Math 278 - Spring 2011
Number Theory

Professor: Erika L.C. King
Email: eking@hws.edu
Office: Lansing 304
Phone: (315) 781-3355
Home Page

Office Hours: and by appointment
Class Schedule: held TTh 10:20-11:45 in Napier 202
Course Syllabus
Proof Writing and Presentation Tips
Course Grade Scale

Colloquium Website

MAA NumberADay Website

READING/EXAM WEEK

Review Session: Friday, May 6th 11:00am-NOON in Napier 202.

Office Hours:

• Wednesday, May 4: 1:00pm-3:00pm
• Thursday, May 5: 11:00am-NOON and 2:30pm-4:00pm
• Friday, May 6: 1:00pm-2:30pm
• By appointment

In-Class Final Exam: Sunday, May 8th 8:30am-11:30am in Napier 202.

Take-Home Final Exam Due: Sunday, May 8th at 8:30am.

Thanks for a great class! Have a wonderful summer! Keep in touch!

WEEK 15

Reading Assignment for class Tuesday, May 3:

• Review the material in Chapters 1-6 (pages 7-81), particularly the material from the presentations. Try exercises and questions from the project sections that were not included in the presentations. Bring thoughts and questions, and be ready to answer questions on your project section if others have questions. We will spend class going over exam 2, talking about end of the semester details, addressing questions you bring, working on some practice problems, and doing evaluations.

Collected Homework (Due Tuesday, May 3 at 4:00pm):

• Complete the problems on this handout.
• You may also resubmit the Notebook problems that were due April 6 or April 20. Note that you may turn in your resubmissions on any day of the week up to one month after they were originally due. Remember that you must turn in your previous draft(s) with any resubmission. Please do not write on your previous submissions after they have been returned.

WEEK 14

Reading Assignment for class Tuesday, April 26:

• Work on preparing your projects. We will see presentations on April 26 and 28. If you would like to make overheads or copies for the class, let me know if you need assistance (this is not necessary, and might work more for some presenations than others). If you would like to use some sort of computer presentation (like Power Point), let me know way in advance so that I can try to figure out how to set things up (if possible) in our classroom. Have fun!
• You should read the material to be presented in each class so that you are ready to ask questions and learn the material. There will be at least one question on the final pertaining to the information given in these presentations. Thus for this Tuesday you should read about Lagrange's Theorem and about Primitive Roots, which encompasses pages 73-76. It is not expected that you necessarily work through exercises or proofs before class, but you should familiarize yourself with the material.

Remember the Extension for the Collected Homework due Wednesday, April 20, ends at 4:00pm on April 27. You may also resubmit the Notebook problems that were due March 28 (last chance for this one) or April 6. Note that you may turn in your resubmissions on any day of the week up to one month after they were originally due. Remember that you must turn in your previous draft(s) with any resubmission. Please do not write on your previous submissions after they have been returned.

Reading Assignment for class Thursday, April 28:

• Work on preparing your projects. We will see our last set of presentations on Thursday. If you would like to make overheads or copies for the class, let me know if you need assistance (this is not necessary, and might work more for some presenations than others). If you would like to use some sort of computer presentation (like Power Point), let me know way in advance so that I can try to figure out how to set things up (if possible) in our classroom. Have fun!
• You should read the material to be presented in class so that you are ready to ask questions and learn the material. There will be at least one question on the final pertaining to the information given in these presentations. Thus for this Thursday you should read about Euler's phi-function and sums of divisors and about how Euler's phi-function is multiplicative, which encompasses pages 77-81. It is not expected that you necessarily work through exercises or proofs before class, but you should familiarize yourself with the material.

Remember that your write up for your Project is due Friday, April 29 by 4:00pm.

WEEK 13

Reading Assignment for class Tuesday, April 19:

• Read pages 56-60 of Chapter 4 (you can skip the section entitled "An alternative route to Fermat's Little Theorem"). Prove Theorems 4.15, 4.16, 4.17, 4.31 and 4.32. Be ready to claim which you are ready to present at the beginning of class. Please feel free to come and discuss them with me.
• Remember that a reading assignment includes working through all exercises, examples and questions in the reading as well proving the specified Theorems and Lemmas so that you are ready to ask questions about, discuss and present the material.
• Work on preparing your projects. We will see presentations on April 21, 26 and 28. If you would like to make overheads or copies for the class, let me know if you need assistance (this is not necessary, and might work more for some presenations than others). If you would like to use some sort of computer presentation (like Power Point), let me know way in advance so that I can try to figure out how to set things up (if possible) in our classroom. Have fun!

Collected Homework (Due Wednesday, April 20 at 4:00pm, extension until April 27 if needed):

• Complete the problems on this handout.
• Notebook Problems: This week's notebook problem are also on this handout. (Remember: (1) Turn these in on a separate piece of paper from your other homework, (2) notebook problems must be done on your own, and (3) you should give extra attention to form for these proofs.)
• You may also resubmit the Notebook problems that were due March 21 (this one is due on April 20th for last resubmission - no extension), March 28 or April 6. Note that you may turn in your resubmissions on any day of the week up to one month after they were originally due. Remember that you must turn in your previous draft(s) with any resubmission. Please do not write on your previous submissions after they have been returned.

Reading Assignment for class Thursday, April 21:

• Work on any exercises you did not yet complete in the sections on Fermat's Little Theorem and Euler's Theorem (pages 56-60).
• Work on preparing your projects. We will see presentations on April 21, 26 and 28. If you would like to make overheads or copies for the class, let me know if you need assistance (this is not necessary, and might work more for some presenations than others). If you would like to use some sort of computer presentation (like Power Point), let me know way in advance so that I can try to figure out how to set things up (if possible) in our classroom. Have fun!
• You should read the material to be presented in each class so that you are ready to ask questions and learn the material. There will be at least one question on the final pertaining to the information given in these presentations. Thus for this Thursday you should read about Wilson's Theorem and about Public Key Cryptography, which encompasses pages 61-71. It is not expected that you work through exercises or proofs before class, but you should familiarize yourself with the material.

WEEK 12

Rememember our second exam will be Sunday, April 10th at 7:00pm in Napier 101.

Since we have an exam on Sunday, there will be no homework assignment due on Wednesday of this week. This will be a great time to make sure you are ready to present proofs and exercises in class! Note that you are also welcome to turn in Notebook resubmissions, though none of the remaining problems have a final deadline of this week. Also you should begin work on your projects.

Due to committee meetings, I will need to start my office hours this Wednesday a little later. They will be 2:30-4:00. It is possible that I will be done earlier and able to start my office hours earlier, but I will not know until then. PLEASE let me know if you have questions and cannot make those hours.

Reading Assignment for class Tuesday, April 12:

• Review our work on the Chinese Remainder Theorem. Prove the uniqueness part. Then go back to Exercises 3.25 and 3.26 to see if you can apply the technique we constructed in the proof of the Chinese Remainder Theorem.
• Read pages 53-55 of Chapter 4. Prove Theorems 4.6, 4.8 and 4.9. Really work on getting your proofs done! and refined to present in class. Please feel free to come and discuss them with me.
• Remember that a reading assignment includes working through all exercises, examples and questions in the reading as well proving the specified Theorems and Lemmas so that you are ready to ask questions about, discuss and present the material.

Reading Assignment for class Thursday, April 14:

• Read pages 55-56 of Chapter 4. Prove Theorems 4.8, 4.9, 4.10, 4.13 and 4.14. Really work on getting your proofs done! and refined to present in class. Please feel free to come and discuss them with me.
• Remember that a reading assignment includes working through all exercises, examples and questions in the reading as well proving the specified Theorems and Lemmas so that you are ready to ask questions about, discuss and present the material.

WEEK 11

Rememember our second exam will be Sunday, April 10th at 7:00pm in Napier 101.

Due to a committee meeting, I will need to start my office hours this Wednesday a little later. They will be 3:00-4:30. It is possible that I will be done earlier and able to start my office hours earlier, but I will not know until then. Please let me know if you have questions and cannot make those hours.

Reading Assignment for class Tuesday, April 5:

• Great work in class on Thursday! Let's see repeat performances!
• Reread/read pages 49-52 of Chapter 3, and start reading Chapter 4. Prove Theorems 3.24, 3.27, 3.28 and 3.29. Really work on getting your proofs done! and refined to present in class. Please feel free to come and discuss them with me.
• Remember that a reading assignment includes working through all exercises, examples and questions in the reading as well proving the specified Theorems and Lemmas so that you are ready to ask questions about, discuss and present the material.

Collected Homework (Due Wednesday, April 6 at 4:00pm):

• Complete the problems on this handout.
• Notebook Problems: This week's notebook problem are also on this handout. (Remember: (1) Turn these in on a separate piece of paper from your other homework, (2) notebook problems must be done on your own, and (3) you should give extra attention to form for these proofs.)
• You may also resubmit the Notebook problems that were due March 7 (last opportunity for this one), March 21 or March 28. Note that you may turn in your resubmissions on any day of the week up to one month after they were originally due. Remember that you must turn in your previous draft(s) with any resubmission. Please do not write on your previous submissions after they have been returned.

Reading Assignment for class Thursday, April 7:

• Reread/read pages 49-52 of Chapter 3, and pages 53-55 of Chapter 4. Prove Theorems 3.27, 3.28, 3.29 and 4.6. Really work on getting your proofs done! and refined to present in class. Please feel free to come and discuss them with me.
• Remember that a reading assignment includes working through all exercises, examples and questions in the reading as well proving the specified Theorems and Lemmas so that you are ready to ask questions about, discuss and present the material.

Rememember our second exam will be Sunday, April 10th at 7:00pm in Napier 101. Since we have an exam on Sunday, there will be no homework assignment due on Wednesday of next week. This will be a great time to make sure you are ready to present proofs and exercises in class!

WEEK 10

Due to various committee meetings and the colloquium, I will need to change my office hours this Friday. They will be NOON-1:30. Please let me know if you have questions and cannot make those hours.

Quiz 4 will be on Thursday, March 31st. It will cover material beginning on page 35 through what we cover in Tuesday's class.

Collected Homework (Due Monday, March 28 at 4:00pm):

• Complete the problems on this handout.
• Notebook Problem: This week's notebook problem are also on this handout. (Remember: (1) Turn these in on a separate piece of paper from your other homework, (2) notebook problems must be done on your own, and (3) you should give extra attention to form for these proofs.)
• You may also resubmit the Notebook problems that were due February 21 (last opportunity for this one), March 7 or March 21. Note that you may turn in your resubmissions on any day of the week up to one month after they were originally due. Remember that you must turn in your previous draft(s) with any resubmission. Please do not write on your previous submissions after they have been returned.

Reading Assignment for class Tuesday, March 29:

• Reread/read pages 45-49 of Chapter 3. I hope to see several proofs presented on Tuesday! :-) Prove Theorems 3.14, 3.16, 3.17, and 3.20, and Corollary 3.9. Really work on getting your proofs done! and refined to present in class. Please feel free to come and discuss them with me.
• Remember that a reading assignment includes working through all exercises, examples and questions in the reading as well proving the specified Theorems and Lemmas so that you are ready to ask questions about, discuss and present the material.

Reading Assignment for class Thursday, March 31:

• Fill in the details for the proof of Theorem 3.17 presented at the end of class. The group(s) that worked on that proof should try to put it on the center board behind the screen before class starts. The group(s) that worked on Theorem 3.16 should be prepared to present a proof after the quiz.
• Reread/read pages 47-49 of Chapter 3. Prove Theorems 3.16, 3.17, 3.20 and 3.24. Really work on getting your proofs done! and refined to present in class. Please feel free to come and discuss them with me.
• Remember that a reading assignment includes working through all exercises, examples and questions in the reading as well proving the specified Theorems and Lemmas so that you are ready to ask questions about, discuss and present the material.

WEEK 9

Have a great spring break!!!

Due to various committee meetings and the colloquium, I will need to change my office hours this Friday. They will be NOON-1:30. Please let me know if you have questions and cannot make those hours.

Collected Homework (Due Monday, March 21 at 4:00pm):

• Complete the problems on this handout.
• Notebook Problems: This week's notebook problems are also on this handout. (Remember: (1) Turn these in on a separate piece of paper from your other homework, (2) notebook problems must be done on your own, and (3) you should give extra attention to form for these proofs.)
• You may also resubmit the Notebook problems that were due February 14 (last opportunity for this one), February 21 or March 7. Note that you may turn in your resubmissions on any day of the week up to one month after they were originally due. Remember that you must turn in your previous draft(s) with any resubmission. Please do not write on your previous submissions after they have been returned.

Reading Assignment for class Tuesday, March 22:

• Read pages 43-47 of Chapter 3. Now we return to congruences! Don't forget your results from Chapter 1. Prove Theorems 3.8 and 3.14. Be sure to work through all the Questions as well. Really work on getting your proofs refined to present in class. Please feel free to come and discuss them with me.
• Remember that a reading assignment includes working through all exercises, examples and questions in the reading as well proving the specified Theorems and Lemmas so that you are ready to ask questions about, discuss and present the material.

Reading Assignment for class Thursday, March 24:

• Reread/read pages 44-48 of Chapter 3. Prove Theorems 3.8, 3.14, 3.16 and 3.17, and Corollary 3.9. Really work on getting your proofs done! and refined to present in class. Please feel free to come and discuss them with me.
• Remember that a reading assignment includes working through all exercises, examples and questions in the reading as well proving the specified Theorems and Lemmas so that you are ready to ask questions about, discuss and present the material.

EXAM BONUS (Due Friday, March 25 at 3:00pm):

• Complete the bonus problem from exam 1. If you choose to do this assignment you should (1) complete it entirely on your own except for possible discussions with me, (2) complete problem 3 on the exam and show it to me (I will not be collecting it, but I want to see that you reworked it and wrote out the details before I will accept your bonus problem.), and (3) give extra attention to form for this proof (I do grade bonus a bit tougher than regular problems). You may earn up to five points towards your exam grade for this.

WEEK 8

Quiz 3 will be on Thursday, March 10th. It will cover material beginning on page 27 through what we cover in Tuesday's class.

Collected Homework (Due Monday, March 7 at 4:00pm):

• Complete the problems on this handout.
• Notebook Problems: This week's notebook problems are also on this handout. (Remember: (1) Turn these in on a separate piece of paper from your other homework, (2) notebook problems must be done on your own, and (3) you should give extra attention to form for these proofs.)
• You may also resubmit the Notebook problems that were due February 7 (this is the last chance for this one), February 14 or February 21. Note that you may turn in your resubmissions on any day of the week up to one month after they were originally due. Remember that you must turn in your previous draft(s) with any resubmission. Please do not write on your previous submissions after they have been returned.

Reading Assignment for class Tuesday, March 8:

• Check out the NumberADay website set up by the MAA. Each day they feature a different number and give you facts about it. You might find out something really cool! I will put a link at the top of our website as well so that you can have an easy way to click on it every day. :-)
• After you review Nick's cool proof for Theorem 2.33, work through the details of the alternate proof that we discussed to make sure that the alternate also makes sense. Although Nick's is more elegant, the ideas in the second proof might also be helpful in other work that you do.
• Write out a complete proof of Theorem 2.34. There were lots of good ideas and decent proofs on the board when we ended class on Thursday, but I think you could write an even better proof based on these. At any rate, it would be worthwhile to go through the details and make sure it all makes sense.
• Read/reread pages 35-42 of Chapter 2. Prove or revise your proofs to Theorems 2.35 (there are several ways to do this and I would love to see more than one from the class!), 2.37 and 2.38. Really work on getting your proofs refined to present in class. Please feel free to come and discuss them with me.
• Remember that a reading assignment includes working through all exercises, examples and questions in the reading as well proving/solving the specified Theorems and Lemmas so that you are ready to ask questions about, discuss and present the material.

Reading Assignment for class Thursday, March 10:

• Read/reread pages 35-42 of Chapter 2. Prove or revise your proof of Theorem 2.38. Note that Exercise 2.40 asks you to do some research on the internet. Bring some ideas about arithmetic progressions to class and be ready to discuss them. Be sure you have worked through all the exercises. Start reading Chapter 3.
• Remember that a reading assignment includes working through all exercises, examples and questions in the reading as well proving/solving the specified Theorems and Lemmas so that you are ready to ask questions about, discuss and present the material.

BONUS (Due Friday, March 11 at 3:00pm):

• Redo your proof of Theorem 1.55 or 1.57, whichever you earned a lower score on (your choice if you earned the same on both problems). If you choose to do this assignment you should (1) complete it entirely on your own except for possible discussions with me, (2) turn in your original proof with your redo, and (3) give extra attention to form for these proofs (I will grade them a bit tougher since they are bonus now). You may earn up to four points towards your homework grade for this redo regardless of the number of points you originally missed.

WEEK 7

Rememember our first exam will be Sunday, February 27th at 4:00pm in Napier 201.

Since we have an exam on Sunday night, you do not have a collected assignment due on Monday. Concentrate on preparing for class on Tuesday. Also remember that you can resubmit Notebook problems. The last day I will accept a resubmission for the problem originally due on January 31st is Tuesday.

Reading Assignment for class Tuesday, March 1:

• Read/reread pages 31-34 of Chapter 2. Prove or revise your proofs to Theorems 2.9, 2.18, 2.19 and 2.20. Really work on getting your proofs refined to present in class. Please feel free to come and discuss them with me.
• Remember that a reading assignment includes working through all exercises, examples and questions in the reading as well proving/solving the specified Theorems and Lemmas so that you are ready to ask questions about, discuss and present the material.

Reading Assignment for class Thursday, March 3:

• Read/reread pages 33-37 of Chapter 2. Revise your proof of Theorem 2.20. Prove Theorems 2.32-2.35. If you have time, also tackle 2.37. Really work on getting your proofs refined to present in class. Please feel free to come and discuss them with me.
• Remember that a reading assignment includes working through all exercises, examples and questions in the reading as well proving/solving the specified Theorems and Lemmas so that you are ready to ask questions about, discuss and present the material.

WEEK 6

Rememember our first exam will be Sunday, February 27th at 4:00pm in Napier 201.

Collected Homework (Due Monday, February 21 at 4:00pm):

• Complete the problems on this handout.
• Notebook Problems: This week's notebook problems are also on this handout. (Remember: (1) Turn these in on a separate piece of paper from your other homework, (2) notebook problems must be done on your own, and (3) you should give extra attention to form for these proofs.)
• You may also resubmit the Notebook problems that were due January 31, February 7, or February 14. Note that you may turn in your resubmissions on any day of the week up to one month after they were originally due. Remember that you must turn in your previous draft(s) with any resubmission. Please do not write on your previous submissions after they have been returned.

Reading Assignment for class Tuesday, February 22:

• Consider the set E of positive even integers. (a) Is E closed under multiplication? (b) Find the first six "prime" numbers and the first six composite numbers in E. (c) Show 180 has three distinct "prime" factorings. Be prepared to discuss this at the begining of Tuesday's class.
• Read pages 29-33 of Chapter 2. Prove Theorems 2.3, 2.7, 2.9, 2.18 and 2.19; and Lemma 2.8. Really work on getting your proofs refined to present in class. Please feel free to come and discuss them with me. From now on, assume that any Questions in the reading should be addressed the same way exercises and examples always are.
• Remember that a reading assignment includes working through all exercises, examples and QUESTIONS in the reading as well proving/solving the specified Theorems and Lemmas so that you are ready to ask questions about, discuss and present the material.

Reading Assignment for class Thursday, February 24:

• Now that you have a huge table of primes, experiment with evaluating pi(n) for larger numbers. Do you think you need to change your original conjecture or do these experiments confirm your previous ideas?
• What is Euclid's Lemma? I called the wrong theorem by this name Tuesday. Remind yourselves what it actually is! It is important!
• Reread pages 31-33 of Chapter 2. Jump ahead and prove Theorem 2.27, which might help in proving Lemma 2.8. Also prove or revise your proofs to Theorems 2.7, 2.9, 2.18 and 2.19; and Lemma 2.8. Really work on getting your proofs refined to present in class. Please feel free to come and discuss them with me. From now on, assume that any Questions in the reading should be addressed the same way exercises and examples always are.
• Remember that a reading assignment includes working through all exercises, examples and QUESTIONS in the reading as well proving/solving the specified Theorems and Lemmas so that you are ready to ask questions about, discuss and present the material.
• Part of class will be spent in review for the exam. Come to class prepared with questions.

WEEK 5

Quiz 2 will be on Thursday, February 17th. It will cover material beginning on page 16 through what we cover in Tuesday's class.

Collected Homework (Due Monday, February 14 at 4:00pm):

• Complete the problems on this handout.
• Notebook Problems: This week's notebook problems are also on this handout. (Remember: (1) Turn these in on a separate piece of paper from your other homework, (2) notebook problems must be done on your own, and (3) you should give extra attention to form for these proofs.)
• You may also resubmit the Notebook problems that were due January 31 or February 7. Note that you may turn in your resubmissions on any day of the week up to one month after they were originally due. Remember that you must turn in your previous draft(s) with any resubmission. Please do not write on your previous submissions after they have been returned.

Reading Assignment for class Tuesday, February 15:

• Reread pages 19-25 of Chapter 1. Prove Theorems 1.53, 1.57 and 1.58. Really work on getting your proofs refined to present in class. Please feel free to come and discuss them with me. Also address and be ready to present/discuss Questions 1.49 and 1.52.
• Start reading Chapter 2 (pages 27-29). Prove Theorems 2.1 and 2.3.
• Remember that a reading assignment includes working through all exercises and examples in the reading as well proving/solving the specified Theorems and Questions so that you are ready to ask questions about, discuss and present the material.

Reading Assignment for class Thursday, February 17:

• Remember to be ready with Exercises 1.50 and 1.54 at the beginning of class.
• If you haven't done Blank Paper Exercise 1.59 yet, you should.
• Read/reread pages 27-32 of Chapter 2. Prove Theorems 2.1, 2.3, 2.7 and 2.9; and Lemma 2.8. Work on all of them, but really try to get a nice, complete proof of at least one of them.
• Remember that a reading assignment includes working through all exercises and examples in the reading as well proving/solving the specified Theorems and Questions so that you are ready to ask questions about, discuss and present the material.

WEEK 4

Due to the department colloquium on Wednesday, my Wednesday office hours will be shortened to 2:00-3:30. Please let me know if you have questions.

Collected Homework (Due Monday, February 7 at 4:00pm):

• Complete the problems on this handout.
• Notebook Problem: Prove the following theorem, often called the Archimedean Property: If a and b are natural numbers, then there exists a natural number n such that na is greater than or equal to b. (Hint: You may want to use the Well Ordering Axiom.) (Remember: (1) Turn these in on a separate piece of paper from your other homework, (2) notebook problems must be done on your own, and (3) you should give extra attention to form for these proofs.)
• You may also resubmit the Notebook problem that was due Monday, January 31. Note that you may turn in your resubmissions on any day of the week up to one month after they were originally due. Remember that you must turn in your first draft with any resubmission.

Reading Assignment for class Tuesday, February 8:

• Read pages 18-21 of Chapter 1. Prove Theorems 1.33, 1.38, 1.40-1.43 and 1.45. Really work on getting your proofs refined to present in class. Please feel free to come and discuss them with me. Note that you may assume that any previous theorem has been proved when you attempt the next proof. Also address Questions 1.44 and 1.46. Remember that a reading assignment includes working through all exercises and examples in the reading as well proving/solving the specified Theorems and Questions so that you are ready to ask questions about, discuss and present the material.

Reading Assignment for class Thursday, February 10:

• Read pages 19-25 of Chapter 1. Prove Theorems 1.40, 1.43, 1.45 and 1.48. I would really love to see a proof of 1.40 from someone! Really work on getting your proofs refined to present in class. Please feel free to come and discuss them with me. Also address Questions 1.44, 1.46, 1.47 and 1.49. Remember that a reading assignment includes working through all exercises and examples in the reading as well proving/solving the specified Theorems and Questions so that you are ready to ask questions about, discuss and present the material.

WEEK 3

Quiz 1 will be on Thursday, February 3rd. It will cover material beginning on page 7 through what we cover in Tuesday's class.

Collected Homework (Due Monday, January 31 at 4:00pm):

• Complete the problems on this handout.
• Notebook Problem: Prove that for any integer x, one of the integers x, x+2, x+4 is divisible by 3. (Remember: (1) Turn these in on a separate piece of paper from your other homework, (2) notebook problems must be done on your own, and (3) you should give extra attention to form for these proofs.)

Reading Assignment for class Tuesday, February 1:

• Read pages 14-18 of Chapter 1. Prove Theorems 1.22 and 1.23 (note that 1.22 and 1.23 are the two parts of the theorem listed at the top of page 14), and also Theorems 1.26 and 1.27 (really two parts of the Division Algorithm Theorem), and Theorem 1.28. Note for 1.26 the hint suggests that you define q and then choose r from there, but it is possible to do it the other way around. Also address Questions 1.29 and 1.30. What are the authors getting at with these questions? Remember that a reading assignment includes working through all exercises and examples in the reading as well proving/solving the specified Theorems and Questions so that you are ready to ask questions about, discuss and present the material.

Reading Assignment for class Thursday, February 3:

• Read pages 16-20 of Chapter 1. Prove Theorems 1.27, 1.28, 1.33, 1.38 and 1.40. Note that you may assume that any previous theorem has been proved when you attempt the next proof. Also address Questions 1.29 and 1.30. Note that Exercises 1.35-1.37 are very important! They are asking you to develop the idea behind the Euclidean Algorithm. Try to write as explicit an algorithm as you can. Remember that a reading assignment includes working through all exercises and examples in the reading as well proving/solving the specified Theorems and Questions so that you are ready to ask questions about, discuss and present the material.

WEEK 2

Remember to keep your appointments!!!

Note that due to individual appointments, my open office hours on Wednesday are shortened this week. The revised hours for this week are: Monday 1:00-3:00, Wednesday 2:00-3:30pm, and Friday 1:30-3:00. If you cannot make these times and need to see me, please make an appointment.

Collected Homework (Due Monday, January 24 at 4:00pm):

• Write a proof of Theorem 1.3 and answer Question 1.4. Note that to justify your answers to Question 1.4, you will want to write proofs.
• There will be no Notebook Problem with this assignment. Remember that although you may discuss this assignment with others, your write up should be your own.

Reading Assignment for class Tuesday, January 25:

• Read the syllabus. Note there is a link to it at the top of our class website.
• Check that you have no conflict with the dates and times of the midterm exams. Speak with me ASAP if you do have conflicts.
• Familarize yourself with this website. Note that there is a link at the top of the page to our syllabus, should you lose the green one I handed out in class. The syllabus has a lot of vital information on it and you will likely want to refer back to it regularly. Also at the top of the page is a link to my grade scale. This will let you know what percentage you need to earn in order to obtain specific grades. In addition, there is a website I developed, Proof Writing and Presentation Tips, for my First Steps into Advanced Mathematics classes. It would be valuable for you to use this as a reference when you are preparing your homework and presentations for class.
• Work on Exercise 2 from the class handout before you start reading the text.
• Read the introduction chapter (pages 1-3), and pages 7-13 of Chapter 1. Address Question 1.5 and prove Theorems 1.6, 1.9-1.14 and 1.18. If you have time, feel free to keep going!!! Remember that a reading assignment includes working through all exercises and examples in the reading as well proving/solving the specified Theorems and Questions so that you are ready to ask questions about, discuss and present the material.

Reading Assignment for class Thursday, January 26:

• Read pages 12-17 of Chapter 1. Prove Theorems 1.18, 1.21, 1.22 and 1.23 (note that 1.22 and 1.23 are the two parts of the theorem listed at the top of page 14). Also address Questions 1.20, 1.29 and 1.30. If you have time, also tackle Theorems 1.26 and 1.27, which are the two parts of the Division Algorithm Theorem. Remember that a reading assignment includes working through all exercises and examples in the reading as well proving/solving the specified Theorems and Questions so that you are ready to ask questions about, discuss and present the material.

WEEK 1

Welcome to Number Theory!!!

Collected Homework (Due Friday, January 21st at 3:00pm):

• Write an autobiographical essay or poem as assigned on the syllabus. Sign up for an appointment to meet with me when you drop off your essay. The sign-up sheet should be on my bulletin board.

Last modified: Tuesday 3 May 15:27:30 EDT 2011