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Course Information for Math 4031: Advanced Calculus I

General Information for Section 1, Fall 2008

Time TTh: 9-10:30
Location Room 132 Lockett
Jerome W. Hoffman
Office 374 Lockett
Office Hours MW 8:30 -9:30; F 8:30 -11:30. I am available at many other times. Call first to make sure I'm able meet with you. I answer email many times daily.
Telephone 578-1575
E-Mail hoffman@math.lsu.edu
Text Richardson, L., Advanced Calculus: An Introduction to Linear Analysis, John Wiley & Sons, 2008. ISBN 978-0-470-23288-0.
Graduate Assistant   Liqun Fang  will grade your homework. Her office: 343 Lockett.

Math Major Requirements and Recommendations

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


Mathematics 2057 and 2085, or the equivalent, are both required prerequisites.


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! If you have no idea how to start a problem, you can make a good start by writing:
  1. an accurate statement of the question
  2. an accurate definition of each technical term in the question
  3. an accurate statement of at least one theorem related to the question, or at least one good example to illustrate what is to be proved.
In many cases, you will then see better how to proceed with the proof. 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 Passes gives you the best final average.
  1. Pass #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, Pass #1 raises your final average to 90%, which is an A.
  2. Pass #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)/2.
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 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. 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 well-prepared 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. You can download and view last year's tests from Math 4031 where they are listed among the assignments in the table below.


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.


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.

Homework Assignments and Downloads

We will update the list of assignments and tests from last year 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. 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. 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.
August 26
Read Advice to the Student, pages 10-11, and Section 1.1. Exercises 1.1 / 1-6, 8, 10, 7, 9, 11
August 28 Exercises 1.2 / 12, 14, 16, 18, 20, 23, 24.
Sept. 9
Exercises 1.2 / 19, 22, 25; 26.
Sept. 11
Finish reading section 1.3. Exercises 1.3 / 28, 31, 33 - 39, 42.
Exercises 1.3 / 29, 32; 40, 41,43
Sept. 18

Exercises 1.4 / 47 - 50, 54, 55, 51, 53, 57.
1.5 / 59 - 61, 63, 66, 62, 65. 1.4 / 52 is a bonus problem worth up to 20 extra homework points, if turned in on a separate sheet from the regular homework today.
Sept. 25
Exercises 1.6 / 67 - 70, 72.
Sept.30 Exercises 1.6 / 71, 74; 1.7 / 76- 81, 83, 85, 82, 84, 86.
Oct 2
1.8 / 87, 89 - 92, 94.   Number 96 is a bonus problem - 20 points - if turned in to me separate from regular homework before the day of the first hour test.
Oct 7
Bring a List of Questions to Review for Hour Test!
Oct. 9
First Hour Test: Sections 1.1 - 1.8
Oct. 14
2.1 / 1 - 3, 5, 6, 11.
Oct. 16 Exercises 2.1 /4, 7, 9, 10. Also 2.1 / 8, 12. Number 14 is a bonus problem - 20 points - if turned in to me separate from regular homework by October 23.
Oct. 21
Exercises 2.2 / 19, 22, 23, 25, 20, 21, 24; Numbers 26 and 27 are bonus problems, 20 points each, if turned in separate from homework by October 28.
Oct. 23 Exercises 2.3 / 29 - 34, 37, 41 - 43, 45, 46, 35, 38, 47.
Oct. 28
Exercises 2.4 / 48, 50, 52, 54, 55, 58, 59.
Oct. 30
Exercises 2.4 / 49, 51.
Nov. 4
Exercises 2.5 / 60 - 63, 66 - 68,  64, 65, 69.    Bring a List of Questions to Review for Second Hour Test!
Nov. 6
Second Hour Test: Sections 1.8 - 2.5
Nov. 11
Download questions, class statistics and solutions for Hour Test #2.
Nov. 13 Exercises 3.1 / 1, 3, 4, 5, 6, 7, 8, 11, 12.
Nov. 18 Exercises 3.1 / 9, 10, 15. Finish reading Section 3.2. Do exercises 3.2 /17, 20, 23, 25 - 27, 29.
Nov. 20
Exercises 3.2 / 18, 21, 22, 24  and 3.3 / 32, 33, 35-37, 39, 42, 34, 38, 40.
Nov. 25 Exercises 3.4 /  45, 46.  Bring a List of Questions to Review for Third Hour Test!
Dec. 2
Third Hour Test: Sections 2.5 - 3.4.
Dec. 4
Download questions, class statistics and solutions for Hour Test #3. Bring a List of Questions to Review for the Final Exam! Bring a #2 pencil to fill out the end-of-semester course evaluation forms which will be distributed in class.
Dec 10,
Final Exam: in 132 Lockett, our regular classroom. 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. 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.

Download questions, solutions, and class statistics for 2007 Final Exam and Final Grade Statistics