MATH 109 MATHEMATICAL REASONING AUGUST 4, 2008
INSTRUCTOR: Carl FitzGerald 5260 AP&M (858)-534-3961 cfitzgerald@ucsd.edu
Office hours 10:00-10:50 A. M. Monday and Wednesday in AP&M B412 and after lecture
TEACHING ASSISTANT: Gordon Honerkamp-Smith ghonerka@math.ucsd.edu
Office hours Monday 5:00 – 6:00 PM and Wednesday 3:00 – 4:00 P. M. 5412 AP&M
TEXT: FOUNDATINS OF HIGER MATHEMATICS 3rd edition by Peter Fletcher and C. Wayne Patty,
International Thomason Publishing, 1988.
GRADING: Homework 10% Midterm Examinations 25% each Final 40%
HOMEWORK: The date is when the homework is due. It must be turned in at the section meeting. No
late homework will be accepted, except for medial or other emergency beyond the student’s control. In
doing homework, help may be sought from books, fellow students, the teaching assistant and the
instructor. Homework must not be a copy of another person’s work. Grades will be assigned by the
grading of a small sample of submitted problems plus a small amount for the overall work. Each
assignment may include a small number of “look at” problems. Students are not expected to hand in
written solutions to these problems.
MIDTERMS: The fist midterm will be in the lecture period on Thursday, August 14. The second
midterm will be in the lecture period on Thursday, August 28. – Students are no to use any of the
following items: notes, texts, calculators, cell phones, other electronic devices. Students are not to
receive help, except from the teaching assistant or the instructor. --- Students should bring a pictureidentification. --- Extended absences from the lecture room are not acceptable. Some of the test
questions will be homework problems with minor changes.
ACADEMIC INTEGRITY: Cheating is unacceptable. Possible penalties include an F in the course and a
report to the University administration.
GOALS AND MATERIAL: This course is to help students make the transition from the intuitive
presentations of calculus, differential equations and linear algebra to mathematically rigorous treatment
of analysis and algebra. Time will be spent examining methods of proofs, set theory, mathematical
induction, formal logic, and introductory material for analysis and algebra. In short, most of the
material of the text will be studied, except for chapter 6. Students are expected to write carefully and to
provide rigorous proofs
FINAL EXAMINATION: The Final is scheduled to be on Saturday, September 6, 2008 from 8:00 –
10:59 A.M. The location is to be announced.
Homework: (Note that there is a section “Selected Answers and Hints” starting on page 296.)
I. August 5: Read section 1.1, pages 9 and 10
page 7 #3, 5, 8, 11, 12.
page 15 #16, 18ab.
II. August 7: Read sections 1.3 1.4, 1.5, and 1.6.
page 15 #26, 35d, 36, 38.
page 23 #41, 42, 43, 47, 54, 55.
page 30 #58, 59, 71, 72, 74.
page 33 #76, 78, 80.
page 39 #96, 99, 100.
III. August 12: Read sections 1.6 and 2.1.
Show that if
divides a number , then
Show that if
divides
, then
divides
divides
.
. (Suggestion: Otherwise there is an integer
such that
can be written in one of the following ways:
,
the form of
.)
Show that there is no rational number whose square is
,
,
. In each case, consider
.
For each of the previous three propositions, indicate the method of proof that you used.
page 39 #94.
Is the following statement true or false? “If
, then
.” Justify your answer.
page 44 #1, 2, 4, 5, 9, 10a-i Give a brief justification for each answer.
THE FIRST MIDTERM EXAMINATION
WILL BE IN CLASS ON THURSDAY, AUGUST 14
It will cover the material through Homework assignment IV.