Course Information for Math 4031:
Advanced Calculus I
General Information for Section 1, Fall 2008
|| TTh: 9-10:30
|| Room 132 Lockett
|Office 374 Lockett
||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.
||Richardson, L., Advanced Calculus: An
Introduction to Linear Analysis, John Wiley & Sons, 2008. ISBN
|| 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
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:
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.
- an accurate statement of the question
- an accurate definition of each technical term in the
- an accurate statement of at least one theorem related
question, or at least one good example to illustrate what is to be
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!
- Pass #1: Add your average homework score
on a 10-point scale to the average of your 3 hour tests with the final
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.
- 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.
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.
||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.
in problems in red for grading.
|Read Advice to the Student, pages 10-11,
and Section 1.1. Exercises 1.1 / 1-6, 8, 10, 7,
||Exercises 1.2 / 12, 14, 16, 18, 20, 23, 24.
|Exercises 1.2 / 19, 22, 25;
|Finish reading section 1.3. Exercises 1.3 / 28,
31, 33 - 39, 42.
|Exercises 1.3 / 29, 32;
|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.
|Exercises 1.6 / 67 - 70, 72.
||Exercises 1.6 / 71, 74;
1.7 / 76- 81, 83, 85, 82, 84, 86.
|1.8 / 87, 89 - 92, 94. Number
is a bonus problem - 20 points - if turned in to me separate
from regular homework before the day of the first hour test.
|Bring a List of
Questions to Review for Hour Test!
|First Hour Test:
Sections 1.1 - 1.8
|2.1 / 1 - 3, 5, 6, 11.
||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.
|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.
||Exercises 2.3 / 29 - 34, 37, 41 - 43, 45, 46, 35, 38, 47.
|Exercises 2.4 / 48, 50, 52, 54, 55, 58, 59.
| Exercises 2.4 / 49, 51.
|Exercises 2.5 / 60 - 63, 66 - 68,
64, 65, 69.
Bring a List of Questions to Review for Second
|Second Hour Test:
Sections 1.8 - 2.5
class statistics and solutions for Hour
||Exercises 3.1 /
1, 3, 4, 5, 6, 7, 8, 11, 12.
||Exercises 3.1 / 9, 10, 15.
Finish reading Section 3.2. Do exercises 3.2
/17, 20, 23, 25 - 27, 29.
|Exercises 3.2 / 18, 21,
and 3.3 / 32, 33, 35-37, 39, 42, 34, 38, 40.
||Exercises 3.4 / 45,
46. Bring a List of Questions to
|Third Hour Test:
Sections 2.5 - 3.4.
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.
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.
solutions, and class statistics for 2007
Final Exam and Final Grade Statistics