MATH 310 Number Theory
Syllabus for Spring 2008

Tuesdays and Thursdays, 9:30-10:50am

326 Gildemeister Hall

Prerequisite: Passing grades in MATH165 and MATH210.

Text & Calculator: “Introduction to Number Theory” by Peter Schumer. This book is out of print, see the instructor for a photocopied version.

Course Website:     http://course1.winona.edu/eerrthum/math310

Instructor: Dr. Eric Errthum                          Office: 203L Stark Hall

Winona Email Username: eerrthum             Office Phone: 474-5775

Office Hours:  See schedule on my home page.

Grading:         Quizzes (8 @ 20 points each, drop lowest)          140 points-------- 17.95%
                        Homework (scaled as needed)                              110 points-------- 14.10%
                        Online Discussions Participation                            30 points--------- 3.85%
                        Midterms (3 @ 100 points)                                   300 points-------- 38.46%
                        Final                                                                      200 points-------- 25.64%
                                                                                                  --------
                                                                                                      780 points total

Grades:  A = 90% (702 pts), B = 80% (624 pts), C = 70% (546 pts), D = 60% (468 pts)

Quizzes:    We will have eight short (~10 minute) quizzes (see schedule below). Each quiz will count for 20 points and the lowest quiz score will be dropped from your grade.

Homework:    Homework will be assigned periodically and will be collected every Tuesday. You are encouraged to do extra problems from the text.

Online Discussions:   You will be expected to contribute to the online Discussion boards on D2L. Contributions include both asking questions and answering questions posed by other students. Posts containing no content (e.g. “I agree” or “What were the homework problem numbers?”) will not be counted. The discussion board is NOT a place to exchange homework solutions. If you wish to receive credit for an anonymous question or post, you can do so by emailing the instructor immediately after posting.

Exams:     There will be three in-class exams and one comprehensive final exam. Exam dates are tentative until officially announced in class. The final exam is tentatively scheduled for Wednesday, April 30, 1:00 – 3:00pm.

Late/Missed Work: Late homework or missed quizzes will result in a score of zero. There are no make-up quizzes. Make-up exams will be given at the discretion of the instructor. If you miss class, it is your responsibility to obtain notes and assignments from fellow students. If you have an unavoidable absence, please inform the instructor beforehand.

Desire2Learn:            Many course materials can be found on D2L including projects, solutions to quizzes and exams, sample exams, the Discussion boards and approximate grades.

Academic Dishonesty:  Any type of academic dishonesty (cheating, copying, plagiarism, using a solutions manual to do homework, etc.) will result in failure and will be reported to school authorities. If you are having trouble with an assignment, please see the instructor first.

Note:   This syllabus is subject to change if deemed necessary by the instructor.

 

Tentative Schedule of Events – Math 310

(subject to change)

Week Beginning

Tuesday

Thursday

1/14

Introductions
1.1 & 1.2
Preliminaries, Induction

HW: 1.1 (pg 4): 10, 14, 22, 26

1.2 (pg 10): 8, 9, 11, 12

1.3 & 1.4
Divisibility & Congruences
Combinatorics

Polynomial Time Algorithms

HW: 1.3 (pg 15): 2, 3, 4, 15, 20

1.4 (pg 20): 10, 17, 20ad

1/21

Quiz 1
2.1
The Euclidean Algorithm
& Some Consequences

HW: 2.1 (pg 28): 1, 4, 7, 15, 16, 18

2.2
Congruence Equations

1/28

Quiz 2

2.2, cont.

Chinese Remainder Theorem

HW: 2.2 (pg 36): 2, 4, 6, 8, 14, 15, 20

2.3 & 2.4
Primes, Fundamental Theorem of Arithmetic
Primality Testing & Factoring

HW: 2.3 (pg 41): 2b, 3b, 9, 13, 14, 17b

HW: 2.4 (pg 44): 1, 3, 8c

2/4

Quiz 3
2.5
Important Congruence Relations

HW: 2.5 (pg 51): 5, 6, 8, 10, 11, 23

Review / Worksheet

2/11

No Office Hours on Monday or Tuesday

Office Hours for Wednesday: 9am – 4pm

NO CLASS

Exam I

2/18

7.7
RSA & Basic Cryptography

HW: 7.7 (pg 196): 1, 5, 8, 10, 14

3.1 & 3.2
Arithmetic Functions
Multiplicativity

HW: 3.1 (pg 58): 1, 4, 9, 12

HW: 3.2 (pg 62): 3

2/25

Quiz 4
3.2, cont.

HW: 3.2 (pg 62): 4b, 5, 6, 12, 13

3.3
Mobius Inversion

HW: 3.3 (pg 66): 1, 4, 6, 10, 12, 13, 14

3/3

SPRING BREAK

3/10

3.3, cont.

3.4

Perfect Numbers

Quiz 5
Review / Worksheet

3/17

EXAM II

4.1
Primitive Roots

HW: 4.1 (pg 80): 2, 5, 8, 9, 10, 12, 20

Due April 1

3/24

4.1, cont.

4.2 & 4.3
Quadratic Residues & Legendre Symbol

HW: 4.2 (pg 84): 8, 11, 12

Take-Home Quiz 6

(available on D2L)
No Official Class

Computational Worksheet/Study Session

3/31

4.4
Quadratic Reciprocity

Solving Quadratics

HW: 4.4 (pg 96): 1, 4, 5, 14, 15, 16

Quiz 7
6.1
Finite Simple Continued Fractions

HW: 6.1 (pg 133): 1, 4, 6, 14, 16

4/7

6.1, cont.

6.3

Infinite Simple Continued Fractions

HW: 6.1 (pg 133): 12

6.3 (pg 144): 1, 2, 4, 6, 8

6.4
Rational Approximations of Irrationals

HW: 6.4 (pg 152): 3, 4, 6, 8

“A Short Proof of the Simple Continued Fraction Expansion of e”
by Henry Cohn

4/14

Quiz 8
Review / Worksheet

EXAM III

4/21

Final Review

Chapters 1, 2, 3

Final Review

Chapters 4, 6

 

Final Exam

Wednesday, April 30

1:00 – 3:00pm

 

 

The Extra Credit List

 

Below is a list of problem numbers from the free number theory text “Number Theory for Mathematical Contests” (also a great source of additional examples). Each problem is worth 6 missed points on previous homework questions (before scaling). Since these are extra credit and I don’t know the solutions, you MUST present a clear argument or solution for each problem. Incomplete answers will receive no credit. Obviously, there are far too many problems listed to be done, so feel free to do any, some, or none of the problems on the list. Problems do not have a specific due date, but you can only hand in up to 5 extra credit problems per week. Hand them in when you hand in your homework, but make sure it’s on a separate sheet of paper clearly labeled as extra credit work. All extra credit work will be returned during the final week of class.

 

1.2.1, 1.2.2,

1.3.1, 1.3.2, 1.3.3, 1.3.6, 1.3.7, 1.3.8, 1.3.9, 1.3.10, 1.3.21,

1.4.2,

1.5.2, 1.5.3, 1.5.6, 1.5.8, 1.5.17,

2.2.3, 2.2.4, 2.2.7, 2.2.8, 2.2.9,

2.3.1, 2.3.2, 2.3.4, 2.3.7, 2.3.9, 2.3.11, 2.3.12, 2.3.19, 2.3.20, 2.3.23, 2.3.31,

3.1.1, 3.1.2, 3.1.3, 3.1.5, 3.1.7, 3.1.9, 3.1.10, 3.1.13, 3.1.16, 3.1.18,

4.1.2, 4.1.4, 4.1.5, 4.1.8, 4.1.10, 4.1.13,

4.2.3, 4.2.7,

4.3.3

 

 

Welcome to college math!

 

If this is your first math class taken in college, there are some important things you need to know. College math classes are run very differently from high school math classes. On the surface it may seem they are similar as you listen to the lecture and take notes, but there are significant underlying differences. Knowing these ahead of time can help you make the most of this coming semester.

 

#1: College math classes generally stay on the schedule in the syllabus. If there is one day allotted to the topic that is probably all of the class time that will be spent on it, even if “most” of the students “don’t get it.”

 

#2: It is expected that you will read the text and do the problems in order to learn the material, even if no one checks up on you. The instructor might never collect the homework, but that doesn’t mean it doesn’t affect your grade.

 

#3: You will sometimes be responsible for material in the textbook that is not covered in class. If there is a text reading and/or homework problems covering a concept that was not discussed in class, you are still expected to learn it. If you don’t understand it, make an appointment with your instructor for help.

 

#4: Some material is covered only in class, is not in the textbook, and may not have any homework problems on it. If you miss class, you may miss content that you are responsible to know. If you have an unavoidable absence, be sure to get the notes and any announcements from a classmate.

 

#5: There will be test questions that don’t look “just like the homework.” In college, you are expected to focus on learning the concepts, not just memorizing how to do certain types of problems. These concepts can – and will – appear in very different forms on tests and quizzes.

 

#6: At times you will be expected to be able to explain why a problem is done a certain way in addition to being expected to do the problem. As you work on problems in class and on homework, don’t be satisfied with getting the correct answer; ask yourself why that method is logical, and how you could explain that logic to someone else.

 

#7: Most importantly, you are responsible for your own learning. If you attend class faithfully, get the notes and announcements if you have an unavoidable absence, read the text, do the homework and question yourself (as in #6), and still don’t understand something, it is up to you to get the extra help you need. Visit the instructor during office hours or make a special appointment to ask questions, form a study group, etc. There are many resources and people willing and happy to help, but you need to take the initiative and seek out the help you need.

 

Good luck on a happy and successful semester!

Commitment to Inclusive Excellence:  WSU recognizes that our individual differences can deepen our understanding of one another and the world around us, rather than divide us. In this class, people of all ethnicities, genders, religions, ages, sexual orientations, disabilities, socioeconomic backgrounds, regions, and nationalities are strongly encouraged to share their rich array of perspectives and experiences.  If you feel your differences may in some way isolate you from WSU’s community or if you have a need of any specific accommodations, please speak with the instructor early in the semester about your concerns and what we can do together to help you become an active and engaged member of our class and community. 

 

Campus Resources (Short version):

 

Campus Resources (Long version):

 

The Standard Disclaimer applies.