Math 373: Theory of Positive Integers, Fall 2010
Final Exam: Friday, 10 Dec, 7:30 - 9:30 am.
Review Tuesday, 7 Dec. Please bring questions!
Here is the updated review sheet
for the material not covered on previous tests.
Here are the earlier review sheets
Test I, Test II.
Current homework assignment:
No homework due but here are some
practice problems:
11.13, 11.15, 11.27, 11.29, 11.31, 11.37, 11.43
Read §§ 11.1-11.5.
Tentative schedule.
Instructor:
Alex Kumjian,
DMS 317,
tel: 784-4615, email: alex@unr.edu
Office Hours: MW 9:30 - 10:45 am, TT 1:40-2:30 or by appointment
Time and Place: TT 9:30 - 10:45 am,
AB 634.
Test dates: 23 Sept, 28 Oct.
Final Exam: Friday, 10 Dec, 7:30 - 9:30 am.
Text:
Text: Mathematical Proofs:
A Transition to Advanced Mathematics, 2nd Ed.
by Gary Chartrand, Albert D. Polimeni, Ping Zhang
Prerequisites: Math 181 and the ability to write good English.
Solutions
Tests:
t1;
t2;
Quizzes:
q1,
q2,
q3,
q4,
q5,
q5,
q6,
q7,
q8,
q9,
q10,
q11,
Homework:
h1,
h2,
h3,
h4,
h5,
h6,
h7,
h8,
h9,
h10,
h11,
h12.
The focus of this course is on the theory of proof
as a gateway to abstract Mathematics.
This course is an introduction to the art and practice of mathematical
reasoning. It will culminate in a brief introduction to number theory.
The intended goal is for the student to acquire familiarity with and
mastery of the tools needed to write proofs.
I hope this course will provide you with the theoretical understanding
and the skills, which will help you in your further
studies in Mathematics.
Syllabus:
These are the sections of the text we will cover in this course:
| Ch. 1: |
Sets |
§§1-5 |
2 lectures |
| Ch. 2: |
Logic |
§§1-10. |
4 lectures |
| Ch. 3: |
Proofs: Direct and contrapositive |
§§1-4. |
2 lectures |
| Ch. 4: |
More examples of these proofs. |
§§1-5. |
2 lectures |
| Ch. 5: |
Existence and proofs by contradiction |
§§1-5. |
3 lectures |
| Ch. 6: |
Mathematical induction |
§§1-3. |
2 lectures |
| Ch. 8: |
Equivalence relations |
§§1-6. |
2.5 lectures |
| Ch. 9: |
Functions |
§§1-6. |
2.5 lectures |
| Ch. 10: |
Cardinalities of sets |
§§1-3 |
1.5 lectures |
| Ch. 11: |
Proofs in number theory |
§§1-5. |
1.5 lectures |
Class policy:
Attendance is encouraged but not mandatory; however you are responsible for everything
done in class. You should monitor this page for the current assignment and course
announcements. Class participation is strongly encouraged!
Please ask questions.
Grading policy:
Your grade will be a function of your scores on tests,
quizzes, homework and the final. There will be two tests
and a quiz on most Thursdays.
The lowest quiz score will be dropped so no make-ups will be allowed.
Your grade will be computed with the following weights:
| Tests (2) |
Final Exam |
Quizzes |
Homework |
| 40% |
30% |
15% |
15% |
If however your score on the final exam is higher than your cumulative
prefinal average, your final exam score will be weighted 50% and the other
weights will decrease accordingly.
The grading scale will be as follows:
A : 88%, B : 76%, C : 64%, D : 52%
The instructor reserves the right to lower these cut-offs slightly;
plusses and minuses may be given in borderline cases.
Homework:
Doing mathematics is the best way of learning it especially in a class like this;
writing proofs well only comes through practice. Therefore homework will constitute
an important part of this class and it will be assigned regularly (it will usually
be due on Tuesdays). All submitted work shuld be written neatly and in complete
grammatical sentences. Tutoring is available in the Math Center in AB 610. The
grader, T.J. Gaffney, works at the Math Center; here are his
hours.
You are encouraged to work in groups of two or three and submit one homework assignment
per group. All students in the group will be given the same score for each assignment
they collaborate on (so each student's name must appear on each page). For each assignment
one member of the group should write up the assignment in consultation with the rest of
the group. Written collaboration between groups is not allowed.
Previous homework assignments:
due 31 Aug: 1.2bd, 1.4bd, 1.6c, 1.10, 1.14, 1.18b, 1.22, 1.28; solutions.
due 7 Sept: 1.32, 2.4, 2.6, 2.8, 2.10, 2.16, 2.18, 2.20abc; solutions.
due 14 Sept: 2.24b, 2.26, 2.32, 2.34, 2.38, 2.40, 2.46, 2.48abef; solutions.
due 28 Sept: 3.2, 3.4, 3.6, 3.8, 3.12, 3.14, 3.20, 3.24; solutions.
TJ has some
tips on writing up proofs.
due 5 Oct: 4.4, 4.6, 4.10, 4.12, 4.18, 4.24, 4.324; solutions.
due 12 Oct: 4.38, 5.6, 5.8, 5.16, 5.22, 5.26; solutions.
due 19 Oct: 5.30, 5.36, 6.6, 6.8, 6.10; solutions.
due 2 Nov: 6.14, 6.16, 6.24, 8.6, 8.20; solutions.
due 9 Nov: 8.16a, 8.26, 8.36, 8.38, 8.40; solutions.
due 16 Nov: 9.6abc, 9.12, 9.14, (9.15), 9.20, 9.22; solutions.
due 23 Nov: 9.30, 9.34, 9.48a, 10.6, 10.11; solutions.
due 30 Nov: 10.16, 10.18, 11.4, 11.6; solutions.
As a courtesy to your fellow students please arrive on time and keep your cell phones
switched off during class.
The Department of Mathematics and Statistics supports providing equal
access for students with disabilities. I encourage any student needing
to request accommodations for a specific disability to please meet
with me at your earliest convenience to ensure timely and appropriate
accommodations.
Math Dept,
UNR