First-day Handout

Spring 2016

M 328K – Number Theory – IBL

TTh 11:00 – 12:30, RLM 7.113 (53460)

 

Instructor:                  Dr. Jane Arledge, RLM 9.144, arledge@math.utexas.edu

Office hours:                Tuesday 12:30 – 1:30, Thursday 8:30 – 9:15, (Tuesday 8:30 – 9:15 by appointment)

Web page:                    www.math.utexas.edu/users/arledge                     

 

TEXT:  Number Theory Through Inquiry, by Marshall, Odell and Starbird

 

OVERVIEW OF COURSE:  In terms of content, successful students will understand, and become proficient in proving, introductory number theoretical results.  This course will be run in an Inquiry Based Learning (IBL) format, in which students are required to prove results as needed and present them to the class.  During presentations, the non-presenters will ask questions of the presenter and discuss the proof, to ensure that they completely understand the concepts and execution.  The IBL format requires students to directly engage with the learning process, and to prove results without having similar results as examples – to create the proofs from scratch.  As a result, students should obtain a deeper understanding of the material covered, and will become better at writing and communicating mathematics.  The course will cover most of the first 5 chapters of the book: divisibility, prime numbers, modular arithmetic, Fermat's little theorem, Euler's theorem, and cryptography.  Additional material may be covered.  Class attendance is mandatory and will be recorded.

 

PREREQUISITES:  This course is designed for students who have succeeded in a course that introduces students to mathematical proof writing; for example M 325K or M 341.  You will not be allowed to stay in this class without meeting this prerequisite.  Please see me if you have questions about your readiness for this class.

 

HOMEWORK:  There will be assignments due every day, mostly consisting of theorems to be proven, questions to be thought through and answered, and computational exercises.  Late assignments will not be accepted.  Both the quality and correctness of selected portions of the assignment will be graded.  The homework grades will not be averaged in with your final grade; however, if you do not average 60% or better on the homework assignments, you will receive a grade of F in this class.  By the way, it is expected that there will be a few homework problems that you cannot solve.  While a passing homework grade will not affect your final grade directly, being able to do the assigned work without any help from others will certainly help you do a better job on the participation portion of the grade, as well as being a clear indication of how you will do on exams.

 

You are required to write your assignments neatly, and they must be easily readable.  You may type up solutions if you wish, using LaTeX or MSWord, for example.  If your work cannot be easily read, you will receive a grade of 0 for it.  Your papers will be submitted before class begins.

 

Proofs should be written in complete sentences.  This standard requirement helps you organize your thoughts, and leads to clearer and more concise proofs and superior presentations.  Using technical symbols should be avoided when writing proofs for assignments; such symbols may be used when writing proofs on the board. 

 

The lowest 3 assignment scores will be dropped from the computation of your homework average. This is to accommodate occasions when, for whatever reason (left it at home, out sick, computer crashed, didn’t realize it was due, etc.), you are unable to hand in an assignment on time.  You should still do the work from homework assignments you miss; when writing exams, I will assume you have a complete understanding of all of the assignments and all of the problems worked in class.

 

PARTICIPATION:  You will be working actively every day in class.  This work will typically consist of items from the homework assignments.  There may be group work, both at the board and in your seats, and group presentations, as well as individual presentations.  I will assign you a grade based on your participation in these activities.  Each time you are absent or late to class, or if you do not present material regularly, your participation grade will drop.  This portion of your grade will be based mostly on effort, rather than correctness.  My expectation is that everyone will do very well on this portion of the grade, which is possible if you come to class and participate fully in the classroom work. 

 

EXAMS:  You may not even look at calculators, phones, or any other electronic devices during exams, and you will not be allowed to leave and come back once the exams are distributed.  Exams will consist of questions of similar difficulty as those done in homework and in class, and the grading will be based only upon the correctness of the solution presented.  There will be three exams.  The planned dates are listed (these dates are unlikely to be changed during the semester, but it is possible – you will be notified in class of any such changes.)

Exam  I:           Thursday, March 3

Exam II:          Thursday, April 28

Final Exam:     Tuesday, May 17, 10 am – 12 noon (in a different room, determined later in the semester)

The lowest of your three exam grades will be dropped.  Thus, if you are happy with your first two exams, you do not need to take the final exam.  As a result of this policy, there will be no makeups of exams; rather, if you miss an exam, that 0 will be dropped.  If, for any reason, you miss two exams, you will not pass the course.  You should carefully examine the exam dates above, since being available to take each exam is a requirement for this course and there are no makeups.  (An exception may be allowed for a religious holy day – you must let me know by February 3 of any such conflict.)

 

GRADES:  On exams and homework, your grade will be computed as a percentage: the number of points you earn divided by the number of points possible.  Grades will be assigned no more strictly than:  93-100 A; 90-92 A-; 87-89 B+; 83-86 B; 80-82 B-; 77-79 C+; etc.  It is unlikely that any grade will be curved.  The percentages of each type of work that will be used to compute your final grade are as follows.

 

            Homework                   0%       (minimum average is required, see above)

            Participation                10%

            Exams                          90%     (the highest two exam scores will be averaged)                        

 

ACADEMIC INTEGRITY:  In this class, looking up any result in any book (other than your text), or online, or from a human not in this specific class, or from prior class notes, or any other access or use of material not in your own head is cheating.  Your text consists mostly of statements you will be proving and presenting in class. You are encouraged to discuss the work with your fellow students, but your write-up must be your own. If you cannot achieve the minimum required homework average on your own, you will not pass the exams anyway, and so you may as well not cheat.  Cheating is dishonorable and disgusting.  Keep in mind that most students are honest, and honest students do not like cheaters, and often report what they see or hear.  If you are caught cheating on the homework or an exam, you will be penalized as harshly as possible under the rules of UT, including earning an F in this class.  Do not cheat.

 

DEADLINES FOR DROPPING A COURSE:  If you drop a class on or before February 3, the class will not show up on your transcript.  If you drop a class after that date, the course will show up on the transcript with a “Q” grade.  After April 4, it is not possible to drop a course except for extenuating (usually non-academic) circumstances.

 

STUDENTS WITH DISABILITIES:  Upon request, the University of Texas at Austin provides appropriate academic accommodations for qualified students with disabilities.  For more information, contact the Office of the Dean of Students at 471-6259 or 471-6441 TTY.  If you require accommodations, you must let me know before February 3.

 

STUDENT CONDUCT:  Coming and going during class is distracting to your fellow students, and will affect your participation grade.  Do not be surprised if I question you about any late arrivals or early departures.  It is important to be respectful of your fellow students, especially when they are presenting.  Constructive comments are welcome, but rude or insulting comments are not.

 

IBL Course Designation – Independent Inquiry Flag:  This course carries the Independent Inquiry flag. Independent Inquiry courses are designed to engage you in the process of inquiry over the course of a semester, providing you with the opportunity for independent investigation of questions related to the course material.  The effectiveness of your independent investigations throughout the semester will be demonstrated by your class participation as well as by your proficiency with the material on exams.

 

© Jane Arledge, The University of Texas, January 2016 -- Distribution of this document to a third party (other than for evaluation of the course as transfer credit) is a violation of the author's intellectual property rights.