Linear Algebra

15-Math-2076

Section 003

Department of

Mathematical

Sciences

This page is a work in progress! All information is subject to change (Last revised 7 January 2013)

Instructor Prof David A Herron
4514 French Hall, 556-4075 		My Office Hours
Mon 2:30-3:00, Wed 11:30-12:00, 2:30-3:00,
Th 1:30-2:30, Fri 11:30-12:00, and by appt and by appt		 E-mail me at David's e-address
My web page is at David's w-address

Basic Course Information

Textbook Linear Algebra and its applications (4th edition) by David C. Lay (ISBN-13: 978-0321385178). Also available from Amazon.

General Syllabus Chapters 1 thru 7.

Exams and Important Dates

Daily class attendance and participation is expected. Your final Course Grade will be based on two in class hour exams, weekly quizzes, and a final exam. Here is the precise breakdown: Your grade will be determined solely from your exam and quiz scores---there will not be any possible "extra credit".

There will be NO make-up exams nor make-up quizzes; if you cannot take an exam, you should not expect to be able to make it up, except in the most extraordinary of circumstances. If you have a valid reason for missing an exam, please speak with me about it before the exam and I will try to make arrangements. The exam dates are listed above. Quizzes will be given at random days at the end of the class period. Take home quizzes may also be given. Classroom activities include attendance and participation. I will drop your lowest two quiz scores. In order to receive audit credit for this course, you must attend all lectures and take all quizzes and exams.

The use of calculators or other electronic devices will not be permitted on any exam.

Homework will be assigned (via blackboard), but it will not be collected nor graded. I encourage you to work with other members of the class.

I will start each class by answering questions. I encourage you to talk to other members of the class or to ask me or the TA for help.

The main Course Goal is the study of linear transformations. Here is a brief description of some of the topics we will cover: Linear equations, matrices, Euclidean n-space and its subspaces, bases, dimension, coordinates, linear transformations, orthogonality, determinants, eigenvalues and eigenvectors, diagonalization.

Here is a brief Course Syllabus

  1. Systems of linear equations: Sections 1.1, 1.2, 1.3
  2. Matrix form of equations, linear independence: Sections 1.4, 1.5, 1.7
  3. Linear transformations: Sections 1.8, 1.9
  4. Matrix operations: Sections 2.1, 2.2, 2.3
  5. Vector subspaces: Section 2.8 and Exam 1 over Chapters 1, 2
  6. Dimension and Determinants: Sections 2.9, 3.1, 3.2
  7. Vector spaces: Sections 2.8, 4.1, 4.2
  8. Null space, column space, bases, coordinates: Sections 4.3, 4.4
  9. Dimension, rank: Sections 2.9, 4.5, 4.6
  10. Eigenvectors, eigenvalues, diagonalization: Sections 5.1, 5.2, 5.3
  11. Eigenvectors of LT: Section 5.4 and Exam 2 over Chapters 3, 4, 5
  12. Orthogonality: Sections 6.1, 6.2
  13. Orthogonal Projections: Section 6.3
  14. Gram-Schmidt: Section 6.4 and Diagonalization: Section 7.1
  15. Quadratic Forms: Section 7.2 and Review
Below is a more detailed syllabus along with some suggested homework. As the semester progresses, this will be modified as necessary. After each class, you should first try all of the Practice Problems in the sections covered. Then continue with the suggested exercises.

Week ofMaterial Covered Suggested ExercisesRemarks
Jan 7Sections 1.1, 1.2, 1.3 Section 1.1: 3, 7, 8, 11, 13, 17, 19-22, 25
Section 1.2: 1, 2, 7, 9, 15, 16, 17, 19
Section 1.3: 5, 6, 9-14, 25, 26 		a scan of first week's hwk
Jan 14Sections 1.4, 1.5, 1.7 Section 1.4: 1-4, 6, 7, 11, 12, 15
Section 1.5: 5, 8, 11, 17, 18, 29-34
Section 1.7: 1-4, 5, 6, 8, 11, 12, 32
Jan 21Sections 1.8, 1.9 Section 1.8: 5, 6, 7, 8, 15, 16, 19, 20, 31
Section 1.9: 5, 6, 15, 16, 17, 18, 25		 no classes Monday, January 21
Martin Luther King holiday
Jan 28Sections 2.1, 2.2 Section 2.1: 1, 2, 7, 11, 12, 13, 17-26
Section 2.2: 1, 2, 4, 6, 11-24, 31, 32, 35		  
Feb 4 Section 2.3 and Review Section 2.3: 1-8, 15-20 Exam 1
Week of Material CoveredSuggested Exercises Remarks
Feb 11 Sections 2.8, 2.9, 3.1 Section 2.8: 1-4, 5, 6, 11, 12
Section 2.9: 1, 3-6, 11-13
Section 3.1: 3, 4, 13, 14, 38 		 
Feb 18 Sections 3.2, 3.3 (volume), 4.1 Section 3.2: 7, 8, 11, 12, 15-20, 24, 25, 29, 31-35, 37, 43
Section 3.3: 19, 20, 21, 22
Section 4.1: 1, 2, 9, 10, 15, 17		  
Feb 25 Sections 4.2, 4.3 Section 4.2: 3-6, 17-20
Section 4.3: 1-6, 9, 10, 11, 13, 14, 15, 16, 26		  
March 4 Sections 4.4, 4.5 Section 4.4: 2, 3, 7, 8, 13, 14, 17, 25, 27
Section 4.5: 3, 4, 11, 12, 13-18, 21, 23 		 
March 11Section 4.6 and Review Section 4.6: 1, 2, 4, 5, 6, 8, 15, 16 Exam 2
Week of Material Covered Suggested Exercises Remarks
March 18     Spring Break ☺
March 25 Sections 5.1, 5.2, 5.3 Section 5.1: 1, 3, 15, 16, 25, 26, 27
Section 5.2: 3, 4, 7, 8 (find eigenvalues and eigenvectors), 9, 10, 17
Section 5.3: 4, 5, 7-12, 19, 20		  
April 1 Sections 5.4, 6.1, 6.2 Section 5.4: 1, 3, 4, 5, 7, 8, 9, 14, 19-22
Section 6.1: 1-8, 14, 24, 26 (find a basis in this subspace), 27-31
Section 6.2: 9, 10, 12-15, 26, 27		  
April  8 Sections 6.3, 6.4, 6.5 Section 6.3: 3-6, 7, 8, 13-16 (always check orthogonality of the bases), 19, 21, 22
Section 6.4: 3, 4, 9-12, 19-21
Section 6.5: 1-4		  
April 15 Sections 7.1, 7.2 and Review Section 7.1: 7-12, 13-22, 27, 30
Section 7.2: 3-6, 9-12		  
April  24 Final Exam Wednesday 9:45-11:45am Final Exams week

If you are seeking help, there are Graduate Student Teaching Assistants on duty at the Mathematics Learning Center located in French Hall West room 2133. The MLC is a free, walk-in, mathematics tutoring center for all University of Cincinnati students. The tutoring hours are:

but please check their web page to confirm their hours.

Students can get help at the MLC for all basic mathematics courses through Differential Equations including Statistics and Business Mathematics courses.

Perhaps the best way to get help is to ask your fellow classmates! In addition it is possible to hire a private tutor; see the MLC web page.

Finally, here is some friendly advice. I encourage you to get two notebooks for this course. Use one to write down class notes and problems that I work in class; do your homework problems in the other notebook. You will find it easier to study for exams if your class notes are not cluttered with your homework problems. I will go over as many problems as possible. However, mathematics is not a spectator sport; mathematical knowledge is not gained passively and you will not learn by osmosis; you must be an active participant in the learning process. This means that to learn the material you must work the problems yourself and practice every day. You must work lotsa problems, as many as you can. Don't be afraid to work some of the problems over and over, especially when you're studying for an exam. It is easy to fall behind; try to keep up with the course and seek help immediately if you have problems.

It is a excellent idea to go over your notes as soon as possible after class!

The last day to drop this class (with no entry to your academic record) is January 21, 2013. The last day to withdraw from this class is March 15, 2013. These are official UC dates and something I have no control over. If you withdraw from this course, I will be required to verify whether or not you minimally participated in the class. Although I will try my best to respond accurately, in the absence of any evidence to the contrary, I will state that you did not minimally participate. Ways for you to provide clear evidence of your presence in the class include turning in at least one homework assignment, taking at least one quiz, or taking at least one exam.

Academic Integrity Policy
The University Rules, including the Student Code of Conduct, and other documented policies of the department, college, and university related to academic integrity will be enforced. Any violation of these regulations, including acts of plagiarism or cheating, will be dealt with on an individual basis according to the severity of the misconduct.

Special Needs Policy
If you have any special needs related to your participation in this course, including identified visual impairment, hearing impairment, physical impairment, communication disorder, and/or specific learning disability that may influence your performance in this course, you should meet with the instructor to arrange for reasonable provisions to ensure an equitable opportunity to meet all the requirements of this course. At the discretion of the instructor, some accommodations may require prior approval by Disability Services.

Except for a few courses, all mathematics classes satisfy the University Quantitative Reasoning Requirements. This course satisfies the QRR of UC's General Education program.

Here I explain the Regrading Policy. Mistakes are made in grading, especially when there is only one person responsible for grading all of your work. Sometimes these mistakes are in the student's favor, but unfortunately sometimes they are not. By following the procedure outlined below, you can have mistakes in the grading of your work corrected. Please be aware that just as it is likely that you will receive more points, it is also possible for you to actually lose points -- this generally happens to at least one person each term. Thus there are three possible outcomes of a regrade request: your score may remain the same or your score may increase or your score may decrease.

Note that partial credit is awarded only for work that is mostly correct except for one or two minor errors. You will not be given partial credit for attempting to solve a problem by the wrong method. Nor will you receive credit---even for a correct answer---if no supporting work is present.

Here is the Procedure to Follow for a Regrade Request. If you believe an error was made in grading your work, then you must appeal the grade in writing within one day of the day the work was returned to the class. A late request for regrading will automatically be denied. To have your work regraded, you must return it along with a clearly written note indicating the mistakes that you believe were made in grading. If your point totals were added incorrectly, simply indicate this on your regrade request. Otherwise, please provide the following information for each problem that you believe was graded incorrectly.

  1. The number of the problem to be regraded and the score you think you should receive.
  2. An explanation of why you think you deserve more points. This means that you should indicate which parts of your solution were graded incorrectly. You should be able to distinguish which part of your answer is correct and which part is incorrect. For example, you might say something like "I solved the problem correctly but forgot to multiply by 2 at the third step".
Note that no credit is given if you use the wrong method to solve a problem, even if your computations and/or your answers are correct.

Failure to provide any of the above information may result in your work not being regraded.

Some links to ....a text book, its solutions, another text book, a report.