LSU College of Science
LSU  | Mathematics

Math 4153 Information---Finite Dimensional Vector Spaces

Spring 2014 General Information for Math 4153--Section 1.
Time 10:30 AM -- 11:20 AM M W F. Our class meets from Wednesday, January 15, through Friday, May 2, 2014. Our final exam will be Monday, May 5, 10:00 AM ‐ NOON.
Location Room 239 Lockett Hall
Leonard Richardson Office 386 Lockett
Office Hours 11:30 AM -- 12:20 PM (MWF); 12 PM -- 1 PM (TTh). I am available at many other times. Call or email first to make sure I'm able meet with you. I answer email many times daily---usually quickly.
Telephone 578-1568
E-Mail rich@math.lsu.edu
Text Charles W. Curtis, Linear Algebra: An Introductory Approach, 4th Edition, Springer, 1984. ISBN 0-387-90992-3.
Graduate Assistant Ms. Zhaoxia “Mary” Wang will grade those homework problems that are to turned in---the ones that are assigned in red in the table below. She will be available to answer questions in her office, 105 Lockett Hall, as follows: Monday, 2:25 to 3:25 pm.
Free Math tutorial: Room 141 Middleton Library: ????????????????.

Prerequisites

MATH 2057 or MATH 2085.

Homework is required and will be part of your final grade

Problems, mainly proofs, will be assigned frequently. The assignments are your main work in this course. The assignments will be collected, corrected, and returned at the next class meeting. You are encouraged to seek hints to help you get started with these problems! It is required to turn in every assignment! The key to learning to prove theorems lies in how you study Linear Algebra. It is very important to understand thoroughly how and why the proofs presented in the book and in class work. We will go over every collected homework problem in class, to help you prepare for tests. At the end of the course, your homework average on a 10-point scale will be added to your Exam average to produce your final average. For example, if your average on the homework is 5 points out of 10, and you have an 85% exam average, your final average would be 90%, which is an A.

Proofs assigned for homework are a very important learning experience. Some students try a shortcut - copying the correct proofs from the board after the homework has been graded, without turning in their own efforts. This tends to produce proofs on tests that are written by rote from memory, and these tend to be lacking in logic and thus incoherent. It results also in low grades on Part I of each test, because the student's own conceptual errors have not been turned in and thus have not been corrected. Remember that homework is required!

In order to learn the logical structure of linear algebra, one needs to follow a given set of definitions from start to finish. If you wish to use other definitions or other theorems from a different book, you must also include a proof that the definition or theorem you have chosen is equivalent to the one we used in the course.

Tests

These will be closed-book tests: No books or notes are permitted, electronic, paper, or on any other medium. No electronic devices are permitted other than a watch to check the time. Part I of each hour test will consist of a choice of 8 out of 12 short answer questions, and Part II will offer a choice of 2 out of 3 proofs. (The Final Exam will be equivalent to two hour tests.) The proofs will be modeled closely on the collected homework, and they are sometimes identical. The short questions will be small variations of homework problems---including those not collected---together with examples from the lectures and notes. Thus if you have done the homework conscientiously, you should be prepared well for all tests. If you must miss a test, it is your responsibility to speak to me as soon as possible to determine whether or not your excuse is acceptable.

Grades

There will be three hour tests, worth 100 points each, and a two hour final examination, worth 200 points. Your test average will be the sum of all your grades divided 5. Your Final Average will be your exam average plus your homework average. Final Grading Scale: 90 -100 (A), 80-89 (B), 70-79 (C), 60-69 (D), Below 60 (F). You should save all your graded work for future study and in case you think your final grade is in error.

General Advice

  • Many students need help to learn how to write proofs. If you feel confused, it is important to see me for help as soon as possible. If you don't know how to start a homework problem, ask for a hint---either in class or in my office---or even by email. If you ask me a question about the homework, or if you email such a question to me, I may be able to think of a good hint and then I would email it to the whole class as a hint. I can guarantee you it is possible to learn to write sound proofs: Learning begins with your efforts and your persistence.
  • Attend class and ask questions. Non-attendance or lax attendance is usually the first sign of impending academic difficulty. Sometimes a student feels frustrated because of not understanding the classwork. If that is the case, it is necessary to ask more questions. Linear Algebra is a subject you can learn---but you must participate in this work.
  • Come to class on time. However, anyone may need to arrive a bit late on some occasions for reasons beyond ones own control. If you are in that situation, just come right in and take your seat. You should not miss any more of the class time than is necessary for reasons beyond your control.
  • Assignments to be turned in are collected at the beginning of class. If you arrive late, be sure to turn in your homework at the end of class. Do not turn it in later than that, because it is not fair to the graduate teaching assistant, who will be busy enough with the work of grading the assignments that are turned in at the proper time.
  • LSU offers extensive academic support services to help students adjust to the demands of university studies: List of Frequently Used Services.

Homework Assignments and Downloads

We will update the list of assignments and tests below as the semester progresses. You will know an assignment has been updated if a due-date appropriate to this semester appears in the left-hand column. However, sometimes we will assign a problem for a certain date and then postpone it because we don't cover as much as planned in class. So check regularly for updates as to what is due and when.

Academic Honesty The University has clear policies requiring academic honesty. If you email me about a pending assignment, I may send a hint to the whole class in answer to your question, not giving your name of course! If on the other hand you get a good idea from another book, or from talking with a friend, academic honesty requires that you acknowledge your sources openly. Above all, never copy directly from another person's written work as though it were your own. Remember that your own good name is irreplaceable. This is a sound principle which will serve you well throughout your life. Moreover, on a practical level, it is very foolish claim as your own an argument from a former student in this class or from a textbook. The arguments which are copied can be recognized very easily as not coming from the student, and often the precise source can be identified readily. This means that the honorable course of action is also the practical one.
Due Date Assignments: Hand in problems in red for grading. The problems in red are required. Assignments must be written neatly so that the grader can read them. But there is also a class of optional problems, called Bonus Problems. These are worth up to 20 extra homework points per problem. Bonus problems need to be turned in directly to me on a separate sheet from the regular homework, clearly marked Bonus Problems at the top. Bonus problems are due, if you choose to do one of them, one full week after the date listed, unlike normal graded homework, which is due the date listed. Bonus problems must be handed in separately from the normal homework, and they will be graded more strictly for logical rigor than the required homework.
January 17 Read sections 1 and 2. Do Pp.14-15 / 2, 5, 6. These are not to hand in, but you should write your solutions on paper in order to learn from the work. We will go over some---but not all---of these problems in class according to your requests. You are responsible for asking about the questions with which you need help! You will be responsible for all assigned problems, whether collected or not.
January 22 Do Sec. 2 / 1b, 4. In problem 4, also determine whether or not F is an ordered field. For this it will help to show first that in any ordered field, 1 must be in the set P of positive elements. Please be sure to write your solutions neatly, so that the grader can read them! In problem 4, be sure to show that all the field axioms are satisfied. Also, for practice, do Sec. 2 / 1a.
January 27 Sec. 3 / 1, 2, 4 -- 6, 7, 8.
January 31 Sec. 3 / 9, 10. Also, Sec. 4 / 1, 3, 7 -- 8.
February 3 Sec. 4 / 9, 10. Also Sec. 4 / 4abfg. 5 -- 6.
February 5 Sec. 5 / 1, 4, 5.
February 7 Sec. 5 / 2, 3. Also, do what you can with these: Sec. 6 / 1, 2ace, 3ace. 5.
February 10 Sec. 6 / 4 a, b, d, e.
February 14 Sec. 7 / 1 -- 5.
February 17 Sec. 7 / 6: Be sure to prove the conclusions. No credit just for stating the correct answers!
February 19 sec. 8 / 1abfg, 3;
February 21 Sec. 8 / 2, 4: Be sure to prove the conclusions. No credit just for stating the correct answers, or for quoting the theorem cited in the answer section without explaining clearly why this does the job! Also, Sec. 9 / 1, 3, 5.
February 22 Make-up Class on Saturday for Missed Wednesday class in January. Sec. 9 / 6. No credit just for quoting the outline given in the answer section. Explain the solution clearly in your own words!
February 24 Sec. 10 / 1, 9.
February 26 Bring questions to review for Hour Test #1! Everyone is expected to have a written list of questions. Your questions will help to make the review more useful for yourself and for the whole class. Also: Sec. 10 / 3, 4, 5a, 7, 10.
February 28 First Hour Test today! The test will cover assignments that were due before today and the related subject matter.
March 1 Please download the first hour test. Answers to the short questions and overall class statistics appear on the last page.
March 10 Sec. 11 / 1 -- 6, 8.
March 12 Sec. 11 / 7, 9, 10. No credit just for quoting the outline given in the answer section. Explain the solution clearly in your own words!
March 14 Sec. 12 / 1, 2, 3.
March 17 Sec. 12 / 5, 8. No credit just for quoting the outline given in the answer section. Explain the solution clearly in your own words! For problem 8 you may need to use the theorem we proved in class---that every linear transformation from Fn-->Fm is given by a matrix and we saw how to determine the columns of that matrix. I think the author should probably have included this theorem in Sec. 12 rather than in Sec. 13 where he has it. Also: Sec. 12 / 6, 7.
March 19 Sec. 13 / 11--12.
March 21 Sec. 13 / 4, 9. No credit just for quoting the outline given in the answer section. (I think the 'answer' for #4 in the back of the book is garbled and perhaps not helpful.) Also: Sec. 13 / 1, 7--8.
Marach 24 Sec. 13 / 10. No credit just for quoting the outline given in the answer section. Also: Sec. 13 / 2, 3, 5, 6.
March 26 Bring questions to review for the second hour test!
March 28 Second Hour Test today! This test will cover topics treated since the first hour test.
March 29 Make-up Class on Saturday for Missed Friday class in January.
March 30 Please download Second Hour Test.
March 31 Sec. 15 / 2, 4, 8
April 2 Sec. 15 / 5, 9. No credit just for quoting the outline given in the answer section. Also: Sec. 15 / 1,
April 4 Sec. 15 / 6, 7, 10. No credit just for quoting the outline given in the answer section.
April 9 Sec. 16 / 1, 4.
April 11 Sec. 16 / 2, 3.
April 21 Sec. 17 / 1, 2. No credit just for quoting the outline given in the answer section. Also, please read Theorem 17.13, expansion 17.14, and interpretation 17.15 over the break. Have a good holiday.
April 23 Bring questions to review for the third hour test.
April 25 Third Hour Test. This test will cover work treated since the second hour test.
April 27 Please download Third Hour Test.
April 28 Sec. 18 / 1, 2.
April 30 Sec. 18 / 5, 6. Also: Bring questions to review for the Final Exam.
May 2 Bring a number 2 pencil to fill out course evaluations.

Bring questions to review for the Final Exam! Don't forget to review from the beginning of the course! This 200-point exam will cover the whole course in a uniform manner, so remember to review from the beginning of the course. Your final grade for the course will be the larger of the following two: 1. The grade guaranteed by the formula provided higher on this page. 2. One letter below the final exam grade. Thus the final exam provides a safety net that supplements the calculations specified above.
Monday, May 5, 10:00 AM ‐ NOON. Final Exam in room 239 Lockett.
May 8 Please download Final Exam, Spring 2014_Sol.pdf. Solutions and overall class statistics appear on the last page.