Math 232 Course information and syllabus

Instructor

Prof. Bob Dobrow
Office: CMC 218
Phone: 222-5633, E-mail: rdobrow@carleton.edu
Home page: http://www.people.carleton.edu/~rdobrow
Office Hours: Tues 1-3 pm; Thurs 11 am-noon; Fri 12-2 pm

Welcome to Linear Algebra! Linear Algebra brings together the theory and practice of mathematics, the beauty and elegance of abstraction with the utility and breadth of applications. Here you will start making the transition from the computational-based mathematics of high school algebra and calculus to deeper levels of abstraction. You will explore the interconnection between geometry and algebra; you will travel in high-dimensional spaces, for which there is little physical intuition; and you will learn about many concrete applications that rely on linear algebra, including Markov chains and how Google searches the web.

The text is Linear Algebra with Applications (3rd ed.) by Otto Bretscher. We will also use Mathematica. See this brief introduction to the latest version of Mathematica.

You are expected to attend class regularly and participate in the discussion as best you can. You are responsible for what get's covered in class. If you can't make a session, please let me know, check on what you've missed, and make sure you have access to someone who takes good notes.

Your course grade will be based on (i) class participation, (ii) homework, (iii) three quizes, (iv) two mid-term exams, and (v) either a comprehensive final exam or a final paper, depending on your choice.

Final Exam option

Class participation	5%
Homework	15%
Quizes	15% (5% each)
Midterm with the lowest score	10%
Midterm with the highest score	25%
Final exam	30%

Final Paper option

Class participation	5%
Homework	15%
Quizes	15% (5% each)
Midterms	50% (25% each)
Final paper	15%

Homework will be assigned daily. Doing problems is one of the most important ways you have to learn and master the material. Many problems will be assigned from the odd-numbered exercises in the textbook so you can check your answers in the back of the book. You will be assigned a range of problems from easy to hard. Quiz and exam problems may be picked from the homework exercises. A few of the assigned problems will be starred for grading. These are the problems you should turn in each class period. For these problems, you must write up the solution clearly using complete sentences and good English. The problems will be assessed in part on mathematical correctness, but also on overall writing and clarity of explanation.

Writing mathematics well is an important component of this class. Why is writing important? First, mathematicians and scientists spend a lot of their time communicating, and the ability to write well is an essential skill in what you aspire to be.

Every year, we buy ten cases of paper at $35 each; and every year we sell them for about $1 million each. Writing well is very important to us.
-- Bill Browning, President of Applied Mathematics, Inc.

But more importantly, the ability to write about mathematical concepts logically and clearly is a mark of your understanding of the material. Sharpening your writing and your ability to explain a problem well will translate into big dividends in your understanding of the concepts and your mastery of the material. Many problems will require more than just a simple computational solution. They may require an argument, some explanation, a justification, and a conclusion. It is important that solutions be written up carefully, using complete English sentences. Mathematical terminology must be used precisely. Punctuation and spelling must be correct. This does not mean that everything has to be written out in words, without the use of mathematical symbols or notation. It does mean that the solution must have a beginning, a middle, and an ending, with a logical flow. Note that

Thus, x = 3.

is an English sentence, with a noun and a verb, capitalization and punctuation. On the other hand,

2x=4    x=2

is not a sentence. See the Writing Mathematics handout for more guidelines and suggestions on good writing. Use the writeup of problems in the textbook and my posted solutions of problems as examples to follow.

You are welcome to collaborate with other students on homework. But you must write up the homework yourself using your own words. I encourage you to come see me as often as you like to discuss homework. In working with other students on homework be careful that you do not become too dependent on your study partners. Strive to become an independent learner. Late homework will not be accepted under any circumstances (including sickness and personal emergencies). In computing your final grade, I will delete your two lowest homework scores. Finally, make sure your written homework is legible and neat. Do not scratch out, do not rip paper from spiral notebooks, do not write too small or too faintly so that the grader can't read your writing. Make sure to staple your pages together. In summary, put care into your work!

All quizes and exams will be closed book. There will be two short in-class quizes throughout the term (roughly about 20 minutes long). Quiz problems will be very similar to homework exercises. Midterm exams will take up the entire class period and will generally be more challenging than quizes. The final exam is comprehensive. See the scheduled final exam time on the syllabus below. The final exam is not self-schedulable. Toward the end of the term, if you are satisfied with your midterm test scores and your cumulative grade you may elect to write a final paper rather than take the final exam. This is an opportunity to explore an interesting topic in depth that we did not cover in class. You will need to discuss this option with me and talk to me about possible topics. The final paper is due on the same date and time as the final exam.

Syllabus and Schedule

Class	Date	Tests and Topics
1	Mon 9/15	Introduction
2	Wed 9/17	Gauss-Jordan
3	Fri 9/19	Solutions of linear systems
4	Mon 9/22	Linear transformations I
5	Wed 9/24	Linear transformations II
6	Fri 9/26	Linear transformations III
7	Mon 9/29	Quiz #1; Linear transformations IV and Markov chains
8	Wed 10/1	Image and Kernel
9	Fri 10/3	Span and Linear independence
10	Mon 10/6	Bases and Dimension
11	Wed 10/8	Orthogonality I
12	Fri 10/10	Orthogonality II
13	Mon 10/13	Test #1 (Chap 1, 2, 3)
14	Wed 10/15	Orthogonality III
15	Fri 10/17	Orthogonality IV and Least Squares
Midterm Break
16	Wed 10/22	Determinants I
17	Fri 10/24	Determinants II
18	Mon 10/27	Quiz #2; Eigenvalues I
19	Wed 10/29	Eigenvalues II
20	Fri 10/31	Coordinates and Similarity
21	Mon 11/3	Spectral Theorem and Quadratic Forms
22	Wed 11/5	Linear Spaces I
23	Fri 11/7	Linear Spaces II
24	Mon 11/10	Test #2 (Sections 3.4, 5.1, 5.3, 5.4, 6.1, 6.2, 7.1, 7.2, 7.3, 7.4, 8.1, 8.2)
25	Wed 11/12	Linear Spaces III
26	Fri 11/14	Inner Products I
27	Mon 11/17	Quiz #3; Inner Products II
28	Wed 11/19	Final Thoughts and Review
	Sat 11/22 8:30-11 am	Final exam

Return to Math 232 home page