MATH 406      -        Introduction to Number Theory       -       Fall, 2006

MWF 11-11:50, Math 0407

Prof. Herb

Office: 1111 Math Bldg.

Phone: (301) 405-5056

E-Mail: rah@math.umd.edu

Office Hours: MWF 10-11 or by appointment
 
Text: A Friendly Introduction to Number Theory, 3rd edition, by J.H. Silverman

DESCRIPTION:  We will Chapters 1-18 and 20-25.   
 
Grading: Grades will be based on scores for three midterms, homework and/or quizzes, and a  final exam. 

Exam Dates and Chapters Covered:

Hour Exam 1:   Friday, October 6 -  Covers chapters 1-9.  (Definite now)

Hour Exam  2:  Friday, November 3  -  Covers chapters 10-17.  (Definite now)

Hour Exam 3:  Friday, December 8  - Covers chapters 20-25.   (Definite now)

Final Exam:   Saturday, Dec. 16, 8-10 am  (in regular classroom, MATH 0303)

 The point totals are:

Homework 100

Hour Exams 300

Final 200


Total 600

  Makeup exams will only be given for legitimate, documented absences. Give me advance notification if you will need a makeup exam because of participation in religious observances or official university business.   If you have a documented disability that will require accomodations, please notify me as soon as possible.  

Each day after class I will update the information below to include which chapters I covered, homework assigned, and
other announcements.

Sections Covered and Homework Assigned

W 8/30 -  I covered Chapter 1 and started Chapter 2.     Homework problems assigned are:
1.2, 1.3, 2.2, 2.6.    They are due Wed. Sept. 6.
F 9/1 -  I finished Chapter 2.
W 9/6 - I covered Chapter 3 and started Chapter 5.   (Chapter 4 is historical.   You are welcome to read it, but I won't cover it in class or on exams.)    The second homework assignment is problems 3.2, 5.1, 5.4.   It is due Monday, Sept. 11.  
F 9/8  - I finished Chapter 5 and started Chapter 6.
M 9/11 -  I finished Chp. 6, and assigned problems 6.1a, 6.2ab, 6.5.   They (together with some problems from Chp 7) are due next Monday, 9/18.
W 9/13 - I talked about mathematical induction and started Chapter 7.   I added 7.3d to the list of problems due 9/18.
F 9/15 - I continued with Chp. 7.    The complete HW due 9/18 is 6.1a, 6.2ab, 6.5,7.3d.
M 9/18 - I finished Chp. 7 and started Chp. 8.   Homework due 9/25 is 7.1, 7.5, 8.1, 8.3ace.
W 9/20 - Students presented solutions to problems from HW 2.  I continued with Chp. 8.
F 9/22 - I almost finished Chp. 8.  Monday I will finish Chp. 8 and go on to Chp. 9.  
Reminder - The first midterm is Friday, Oct. 6.  The exam will have some computational problems, some proofs, and some true/false.   Computational problems will be similar to 5.1, 5.4, 6.1, 6.2, 6.5, 8.3, 8.5, 8.6, 9.1, 9.4.   Proofs will be similar to
2.2, 7.1, 7.2, 7.3, 8.1, 8.2, 8.4.    You can use a simple calculator for the exam (4 function or scientific).   No programable or graphing calculators are allowed.  
M 9/25 - I finished Chp. 8.  Homework due 10/2 is 8.4a, 8.5ac, 8.6a,  9.1.
W 9/27 - I finished Chp. 9.  Friday students will present solutions to problems from HW 3 and I will start Chp. 10.
F 9/29 - I started Chp. 10.
M 10/2 - I answered questions and finished Chp. 10.  I handed back HW 4 and collected HW 5. 
W 10/4 - Review for Exam 1.   If you have further questions, I will be in my office today 9-11 and  1-2, Thursday 9-12, and Friday 9-11.
F 10/5 - Exam 1 - Covers chapters 1-9 with emphasis on 5-9.    See 9/22 for more information.
M 10/9 - I handed back Exam 1.   The exam and solutions are posted on testbank.  I started Chp. 11.  Next homework (HW 6, due Monday, 10/16) is: 10.3a, 11.1, 11.3, 11.5ab.
W 10/11 - I finished Chp. 11 and started Chp. 12.
F 10/13 - I finished Chp. 12 and started Chp. 13.
M 10/16 - I finished Chp. 13 and Chp. 14, and started Chp. 15.  Next homework (HW 7, due Monday, 10/23) is: 12.2a, 13.1, 14.1, 15.3ab.
W 10/18 - I continued with Chp. 15. 
F 10/20 - I finished Chp. 15 and started Chp. 16.   The next midterm is Friday, Nov. 3.   It will cover Chps 10-17.
M 10/23 - I finished Chp. 16 and started Chp. 17.  Next homework (HW 8, due Monday, 10/30) is 15.5, 15.7ac, 16.1a, 17.2a.
W 10/25 - I continued with Chp. 17.
F 10/27 - I finished Chp. 17 and started Chp. 18.   I will hold extra office hours next week:  Tu 9-10, Th 1-2, F 9-11.
I also recommended the following practice problems from Testbank.   They are on Exam 1 and Exam 2, Summer II, 2005, K. Truman, and are Exam 1: 3,4,6,7,8,9, and Exam 2: 4a.
M 10/30 - I finished Chp 18.
W 11/1 - Review
F 11/3 - Exam 2
M 11/6 - I handed back the exams.   The exam with solutions is posted on Testbank.   I  covered Chp. 20 and started Chp. 21.   The next homework (HW 9, due Monday 11/13) is 20.2, 21.2, 21.4, 21.8.
W 11/8 - I continued with Chp. 21.
F 11/10 - I almost finished Chp. 21.
M 11/13 - I finished Chp. 21 and started Chp. 22.    The next homework (HW 10, due Monday 11/20) is 22.1, 22.2, 22.4, 23.1.
W 11/15 - I finished Chp. 22 and started Chp. 23.
F 11/17 - I finished Chp. 23 and started Chp. 24.
M 11/20 - I finished Chp. 24.   The next homework (HW 11, due Monday 11/27) is 23.3 and 24.1 (2 problems only).
W 11/22 - I reviewed properties of quadratic residues and discussed existence of solutions for general quadratic congruences mod p.
M 11/27 - I started Chp. 25.    The last homework (HW 12, due Monday 12/4) is 25.1, 25.2, 25.4, 25.6.
W 11/29 - I finished Chp. 25.    The third midterm will be Friday Dec. 8 and will cover Chapters 20-25.
F 12/1 - I started discussion of generalization of Chps. 21 and 22 to working modulo a number which isn't prime.
I announced that HW 12, due Monday 12/4, is due by NOON.    Exam 3 will have the usual mix of theory, computational problems, and proofs.    I recommend that you review all assigned HW from Chp 20-25 plus  21.6,  22.3,  24.6.
M 12/3 - Students presented problems from HW 10 and I continued discussion of generalization of Chps. 21 and 22.
W 12/5 - Students presented problems from HW 11 and I went over problems from HW 12.  
Important things to know for exam on Friday:
Chp. 20 - idea of multiplicative function
Chp. 21 - How to compute e_p(a), find primitive roots plus properties of e_p(a) and primitive roots.
Chp. 22 - How to compute I(a), use table of I(a) to solve congruences, use index plus theorem on linear congruences to determine whether equations have solutions.   Be sure to review Theorem 8.1.   We used it alot for this.
Chp. 23 - definition on QR and NR and Legendre symbols
Chp. 24 - know how to use QR's to determine if quadratic congruence has solutions.
Chp. 25 - know how to compute Legendre symbols.
More generally, you are responsible for knowing theorems, knowing how to computations and proofs similar to those in assigned HW problems.    I will have office hours on Thursday, 1-3, and on Friday, 9-11.
M 12/11 - I handed back Exam 3 and reviewed for final.  The final covers the same basic material as the hour exams,
that is chapters 5-17 and 20-25.   The final is 8-10 am on Saturday, Dec. 16 in the normal classroom.  I will have office hours Wed. 11-12 and Friday, 11-12 and 1-3.   If none of these times are good for you, e-mail me to set up an appointment.