Instructor:
Grader:
Nikki Gerardi (email: nikkade3 AT aol DOT com or nagerardi AT yahoo DOT com)
Textbook:
Bretscher, Linear Algebra with Applications, 3rd Ed., Pearson/Prentice-Hall
(one copy is available on reserve in the Math/Physics/Astronomy Library)Instructor's Office Hours:
Math Tower 2-116:
Mondays and Fridays, 11:00am-12:00pm
Math Learning Center:
Wednesdays 11:00am-12:00pm
Prerequisites/Corequisites:
You are assumed to have had at least one semester of calculus. If you have not yet studied integration, you should be taking the relevant calculus course (e.g. MAT 126) concurrently with this one, as some important problems and examples in this course require a knowledge of integration.
The Nature Of The Course:
This course is an introduction to the theory which has developed around the solution of systems of linear equations. The importance of this theory as a tool in the social, natural, and mathematical sciences cannot be overestimated. (To get some idea of why this is the case, click here, check out the links of interest below, or take a look through your textbook.) You should bear this in mind throughout the semester, especially if the course material ever seems "too weird" or "too abstract" to be useful.
You should also bear in mind that this course is quite distinct in nature from others you have taken. Regardless of your performance in previous math courses, do not be discouraged if you find yourself wrestling with a problem or a concept for hours. Doing many computations is essential to understanding the material, but mindlessly applying memorized techniques while ignoring their theoretical framework will not get you very far. You must be proactive in analyzing and even creating examples (not necessarily complicated ones!) that illuminate the theory.
Course Format: (REVISED!)
Wednesday sessions will be spent reviewing homework and/or exams. With the exception of 11/9, Monday and Friday sessions will be lecture. The final exam will be held on 12/21, from 8:00am to 10:30am in Old Chem 144. Please note that there will be no formal review sessions for any of the exams.
Some links of interest
A nice expository paper on the use of linear algebra in search engines
A nice online linear algebra text
Etiquette:
You are expected to arrive at class on time. All cellphones must be set to silent or vibrate mode (if not turned off completely) while class is in session.
Homework:
Homework assignments are listed here, and are due at the beginning of class on their due date. They are graded on a 100-point system as follows.
Five problems (not necessarily the five most difficult ones) will be graded completely, and they each account for 15 points. In order to receive full credit for your solutions to these, each step must be stated clearly and in the correct order, and each statement in English must be a complete and correct sentence. The remaining 25 points are accounted for by a substantial attempt at solving all the remaining problems; a penalty of 3 points will be incurred for each one which has not been adequately attempted. A sequence of relevant calculations and/or a list of relevant ideas counts as an adequate attempt, whereas leaving a blank or writing "I don't know" does not. You can ask me for help if you are truly stuck. Submissions consisting of multiple pages must be stapled together. Late homework will not be accepted under any circumstances. (No, not even under my office door or in my mailbox.) The grader has final say on all homework grades.Math Learning Center:
The Math Learning Center is located in Math Tower S-240A. Its hours of operation are as follows: 10am-9pm Monday-Wednesday, 10am-6pm Thursday, and 10am-2pm Friday. Its first day of operation for the fall semester is Wednesday, August 31st.
Examinations:
Please note that examinations are not graded on a curve, nor is their average computed. What is curved is your final grade as described in the "Grading" section below. A course is a marathon, not a sprint, and the performance (real or imagined) of your classmates is not a valid reason for you to be either demoralized or overconfident. If at any point in the semester you are seriously concerned with your standing in the class, you are invited to discuss your concerns in detail with me.Any use of cellphones, calculators, books, or notes while an exam is underway will be considered cheating. If you miss an exam for an acceptable reason and provide me with an acceptable written excuse, the relevant exam will be dropped in computing your course grade. A letter stating that you were seen by a doctor or other medical personnel is not an acceptable document. An acceptable document should state that it was reasonable/proper for you to seek medical attention and medically necessary for you to miss the exam (for privacy reasons the note/letter need not state anything beyond this point). Incomplete grades will be granted only if documented circumstances beyond your control prevent you from completing 50% or more of all class assignments.
Grading:
Your raw grade will be based on your examination performance and homework, weighted as follows:
| Exam I | 25% |
| Exam II | 25% |
| Final Exam | 35% |
| Homework | 15% |
The grade you receive in the course will be the maximum of your raw and final exam grades.
DSS advisory:
If you have a
physical,
psychological,
medical, or learning disability that may affect your course work,
please contact Disability Support
Services (DSS) office: ECC (Educational Communications Center)
Building, room 128, telephone (631) 632-6748/TDD.
DSS will determine with you what accommodations are necessary and
appropriate. Arrangements should be made early in the semester (before
the first exam) so that your needs can be accommodated. All information
and documentation of disability
is confidential.
Students requiring emergency evacuation are encouraged to discuss their
needs with
their professors and DSS. For procedures and information, go to the
following web site http://www.ehs.sunysb.edu
and search Fire safety and
Evacuation and Disabilities.
Schedule (tentative):
The following is the basic syllabus. Please read the relevant parts of the book before class.
| Day of | Sections Covered |
| August 29 |
Review of syllabus and class procedures, introduction to the course |
| August 31 |
1.1 (Introduction to Linear Systems) |
| September 2 |
1.2 (Matrices, Vectors, and Gauss-Jordan Elimination) |
| September 7 |
1.3 (On the Solutions of Linear Systems; Matrix Algebra) |
| September 9 |
2.1 (Introduction to Linear Transformations And Their Inverses) |
| September 14 |
2.2 (Linear Transformations in Geometry) |
| September 16 |
2.3 (The Inverse of a Linear Transformation) | September 21 |
2.4 (Matrix Products) |
| September 23 |
3.1 (Image and Kernel of a Linear Transformation) |
| September 28 |
3.2 (Subspaces of R^n; Bases and Linear Independence) |
| September 30 |
3.3 (The Dimension of a Subspace of R^n) |
| October 7 |
Exam I (covering everything from 1.1 up to and including 3.3) |
| October 12 |
4.1 (Introduction to Linear Spaces) |
| October 14 |
4.2 (Linear Transformations and Isomorphisms) |
| October 19 |
4.3 (The Matrix of a Linear Transformation) |
| October 21 |
5.1 (Orthogonal Projections and Orthonormal Bases) |
| October 26 |
5.2 (Gram-Schmidt Process and QR Factorization) |
| October 28 |
5.3 (Orthogonal Transformations and Orthogonal Matrices) |
| November 2 |
5.5 (Inner Product Spaces) |
| November 4 |
5.5, continued |
| November 9 |
Exam II (covering everything from 4.1 up to and including 5.5) |
| November 11 |
6.1 (Introduction to Determinants) |
| November 16 |
6.2 (Properties of the Determinant) |
| November 18 |
6.3 (Geometrical Interpretations of the Determinant; Cramer's Rule) |
| November 23 |
6.3, continued |
| November 30 |
7.2 (Finding the Eigenvalues of a Matrix) |
| December 2 |
7.3 (Finding the Eigenvectors of a Matrix) |
| December 7 |
7.4 (Diagonalization) |
| December 9 |
7.4, continued |
| December 21 |
Final Exam (Cumulative) |