Fall 2009, MATH 328K: Introduction to Number Theory
(Sections 57740 & 57745 )
The course provides a transition from the problem-solving approach of mathematics 408C and 408D to the rigorous approach of advanced courses.
The material will cover properties of integers, divisibility, prime numbers, congruences, Fermat's Little Theorem, Euler's Theorem, introduction to Public Key Cryptography (the first five chapters of the course textbook).
General Information
Instructor: Cristina Caputo (caputo@math.utexas.edu) 471-1167
Office hrs:
RLM 11.164
T 4:00-5:30pm, F 11:00-12:30pm, and by appointment
Teaching asst:
Cyntreva Paige (cyntreva@hotmail.com) 232-6191
Office hrs:
RLM 13.152
MW 8:00-9:00am and by appointment
Class meeting :
Section 57740 in RLM 6.112 MWF at 9:00-10:00am &
Section 57745
in RLM 6.112 MWF at 10:00-11:00am
Text:
Number Theory Through Inquiry by Marhsall, Odell and Starbird. Editor: MAA Textbooks.
Course webpage:
http://www.ma.utexas.edu/users/caputo/M328K.html
Course description:
The class will be conducted using a method of
instruction called Inquiry Based Learning or Guided Discovery or the
Modified Moore Method. This method fosters creativity and independent
thinking. It is also fun. Your book contains lists of questions and
theorem statements without proofs. You will answer the questions and prove
the theorems on your own and present your results to the class. These
presentations are a major part of the course.
This course is considered a "transition" course at UT Austin; it is
intended to be a course in which students learn to construct
mathematical proofs. In general, this course is taken after Calculus and
prior to taking any analysis or algebra courses. In the IBL Number
Theory course our goal is not only to give students the opportunity to
investigate Number Theory concepts but to become independent thinkers,
problem solvers, strong communicators, and better proof writers. Because
of its track record, the IBL Number Theory course is required for
students preparing to become mathematics teachers in the UTeach Program. You
may not use any books, websites, or people not in this class!
Course grade:
Your overall course grade will be determined by
your participation ( presentations),
quizzes, and
exam grades.
The proportions will be the following:
Participation (20%), Quizzes (20%), Midterm #1 (12%), Midterm
#2
(12%), Midterm #3 (12%),
Final Exam (24%)
Exams:
There will be three midterms
and a
final exam.
The
final exam will be comprehensive.
The dates for the exams are
Midterm #1 (September 25), Midterm #2 (October 16), Midterm #3 (November
23)
Final Exam:
If your class meets at 9:00-10:00am then it is on Saturday, December 12, 2-5pm;
if your class meets at 10:00-11:00am then it is on Tuesday, December 15, 9-12pm
The midterms will be held during the regular class hour.
Quizzes: there will be in-class 20 minute quizzes about each week. They will be graded; the lowest quiz grade will be dropped.
Participation:
it consists of in-class volunteer presentations. Each time the class meets some students will present problems from the list of problems suggested. The list of problems will be posted regularly on Blackboard. At the end of the class a few problems from the list will be chosen as the ones that will be presented on the following
time the class meets.
Make-up policy:
There will not be make-up exams, except only in very
compelling circumstances or when the University requires me to do
so. If circumstances beyond your control cause you to miss
an exam, please discuss the matter with me as soon as possible.
Failure to contact me (by person, phone or email) within 24 hours
of missing an exam will eliminate the possibility of any make-up, sorry.
Prerequisite Mathematics 341 with a grade of at least C.
Students with disabilities:
The University of Texas at Austin provides upon request appropriate
academic accommodations for qualified students with disabilities.
For more information, contact the Office of the Dean of Students
at 471-6259, 471-4641 TTY.
Drop dates:
The last day to drop the course without possible academic penalty
is September 23, 2009. The last day to drop the course for academic
reasons is October 21, 2009. After this, students may go to the
Dean's office to appeal for non-academic reasons.