outside of class or during review.

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 violation. Simply - please do not read any solutions for problems in this class.

Opening Meeting

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

Quizzes

There will be short quizzes after problem sets have been returned, covering the material from the problem set. For problem sets 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), 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.

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). The final exam will be half an exam focused on the final third of the course, 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, 1.2.1

31 1.2.2

September 5 1.2.3-4

7 2.1.1-4

10 2.1.5-8

12 2.1.9-10 PS 1 (1.1-2.1.4) due

14 3.1.1-3.1.3

17 Q1 (1.1-2.1.4) 3.1.4-3.2.1

19 3.2.2, 4.1-2

21 4.3

24 4.4-4.5, 4.7.1

26 overrun PS2 (2.1.5-4.3) due

28 review

October 1 XM1 (1.1-4.3)

3 4.7.2-3, 4.10.1

5 4.10.2,4.10.4

10 4.10.5

12

15 4.11-4.11.2 PS3 (4.4-4.10) due

17 4.11.3-4

19 Q3 (4.4-4.10) 9.1

22 9.2-3

24 9.4

26 9.5, 5.1-2

29 5.3

31 5.4-5 PS4 (4.11,9.1-5) due

November 2 review

5 XM2 (4.4-4.11,9.1-5)

7 5.6

9 5.7-8

12 5.9, 9.6

14 9.7

16 9.8 PS5 (5.1-9) due

19 9.9

26 Q5 (5.1-9) / 7.1.1

28 7.1.2-7.1.3

30 7.2

December 3 overrun

5 overrun

7 review PS6 (9.6-9.9, 7.1-2) due

10 review

Tuesday, December 18 final exam (half 5, 9.6-9, 7; half 1-4,9.1-5) 8-11a (maybe 8:30-11a? 8-10:30a? 8:30-11:30a?)