MATH 310 Number Theory
Syllabus for Spring 2009

Monday, Wednesday, Friday, 11:00 – 11:50am

326 Gildemeister Hall

Prerequisite: Passing grades in MATH165 and MATH210.

Texts:   “Elementary Number Theory” by Charles Vanden Eynden
“Introduction to Number Theory” by Peter Schumer. This book is out of print, see the instructor for a photocopied version.
“Number Theory for Mathematical Contests” by David A. Santos. This book is here.

Calculator:     No graphing calculators are allowed on tests and quizzes. You are allowed to use a scientific calculator or any other lesser calculator. You may not use your cell phone, PDA, or laptop as your calculator.

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

Instructor: Dr. Eric Errthum                          Office: 124A Gildemeister Hall

Winona Email Username: eerrthum             Office Phone: 474-5775

Office Hours:  See schedule on my home page.

Grading:         Quizzes (9 @ 20 points each, drop lowest)          160 points-------- 17.78%
                        Homework (scaled as needed)                              131 points-------- 14.55%
                        Homework Day Participation                                 45 points--------- 5.00%
                        Midterms (3 @ 100 points)                                   300 points-------- 33.33%
                        Orals (3 @ 38 points)                                            114 points-------- 12.67%
                        Final                                                                      150 points-------- 16.67%
                                                                                                  --------
                                                                                                      900 points total

Grades:  A = 90% (810 pts), B = 80% (720 pts), C = 70% (630 pts), D = 60% (540 pts)

Quizzes:    We will have nine short (~13 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 almost every day and will be collected the class period after Homework Day (see problem numbers and schedule below).

Homework Day:  About once every three or four class periods, we will have Homework Day. During that class period you will be expected to write the solution to a homework problem on the board to be reviewed and discussed by the rest of the class. Make sure you come prepared as time will be limited. The problem numbers can be found in the schedule below.

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 Thursday, May 7, 8 – 10am.

Orals:        During the class period after each exam, we will be holding oral exams. Each student will have 5 minutes to present the solution to a problem on the board. Oral exam problems will be handed out at the written exam and assigned by lot on the oral exam day. Make sure you come prepared as time will be limited. The correctness of your problem will be graded out of 30 points. An additional 8 points will be awarded based on your evaluation of your fellow students’ solutions. Group work is allowed outside of class.

Extra Credit: Below the schedule of events you can find a list of extra credit problems. Each problem is worth 1 point in the course. 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. 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 6 extra credit problems per homework period. 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 and with the date. Extra credit work will not be returned, but the score earned will be included in your mid-semester grades and indicated on D2L.

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. There are no make-up oral exams. 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.

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

Monday

Wednesday

Friday

1/12

Introductions

1.1
GCD & LCM

(PS: 22 – 23, 28)
HW: pg 16: 6, 16, 22, 24, 26
1.2
The Division Algorithm
(PS: 12 – 13)

HW: pg 21: 2, 4, 18, 22, 24, 26, 32, 36

1.3
The Euclidean Algorithm
(PS: 23 – 28)

HW: pg 26: 2, 4, 12, 14, 20, 28

1/19

NO CLASS
Martin Luther King Day

Homework Day

pg 16: 22, 24, 26

pg 21: 22, 32, 36

pg 26: 14, 28

(Brittany off)

Homework Due

Quiz 1.1 – 1.3

1.4
Linear Combinations

HW: pg 31: 2, 4, 6, 10, 16, 22, 24, 28, 36

1/26

1.5
Congruences

(PS: 13 – 15)

HW: pg 36: Evens 2 – 22, 28, 32, 44, 46

1.6
Mathematical Induction
(PS: 7 – 10)

HW: pg 43: 20, 26, 32, 44, 50, 62

Homework Day

pg 31: 28, 36

pg 36: 44, 46

pg 43: 26, 44, 50, 62

(Dan off)

2/2

Homework Due

Quiz 1.4 – 1.6

2.1
Prime Factorization
(PS: 37 – 38)

HW: pg 50: 6, 8, 12, 20, 24, 28

2.2
The Fundamental Theorem of Arithmetic
(PS: 38 – 39)

HW: pg 54: 2, 4, 14, 20, 22

2.3
The Importance of Unique Factorizations

HW: pg 57: 6, 8, 12, 18, 22, 28, 34, 36, 42

Homework Day

pg 50: 28

pg 54: 14, 20, 22

pg 57: 18, 28, 36, 42

(Trisha off)

2/9

Homework Due

Quiz 2.1 – 2.3

2.4
Prime Power Factorizations

HW: pg 63: 2, 4, 10, 16, 18, 28, 32, 42, 48

2.5
The Set of Primes is Infinite
(PS: 39 – 40)

HW: pg 67: 10, 16

2.6
A Formula for t(n)

HW: pg 73: 2, 4, 10, 18, 32, 36, 38, 44, 46, 52

Homework Day

pg 63: 42, 48

pg 67: 10, 16

pg 73: 36, 38, 44, 52

(Zach off)

2/16

Homework Due

Quiz 2.4 – 2.6

Chapters 1 & 2 Review/Activity

Exam I

Orals I

2/23

3.1
The Sum of Divisors

HW: pg 81: 2, 6, 10, 14, 18, 22, 26, 30, 36, 38, 40, 44

3.2
Multiplicative Functions
(PS: 57 – 63)

HW: pg 88: 8, 12, 14, 16, 18, 26, 28

3.3 & 3.4
Perfect Numbers & Mersenne Primes
(PS: 67 – 72)

HW: pg 92: 26, 30, 32

3/2

SPRING BREAK

3/9

Homework Day

pg 81: 38, 40, 44

pg 88: 18, 28

pg 92: 26, 30, 32

(Andy off)

Homework Due

Quiz 3.1 – 3.4

3.5
The Euler Phi Function

HW: pg 105: 22, 24, 28, 34, 36, 40, 46, 50

3.6
The Möbius Inversion Formula
(PS: 63 – 66)

HW: pg 113: 10, 12, 16, 18, 20, 30

3/16

Homework Day

pg 105: 34, 36, 40, 50

pg 113: 16, 18, 20, 30

(Briant off)

Homework Due

Quiz 3.5 – 3.6

4.1
Solving Linear Congruences

(PS: 31 – 33)

HW: pg 122: Evens 26 – 34 (find all solutions)

4.2
The Chinese Remainder Theorem
(PS: 33 – 36)

HW: pg 129: 2, 4, 10, 20, 28

3/23

4.3
The Theorems of Fermat and Euler
(PS: 45 – 51)

HW: pg 138: 6, 8, 14, 18, 22, 28, 32, 36, 44

4.5
Public-Key Cryptography
(PS: 193 – 195)

Homework Day

pg 122: 32, 34

pg 129: 20, 28

pg 138: 28, 32, 36, 44

(Alanna off)

Homework Due

Quiz 4.1 – 4.3, 4.5

Chapters 3 & 4 Review/Activity

3/30

Exam II

Orals II

5.1 & 5.2
 Solving Polynomial Congruences
using Chinese Remainder Theorem
and Lifting

HW: pg 170: Evens 8 – 26 (find all solutions)

4/6

5.3
Quadratic Residues
and the Quadratic Formula
(PS: 82 – 87)

HW: pg 176: Evens 2 – 18, 32 – 36, 40, 46

5.4
Quadratic Reciprocity
(PS: 87 – 96)

HW: pg 184: 2, 6, 10, 14, 18, 22, 28, 30, 50

NO CLASS
Student Spring Break Day

4/13

Homework Day

pg 170: 20

pg 176: 36, 40, 46

pg 184: 18, 28, 30, 50

(Michelle off)

Homework Due

Quiz 5.1 – 5.4

6.2
Finite Continued Fractions
(PS: 125 – 133)

HW: pg 209: 6, 8, 10, 16, 18, 20, 22, 28, 34

6.3
Infinite Continued Fractions
(PS: 138 – 144)

HW: pg 219: 2, 8, 10, 12, 16, 18, 22, 24, 26, 28

4/20

Best Approximation Theorem

(PS: 145 – 152)

HW: Handout

Homework Day

pg 209: 34

pg 219: 16, 22, 24, 26, 28

Handout: 3, 7

(Michael off)

Homework Due

Quiz 6.1 – 6.3

Chapters 5 & 6 Review/Activity

4/27

Exam III

Orals III

Final Review

 

Final Exam

Thursday, May 7
8:00 – 10:00am

 

 

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 1 point in the course. 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. 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 6 extra credit problems per homework period. 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. Extra credit work will not be returned, but the score earned will be indicated on D2L.

 

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.