Linear Algebra

15-Math-2076

Department of

Mathematical

Sciences

This page is a work in progress! All information is subject to change (Last revised 3 April 2017)

Instructor Prof David A Herron
4514 French Hall, 556-4075 		My Office Hours
WF 10:10-11:00 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 (5th edition) by David C. Lay (ISBN-13: 978-0321982384). Also available from Amazon.

General Syllabus Chapters 1 thru 7.

Important Dates

University Information

The last day to drop this class (with no entry to your academic record) is January 24, 2017. The last day to withdraw from this class is March 17, 2017. 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. This course was designed following the guidelines of the University of Cincinnati General Education Program. It satisfies, or partially satisfies, the Quantitative Reasoning distribution requirement. Moreover, of the five Baccalaureate Competencies, this course focuses on Critical Thinking, Effective Communication, and Information Literacy.

Course Goals

The main course objective is to learn about linearity and especially linear transformations. A second objective is to undrestand some simple geometry in Euclidean $n$-dimensional space $\mathbb{R}^n$. Here is a brief list of some of the topics we will cover: systems of linear equations, matrices, Euclidean n-space and its subspaces, bases, dimension, coordinates, linear transformations, orthogonality, determinants, eigenvalues and eigenvectors, diagonalization.

Daily class attendance and participation is expected. You are expected to arrive on time and stay the entire period. You should come prepared; please read the relevant sections of the text before class and be prepared to discuss the material. Most importantly, please work the suggested HW exercises and Bring Questions!

You are responsible for everything that happens in class. This includes any material covered as well as any announcements made like changes in test schedules. If you miss a class, it is your responsibility to check with someone else in the class to find out what you missed.

Calculators: You may want a calculator for this class, but any inexpensive one will do. Unfortunately, the calculator on your cell phone will not work, since you will not be allowed to have it out during exams.

Blackboard: Keep an eye on Blackboard. It will be used to post announcements, assignments, solutions, and scores.

Your Course Grade

Your final grade will be based on three in class hour exams, a final exam, and quizzes. 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; 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 here.

If your Final Exam score exceeds one of your hour exam scores, then it will replace that exam score; so in this case, your Final Exam score will count for 40% of your final grade.

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 quiz score. There will be no make-up quizzes.

In order to receive audit credit for this course, you must attend all lectures and take all quizzes and exams.

Homework will be assigned (see the Weekly Syllabus), 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 for help.

Course Exams

The first exam will cover Chapters 1,2. The second exam will cover Chapters 2,3,4. The third exam will cover Chapters 5,6. The final exam will be cumulative.

Weekly Syllabus

 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, 2.9
  6. Determinants: Sections 3.1, 3.2
  7. Vector spaces, null space, column space: Sections 2.8, 4.1, 4.2
  8. Linear independence, 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
  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 Singular Value Decomposition: Section 7.4
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 of Material Covered Suggested Exercises Remarks
Jan 9Sections 1.1, 1.2, 1.3 Section 1.1: 3, 7, 8, 11, 13, 17, 19-22, 25,27
Section 1.2: 1, 2, 5, 7, 9, 15, 16, 17, 19, 23, 29
Section 1.3: 5, 6, 9-14, 17, 25, 26 		Scan of first week's hwk
Jan 16Sections 1.4, 1.5, 1.7 Section 1.4: 1-11 (odd), 12, 15, 17, 18, 21, 29, 30
Section 1.5: 3, 5, 9, 11, 13, 15, 17, 29-34		 No class Monday
M.L.King birthday
Jan 23Sections 1.7, 1.8, 1.9 Section 1.7: 1, 3, 5, 6, 7, 11, 13, 17, 23, 27, 32
Section 1.8: 5, 7, 8, 9, 11, 15, 16, 17, 19, 20, 31
Section 1.9: 3, 5, 7, 13, 15, 16, 17, 19, 25
Supplementary Exs: 1, 3, 5, 7, 11, 17, 21
Jan 30Sections 2.1, 2.2 Section 2.1: 1, 3, 7, 11, 12, 13, 15, 17, 21, 27
Section 2.2: 1, 3, 7, 9, 15, 19, 21, 31, 33		  
Feb 6 Section 2.3 and Review Section 2.3: 1-8, 11, 15-19, 21, 33, 37 Exam 1
Week of Material Covered Suggested Exercises Remarks
Feb 13 Sections 2.8, 3.1, 3.2 Section 2.8: 1-7, 9, 11, 13, 21, 23, 33
Section 3.1: 3, 5, 9, 13, 27, 29, 37, 39
Section 3.2: 3, 7, 11, 15-20, 27, 29, 31-35, 39		  
Feb 20 Sections 4.1, 4.2, 4.3 Section 4.1: 1, 2, 3, 5, 6, 7, 9, 11, 13, 15, 17, 21, 23, 31
Section 4.2: 1, 3, 5, 7, 11, 15, 17, 21, 25, 31, 33
Section 4.3: 1-6, 9, 11		  
Feb 27 Sections 4.3, 4.4, 4.5 Section 4.3: 13, 15, 19, 21, 25
Section 4.4: 1, 3, 7, 9, 13, 14, 15, 17, 21, 25, 27, 32
Section 4.5: 1, 3, 5, 7, 11, 12, 13-19, 21, 23, 29
March 6 Sections 4.6, 4.7, Review Section 4.6: 1, 3, 5, 7, 9, 13, 15, 17, 21, 23
Section 4.7: 1, 3, 5, 7, 9, 11, 13		 Exam 2
March 13     Spring Break ☺
Week of Material Covered Suggested Exercises Remarks
March 20Sections 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, 17, 19, 23, 25, 23, 26, 31		  
March 27 Sections 5.4, 6.1, 6.2 Section 5.4: 1, 3, 4, 5, 7, 8, 9, 11, 15, 19-22
Section 6.1: 1-10, 13, 17, 24, 25, 26 (find a basis for this subspace), 27-31
Section 6.2: 1, 5, 9, 10, 11-15, 17, 26, 27		  
April 3 Sections 6.3, 6.4 Section 6.3: 1-15 (odd), 16, 19, 21, 22
Section 6.4: 3, 5, 9, 11, 15, 19-21		  
April 10 Sections 7.1, 7.2, and Review Section 7.1: 1-27 (odd), 27, 30
Section 7.2: 1,3-7, 9, 11, 13, 19		  
April 17 Section 7.4 and Review Section 7.4: 1, 3, 7, 9, 11, 13, 23, 25 Exam 3
April  24 Final Exam Monday 9:45-11:45am Final Exams week

Course Help

 If you are seeking help, there are Graduate Student Teaching Assistants on duty at the MASS Center located in French Hall West room 2133. The MASS Center provides free services for the students in this course. During the times listed on their web page, students will be able to work collaboratively with each other under the guidance of a highly-trained tutor. No appointment is necessary for these tutoring sessions, but there are a limited number of seats available on a first-come, first-served in the MASS Center.

There is also one-on-one tutoring available where students will be able to work one-on-one with a qualified and trained peer tutor. Students may schedule individual tutoring appointments to improve their understanding of course materials and develop effective study strategies. The LAC also offers Academic Coaching. Academic Coaches are high achieving UC upperclassmen and graduate students who provide one-on-one support in order to encourage success-building practices and habits in students. Coaching is not course specific, but applicable to all majors and courses. LAC appointments are available Mon-Thurs 9am-8pm and Fri 9am-5pm. Students may schedule appointments online here or by contacting the LAC at (513) 556-3244. More information about the tutoring program is at the LAC website.

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!

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.
  2. The score you think you should receive.
  3. 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. In order to provide the information asked for in part (2) above you may want to compare your solutions with the Answer Key which often will be available via blackboard.

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

Lay's PowerPoint Files

Here are some of the powerpoint slides from the textbook.

David's Slides

Here are slide shows from class lectures; all are best viewed in presentation mode.

GeoGebra

From google, geogebra is "A geometry package providing for both graphical and algebraic input....". Here's a link: geogebra.
Here are some geogebra files---with a brief description---that I have created; some of these appear in various videos.

Videos

Here are some videos---with a brief description---that I have created; more to appear throughout the semester.

Links

Here are some links to ....a text book, its solutions, another text book, a report.