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Math 4035 information

General Information for Math 4035, Fall 2011

Time MWF 10:40 AM -- 11:30 AM
Location Room 132 Lockett Hall
Leonard Richardson Office 386 Lockett
Office Hours M -- F, 12:40--1:30 PM. I am available at many other times. Call first to make sure I'm able meet with you. I answer email many times daily---usually quickly.
Telephone 578-1568
Text Richardson, L., Advanced Calculus: An Introduction to Linear Analysis, John Wiley & Sons, 2008. ISBN 978-0-470-23288-0. There is a list of errata. If you find an error not on this list, please tell me.
Syllabus We will cover most of Chapters 8, 9, 10, and 11.
Graduate Assistant Mr. Haewoong Jeon will grade your homework and hold office hours on Mondays from 1:30 -- 2:30 PM in 365 Lockett Hall.
Free Math Tutoring Service Room 141 Middleton Library. Hours: 10 AM -- 7 PM (MTWTh) and 10 AM -- 3 PM (F).

Math Major Requirements and Recommendations

Math 4031, followed by either Math 4032 or Math 4035, satisfies the Advanced Calculus requirement for the Mathematics major with a mathematics concentration. It prepares students for graduate study of mathematics and its applications. The Department strongly recommends that Mathematics majors planning graduate study in Mathematics take all three Advanced Calculus courses: Math 4031, 4032, and 4035.


Mathematics 4031 and 2085 or the equivalent.


Problems, mainly proofs, will be assigned frequently. These 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! Please turn in every assignment! The key to learning to prove theorems lies in how you study Advanced Calculus. It is very important to understand thoroughly how and why the proofs presented in the book and in class work. Please read the Introduction to your textbook! We will go over every collected homework problem in class, to help you prepare for tests. At the end of the course, you will have the benefit of whichever of the following two Homework Bonuses gives you the best final average.
  1. Bonus #1: Add your average homework score on a 10-point scale to the average of your 3 hour tests with the final exam. For example, if your average on the homework is 5 points out of 10, and you have an 85% exam average, Bonus #1 raises your final average to 90%, which is an A.
  2. Bonus #2: Replace your lowest hour-test grade with your adjusted homework average. This will be calculated as follows. Let S denote your homework average on a 100-point scale. Your adjusted homework average HW=(S+100)MIN(S/50,1)/2 . Notice that with this formula, if you do no homework, so that S=0, then your replacement hour test grade is 0, just like your raw homework score. As another example, if you average 5 points out of 10 on the homework, then your replacement hour test grade is 75%, under this formula. It is extremely foolish in this course not to turn in homework!
Proofs assigned for homework are a very important learning experience. Some students try an easier technique - copying the correct proofs from the board after the homework has been graded, without turning in their own efforts. This tends to produce 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. So please turn in every assignment!


These will be closed-book tests: No books or notes are permitted. 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.


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 the better of the two grades calculated by adjusting the average using either Pass #1 or Pass #2 described above under Homework. 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. 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. Advanced calculus 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 appears in the left-hand column.

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 will be graded more strictly for logical rigor than the required homework. Bonus problems are more challenging than the required problems.
August 22 Today is the first day of class. You should have your texts for your classes and be ready for work.
August 24 Read Pp. 245 -- 249. Be sure to practice reading with a pencil! Do problems 8.1 -- 8.4; 8.6 -- 8.8; 8.10. These are not to hand in, but you should write your solutions on paper in order to learn from the work.
August 26 Do problems 8.9, 8.11, 8.14(a)--(c). These are to be handed in today at the beginning of class. Please be sure to write your solutions neatly, so that the grader can read them!
August 29 8.16--17; 8.21--23.
August 31 Read the remainder of section 8.2 and do the following problems: 8.18--19; 8.24--25; 8.30--31, 8.33. We will go over this work on Wednesday in class.
September 2 8.20, 8.26, 8.28. The first Bonus Problem is 8.32. If you choose to do it, turn it in to me one week from today, separately from the regular homework. Bonus problems are graded strictly for rigorous reasoning.
September 7 8.34 --8.38; 8.42.
September 9 8.39, 8.40, 8.41.
September 12 8.44, 8.51, 8.52.
September 14 8.46, 8.48 -- 8.50, 8.53.
September 16 8.45, 8.47, 8.54.
September 19 9.2, 9.3, 9.6, 9.7. The next Bonus Problem is 9.11, due one week from today if you do it. Turn it in separately from the other homework. In one direction, 9.11 is quite easy, so that bonus credit requires both directions.
September 21 9.4, 9.5.
September 23 9.12, 9.14--9.15, 9.19--9.26.
September 26 9.13, 9.16, 9.28.
September 28 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. In case you did not notice, the 2010 first hour test is available below for you to download. Note however that what we cover in the course does vary somewhat from year to year, as does the coverage of the tests.
September 30 First Hour Test today. This test will cover Sections 8.1 -- 9.2.
October 1 Please download Hour Test #1, 2011, Solution Sketches and Class Statistics.
October 3 9.29 -- 9.32, 9.35, 9.36, 9.38.
October 5 9.33, 9.39, 9.41 . Bonus Problem is 9.42, due one week from today if you do it. Turn it in separately from the other homework.
October 7 9.44 -- 9.48
October 10 9.43, 9.49, 9.50
October 12 10.1--10.3, 10.5--10.7, 10.12.
October 17 10.4, 10.8, 10.16, 10.20.
October 21 10.25 -- 10.29, 10.31, 10.37, 10.42. Typos: In 10.31 E3 should be E2. In 10.42, the domain of the mapping is incorrectly stated. It should read D : En --> Em.
October 24 10.30, 10.32, 10.38, 10.39.
October 26 10.44, 10.46 -- 10.49, 10.51. Bring questions to review for the second hour test.
October 28 Second Hour Test today. This test will cover Sections 9.3 -- 10.3, inclusive. You will be responsible for problems due before this date.
October 29 Please download Hour Test #2, 2011, Solution Sketches and Class Statistics.
October 31 10.45, 10.50, 10.52.
November 2 10.57, 10.58, 10.66.
November 4 10.59, 10.61 . Also, 10.60, 10.62, . Hint for 10.59: For a linear transformation T: En --> Em, compare the dimension of the image of T with the dimension of the domain of T. Hint for 10.61: If the claim were false, show that there is a problem at some local extreme point.
November 7 10.60, 10.63, 10.65.
November 9 10.62, 10.64. (Be sure to prove that your example has the specified properties!)
November 11 10.69 -- 10.71
November 14 10.72 -- 10.74, 10.77,
November 16 Catch-up day for going over homework problems.
November 18 10.76, 10.81, and 10.82(b,d, and e only) . For 10.82(e), you may use either equation (10.8) or (10.10)
November 21 11.48, 11.49, 11.50, 11.56. (Please see the Errata list for the correction of the typos in problem 11.56.)
November 23 Bring questions to review for the third hour test.
November 28 Third Hour Test today.
November 29 Please download Hour Test #3, 2011, Solution Sketches and Class Statistics.
November 30 11.52, 11.54ab, 11.57bc. In 11.57c, you are not expected to prove the Riemann integrability statement, since we do not have time for that topic this semester. Use the Jacobian theorem to transform the integral under the given change of variables. See the small typo on page 357 in the errata list linked at the top of this page. Bring questions to review for the Final Exam.
December 2 Bring questions to review for the Final Exam! Don't forget to review from the beginning of the course! Also, bring a number 2 pencil to fill out the end-of-course evaluation form!
December 7.

Final Exam: Wednesday , December 7, 5:30 -- 7:30 PM 132 Lockett Hall. Please be on time!
The Final Exam will have a choice of 12 out of 18 short questions for 96 points and 4 out of 6 proofs for 104 points. At least one of the proofs and 3 of the short questions will come from the hour tests. There will be two proofs and 6 short questions from each one-third of the semester.

Advice: Be sure to review the first two-thirds of the course. Often students who are doing well overlook the need for this review. Safety Net Policy: Each student is guaranteed at least the grade determined by the test and final exam average, together with the homework bonus credit. However, as an incentive to do well on the final exam, no final grade will be worse than one letter below the final exam grade.

December 10 Please download Final Exam, Fall 2011, Solution Sketches and Class Statistics.