Introduction to Linear Algebra

This is a first course in linear algebra; it prepares students for future studies in all areas of mathematics and for studies in applied sciences. Students should understand the concepts of vector spaces, bases, linear transformation, and matrix algebras. They should be able to deal with these concepts at both the abstract and the concrete level. Students should be able to solve systems of linear equations by means of Gaussian elimination, calculate the inverse of a matrix, determine the projection operator onto a subspace, determine the null space and range space of a linear transformation, prove elementary facts about vector spaces and linear transformations.

Syllabus and General Information

  1. Course Syllabus
  2. Class Time and Place:
    • Section 25115 - Boyd Graduate Research Center (1023), Room: 221, MWF 10:10-11:00
    • Recitation hour - Boyd Graduate Research Center (1023), Room: 221, W 2:30-3:30
  3. Office Hours: MW 11:10-12:00, and/or by appointment.
  4. Course overview can be found here.
  5. Textbook: Linear Algebra: A Geometric Approach (second edition), by T. Shifrin and M.A. Adams
  6. Additional Reading Material:
    • Introduction to Linear Algebra, by G. Strang
    • Linear Algebra with Applications, by O. Bretscher
    • Linear Algebra Done Right, by S. Axler
    • Linear Algebra and Its Applications, by D.C. Lay, S.R. Lay, J.J. McDonald
    • Introduction to Linear Algebra, by L.W. Johnson, R.D. Riess, J.T. Arnold

Announcements

  1. WebWork for online HMW assignments.
  2. eLearning Commons (eLC) for grades, etc.
  3. Free tutoring:
  4. An online course with a distinguished MIT professor Gilbert Strang. You can try to watch the videos as you find time to see the course material from a different perspective.
  5. Some Linear Algebra Applets you may find useful:
  6. Withdrawal Deadline is March 20th.
  7. Midterms will be in the regular classroom. Your practice problems are the HMW assignments. Final will be a cumulative exam.
  8. Matlab, Mathematica, and Maple are strong scientific software for symbolic or numeric computations. You can get a copy of Matlab from UGA licensed software website or here.
  9. You can pick up your tests and quizzes from my office during the office hours. I would like to go over your mistakes with you after the tests.
  10. Your homework grade for each homework set is the number of WebWork problems you answered correctly in that set. I will add them up, scale them to 100, take average of that and the homework assignments through this webpage, and post your final homework grade to eLC at the end of the semester.
  11. Your practice problems for the tests are the HMW assignments. In general you will not need a calculator for the test. Waiting for the last office hour before the test to ask questions is not a good practice, as there may be more traffic and less time to answer yours.
  12. It is important for you to understand that correct answers alone does not help much without a through solution, please read the Written Work section in the Syllabus.
  13. Solutions for your written works must be very well-organized, neatly written, legible, and mathematically well expressed. Think yourself as a math textbook writer and consider your solutions as examples in your book. Turning in scratch papers is not a good idea!
  14. You can find many introductory documents for Matlab online, but here is just one of them. You will have some Matlab projects during the semester. 
  15. Please write down some information about your mathematical background (your major, the math courses you have taken so far, the best or worst practices you've liked or disliked in your previous math classes, how do you feel about math in general, your expectations from this course, or anything else you would like to inform me about related to the course) on a plain piece of paper and turn in with your first homework set on Friday.
  16. Download Matlab linear algebra codes from MathWorks here and start playing with them to familiarize yourself.
  17. In the tentative daily schedule, I posted some video lectures by G. Strang of MIT. It would be good if you can watch the lectures before the class. That will prepare you for the class, help you to see the material from a different perspective, enhance your understanding, and will give me a chance to move a little faster to make some time for additional examples in class.
  18. You have probably noticed already that the midterm dates (M1, M2) are posted to the Daily Schedule below.
  19. Solutions to your quiz and hmw problems and some additional solutions for the problems from the textbook as practice problems are posted below in the Daily Schedule. Click on the blue links to get the solutions. The credit for those solutions goes to my teaching assistant Mentzelos Melistas, a graduate student in the department of mathematics.
  20. Matlab Projects: Repeat all computations in the video lectures posted below with different matrices using Matlab. Due dates are posted in the daily schedule (J1-5). Each project worths 20 bonus points. So, you can earn additional 100 points in total which corresponds to a midterm grade. If there is an error in a code, you can't get credit from that project. So, make sure that your codes are ready to run without any errors. You should email your Matlab codes to me on the due dates before the lectures. J1: video lectures from V1-V5, J2: video lectures from V6-V10, J3: video lectures from V11-V15, J4: video lectures from V16-V21, J5: video lectures from V22-V27.
  21. If your grade for the first quiz is lower than 14/20 (~average), please see me during an office hour.
  22. Tomorrow (February 1st) the WebWork server will be moved onto the UGA VPN. This means that you will be not able to access the server from off-campus without logging into the VPN. Keep in mind that you will need to have ArchPass Duo installed to access the VPN starting tomorrow.
  23. Here is an example for the projects. The file project.m includes computations in the first 20 minutes of the video lecture V3.
  24. I am trying to organize additional recitation hours for discussions solely on the homework problems. I need a screenshot of your weekly Athena class schedules (not in the other forms). I expect and urge the students especially whose quiz grade average is below the class average (~15) to make every efforts to attend these sessions.
  25. Your project report should be a Matlab file (with extension .m), just like the one I posted above, and should be ready to run with Matlab without any errors. It should display all computations.
  26. Midterms will be in the regular classroom. It is a 50 min test. Your practice problems are the HMW assignments. The midterm problems will be similar. You will need to go over your solutions for preparation.
  27. The first project due date is extended. It should be submitted on the due date by email, by midnight. Please have your name and project number appear on the subject line. Example: George Washington - Project 1
  28. The recitation hour is on Wednesday at 2:30-3:20pm in the regular classroom. We will have the first session this week and will continue for the rest of the semester except holidays. I am sorry that I could not find a time that works for all. The ones who have schedule conflicts with the recitation hour can continue to take advantage of my office hours, as usual.
  29. The first midterm will cover Chapter 1 only.
  30. A project file by one of your classmates is here. I hope this gives a better idea about the expectations and becomes useful for the coming projects.
  31. Webwork homework deadline for this week is extended to next monday (02/27/17). The dealine for the texbook problems is still this Friday.
  32. The second project due date is updated.
  33. I extended the deadline for the Webwork problems. The quiz on Friday will cover last two homework sets and problems only from the textbook, not the Webwork.
  34. Your Webwork assignments so far will be counted in your overall grade. The last homework should still be done by the deadline.
  35. Project due date is extended to Monday.
  36. The second midterm will cover Chapter 2 (all sections) and Chapter 3 (except last two sections).
  37. The second midterm will be similar to the first one.
  38. The sections will be in the final exam are: 1.4, 1.5, 2.2, 2.3, 2.5, 3.2, 3.3, 3.4, 4.1, 4.2, 4.3, 5.1, 5.2, 5.3, 6.1, 6.2, 6.4
  39. It is your time to grade now! Please log on at this UGA website using your UGA MyID any time between Thursday, April 13, 2017 8:00am and Thursday, April 27, 2017 11:59pm to submit your evaluations.
  40. I posted your Homework and Quiz grades all together to eLC. Please let me know if there is an error in your grades.
  41. The last homework is due on the final exam day.
  42. Four problems are added from Section 6.4 to the last homework.
  43. Solution for five problems from HMW 15 are posted.
  44. The last HMW grade posted to eLC is your WebWork grade scaled to 35 pts. Grades for projects are also posted. Let me know, if there is any problems with your posted grades.
  45. Finally, it is over! Have a great summer vacation. You deserved it! I wish good luck in your future endeavors..

Assignments

You need to know how to solve all assigned problems from the textbook below for the tests but turn in only the boldfaced problems.

  1. HMW 1
    • 1.1 Exercises: 1, 2, 3, 4,28, 29
  2. HMW 2
    • 1.1 Exercises: 5, 6, 7, 8, 10, 18, 19, 20, 21, 22, 25
  3. HMW 3
    • 1.2 Exercises: 1(c,f,g), 2(c,f,g), 5, 6, 11, 14, 17, 18
  4. HMW 4
    • 1.3 Exercises: 1(b,d,f), 3(c,d), 4(c,e), 5, 7, 9, 10, 13
  5. HMW 5
    • 1.4 Exercises: 1(a,b), 2, 3(b,e,g), 4(a,e), 7a, 10a, 8, 14, 16
    • 1.5 Exercises: 1, 2, 6, 7(b,d)
  6. HMW 6
    • 1.5 Exercises: 3(b,d), 4(a,b), 5(a,b), 8, 10, 10, 12(a,b,e) 13, 15
  7. HMW 7
    • 2.1 Exercises: 1(b,f,g,h,k,l), 2, 4, 5, 7, 9, 10, 11, 13, 14
    • 2.2 Exercises: 1, 2, 3a, 4(a,c,d,f), 6, 8, 9, 11, 12, 13
  8. HMW 8
    • 2.3 Exercises: 1(a,e,g), 2(b), 3, 5, 6(a,c), 7, 8, 11, 12
    • 2.4 Exercises: 1(a,e), 2(a,e), 3(a,e), 4, 5b, 6c, 8, 9, 12
  9. HMW 9
    • 2.5 Exercises: 1(b,e,g,j,k), 2(a,b,f), 3b, 4, 5, 6, 12, 19
    • 3.1 Exercises: 1(b,c,i), 2, 3, 5, 8, 9a, 10, 12, 14
    • 3.2 Exercises: 1, 2a, 3a, 4, 5, 6b, 8a, 9
  10. HMW 10
    • 3.2 Exercises: 10, 11
    • 3.3 Exercises: 3(b,d), 4(b,d), 5(a,c), 6, 10, 11, 13, 14, 15, 21, 23
  11. HMW 11
    • 3.4 Exercises: 1, 2, 3f, 5, 7, 8(a,c), 13, 9b, 10b, 22, 24
  12. HMW 12
    • 4.1 Exercises: 1b, 2, 4, 6, 9, 13, 14
  13. HMW 13
    • 4.2 Exercises: 1, 2c, 4, 5, 7b, 8b, 9a, 11
  14. HMW 14
    • 4.3 Exercises: 1a, 3a, 5a, 7, 11, 14, 16, 19
    • 5.1 Exercises: 1bd, 4, 7, 8c, 10
    • 5.2 Exercises: 1b, 5af
  15. HMW 15
    • 5.2 Exercises: 2, 3, 13
    • 5.3 Exercises: 1a, 2a, 5, 11
    • 6.1 Exercises: 1afgj, 2, 3, 4, 6, 7, 8, 9
    • 6.2 Exercises: 1afgj, 7, 8, 9, 11, 13
    • 6.4 Exercises: 1ade, 2, 6, 12ab

Tentative Daily Schedule

H - homework assignment, Q - quiz, M - midterm, R - review, P - practice problems, V - video lectures.

  Monday Tuesday Wednesday Thursday Friday
Week 1 1/2: 1/3: 1/4: 1/5: 1/6: Syllabus, Sec 1.1
Week 2 1/9: Sec 1.1 1/10: 1/11: Sec 1.1 1/12: 1/13: Sec 1.1, H1, Q1, P1
Week 3 1/16: MLK Holiday 1/17: 1/18: Sec 1.2 1/19: 1/20: Sec 1.2, H2, Q2
Week 4 1/23: Sec 1.3 1/24: 1/25: Sec 1.3 1/26: 1/27: Sec 1.4, H3, Q3, P2, V1, V2
Week 5 1/30: Sec 1.4, V3 1/31: 2/1: Sec 1.5 2/2: 2/3: Sec 1.5, H4, Q4, P4
Week 6 2/6: Sec 1.6 2/7: 2/8: Sec 2.1, V4 2/9: 2/10: Sec 2.2, H5, Q5
Week 7 2/13: Sec 2.3 2/14: 2/15: Sec 2.4, V5 2/16: 2/17: Sec 2.5, H6, Q6, J1, V6
Week 8 2/20: M1 2/21: 2/22: Sec 3.1, V7 2/23: 2/24: Sec 3.2, H7, P5, V8, V9
Week 9 2/27: Sec 3.2, V10 2/28: 3/1: Sec 3.3, V11 3/2: 3/3: Sec 3.3, H8, Q7, V12
Week 10 3/6: Spring Break 3/7: 3/8: Spring Break 3/9: 3/10: Spring Break
Week 11 3/13: Sec 3.4, J2 3/14: 3/15: Sec 3.4 3/16: 3/17: Sec 3.6, H9, Q8
Week 12 3/20: WD, Sec 4.1, V13, V14 3/21: 3/22: Sec 4.2, V15 3/23: 3/24: Sec 4.2, H10, Q9, V16
Week 13 3/27: Sec 4.3, J3 3/28: 3/29: Sec 4.3 3/30: 3/31: Sec 5.1, H11, Q10, V17
Week 14 4/3: M2 4/4: 4/5: Sec 5.2, V18 4/6: 4/7: Sec 5.2, H12, V19
Week 15 4/10: Sec 5.3 4/11: 4/12: Sec 6.1, V20 4/13: 4/14: Sec 6.2, H13, Q11, V21, J4
Week 16 4/17: Sec 6.2 4/18: 4/19: Sec 6.3, V22 4/20: 4/21: Sec 6.3, H14, Q12, V23, V24
Week 17 4/24: Sec 6.4, V25, V26 4/25: 4/26: Sec 6.4, V27, J5 4/27: Reading Day 4/28:
Week 18

5/1: H15, Final Exam, 08:00am-11:00am

5/2: 5/3: 5/4: 5/5: