Course Information

Class Log and Announcements

• On Monday Nov. 23, I will have office hours during 11-12 in the morning, and will not be available in the afternoon.
• Nov. 20: 8.1 The order of an integer modulo n, started.
  homework: None
• This Friday Nov. 20, I teach 2--4pm. Hence I will not be in my office during those hours.
• Nov. 18: 7.4 Some properties of the phi-function; Identities involving the phi-function, finished.
  homework: sec 7.4 #3,6,11,13,15,16. Hand in:#11,15,16
• Nov. 16: 7.3 Euler`s Theorem, finished. 7.4 Some properties of the phi-function; Identities involving the phi-function, started.
  homework: sec 7.3 #4,5,8,11,12(c),13. Hand in:#4,8,12(c)
• Nov. 13: 7.3 Euler`s Theorem, started.
  homework: sec 7.3 #1. Hand in: #1. Add #13 of section 7.2 to hand in.
• Nov. 11: 7.2 Euler`s phi-function, finished.
  homework: sec 7.2 #1,4,10,11,13,20. Hand in: #10,20. If you want more challenging problem, try #17 and the conjecture stated there.
• Nov. 9: 7.2 Euler`s phi-function, started.
  homework: None
• Nov. 6: 6.3 The greatest integer function, finished.
  homework: sec 6.3 #10,12. Hand in: #2(b),6,12
• This Friday (6th), the office hours 2--4pm are canceled due to a faculty meeting of the department.
• Nov. 4: 6.3 The greatest integer function, continued.
  homework: sec 6.3 #2(a)(b)(c)(e) (Please read the lines between Definition 6.4 and Theorem 6.9 at P.117 in order to see how theta in (b) was introduced.) 3,6,7 (I am not sure which ones be handed in yet).
• Nov. 2: 6.3 The greatest integer function, started.
  homework: None.
• No homework due the coming Monday 11/2. However, start your homework on Section 6.2 early enough.
• Oct. 30: Hour exam 3
• Review for the hour exam 3
• Oct. 28: 6.2 The Mobius Inversion Formula, finished.
  homework: sec 6.2. Do #2,3,6,7,8. Hand in: #2,7,8
• Oct. 26: Practice exchanging double sums (and double products.)
  homework: None.
• You can hand-in Summary of Contents on Friday, the 30th, if you want.
• Oct. 23: 6.2 The Mobius Inversion Formula, started.
  homework: None.
• Oct. 21: 6.1 The sum and number of divisors, finished.
  homework: sec 6.1 Do #17,20,22,23. Hand in: #20,23
• Oct. 19: 6.1 The sum and number of divisors, continued.
  homework: sec 6.1 Do #6,7,8,10,11,14. Hand in: #6,10. You will realize that the homeworks in Chapter 6 and onwards are more challenging and takes longer time than before. So, from Chapter 6, I will give two lists, one for you to do and the other to hand-in. I want you to spend less time to write up the solutions. However, remember that you should do ALL the homework to do well on the exams as well as to be able to solve the homework problems to hand-in.
• No homework due the coming Monday 10/19. Enjoy your Fall break.
• Oct. 14: 6.1 The sum and number of divisors: More warm-ups and then the first two pages of the textbook.
  homework: None. Those who missed classed today, make sure you UNDERSTAND the two identities of tau and sigma in p.104 in the middle. It won`t help if you just memorize them.
• Oct. 12: 5.3 Wilson's theorem, finished. 6.1 The sum and number of divisors, started.
  homework: sec 5.3 #9,10,12
• The homework set due Oct. 12 consists of the homeworks assigned this week -- 10/5, 10/7, and 10/9.
• Oct. 9: 5.3 Wilson's theorem
  homework: sec 5.3 #1--6
• Oct. 7: 5.2 Fermat's theorem, finished. 5.3 Wilson's theorem, started.
  homework: sec 5.2 #2(a)(b),4(a)(b),10,11,12,13,14
• Oct. 5: 4.4, Part III, Linear congruences with two variables. 5.2 Fermat's theorem, half way through.
  homework:
  • Finish the proof of Theorem 4.9 and Example 4.11 (You do not have to hand-in.).
  • sec 4.4 #17
• The homework set due Oct. 5 consists of the homeworks from Sections 4.2 and 4.4.
• Oct. 2: 4.4, Part II, Chinese Remainder Theorem, finished.
  homework: sec 4.4 #4,11,12,13
• Sep. 30: 4.4, Part I, Linear congruences, finished. 4.4, Part II, Chinese Remainder Theorem, half way through.
  homework: sec 4.4 #1
• Sep. 28: 4.4, Part I, Linear congruences, half way through.
  homework: None.
• Sep. 25: Hour exam 2
• Sep. 23: Reviewing homework problems.
• Review for the hour exam 2.
• Sep. 21: 4.2 Basic properties of congruence, finished.
  homework: sec 4.2 #1,2,10,11,16,18. (Section 4.2 will be on Hour Exam 2 this Friday. We will discuss some of these problems on Wednesday. Please try them in advance.)
• The homework due Sep.21:
  • Per request, you can hand-in Summary of Contents on Friday, the 25th.
  • The homework set consists of the homeworks assigned during 9/14--9/16.
• Sep. 18: 4.2 Basic properties of congruence, started.
  homework: sec 4.2 The following problems will be assigned next Monday when we finish Section 4.2. We are not quite ready to do these problems yet. I am listing the problems now because they will be part of the hour exam 2, scheduled next Friday. #1,2,10,11,16,18 (Do not include them to the homework submitted this coming Monday.)
• Sep. 16: 3.2 Distribution of prime numbers, finished.
  homework: sec 3.2 Read from the middle of p.46 (After the proof of Theorem 3.4) to p.47. (you do not need to submit.) exercises #3,7,9
• As mentioned in class, I am thinking of a Project on more advanced topics that can replace the homework of Summaries. It is for those who feel confident on the materials from our regular classes. One project will replace ALL the Summaries. Topics will be more challenging than those in the textbook. It is your choice: either submitting Summary before each hour exam or presenting/submit Project once during the semester. We will discuss further on how the project should be presented/submitted.
• Sep. 14: 3.1 Fundamental Theorem of Arithmetic, finished. 3.2 Distribution of prime numbers, started (Theorem 3.4 is done.)
  homework: sec 3.1 #5,6,11,16
• The homework set due Sep.14 consists of the homeworks assigned during 8/31--9/11.
• Sep. 11: 2.5 Diophantine equation ax+by=c, finished. 3.1 Fundamental Theorem of Arithmetic, half way through.
  homework: sec 2.5 #4, sec 3.1 Read the proofs of Corollaries 1 & 2 on p.40. (You do not have to hand in the proofs.)
• My office hours 2-3 this Friday 9/11 are canceled. But I will be in my office during the rest of the regular office hours.
• Sep. 9: 2.5 Diophantine equation ax+by=c, half way through.
  homework: sec 2.5 #1,2(a),3(b)
• The Math Tutoring Hours 12-4, Wed., Sep. 9, by Katie Dawson have been canceled.
• No homework due Sep. 9. Next homework will be due Sep. 14
• Sep. 4: Hour exam 1
• Sep. 2: Review for the hour exam 1.
• Review for the hour exam 1.
  I will be out of town this Friday. Katie (our tutor) will proctor the exam. Her MTC hours are held at Boyd 205, during 11-12.
• Aug. 31: 2.3 g.c.d., finished, 2.4 The Euclidean Algorithm, Part II: l.c.m, finished.
  homework:
  • sec 2.3 #20(a)(f), 23
  • sec 2.4 #5,8
• Guide for the homework of Summary of Contents:
  • Let me remind you the purpose of this homework: Get you prepared better for the upcoming exam, not for you to be graded. I will grade this homework just to see whether you have studied and understand what's going on.
  • Write Definitions and Theorems that we have learned from Sections 1.1, 1.2, 2.2, 2.3, and 2.4. Since we have not been able to cover all the 2.3 and 2.4, do only on those that have been covered. Section 2.1 will not be on the exam.
  • You don't have to include proofs. Of course, you can include them if you want to.
  • While writing theorems (and proofs if you include), do not copy the statements from the textbook or my lecture note but put your thoughts and understand them.
  • For those who feel very comfortable with the materials covered so far and want more challenging tasks, you have an option: Study and submit an essay on (1) the proof of Division Algorithm in Section 2.2 and (2) the proof of Euclidean Algorithm in Section 2.3. Regarding Division Algorithm, it should be clear what to prove if you look at the book. Regarding Euclidean Algorithm, you need to prove the reason why the last divisor that finishes the algorithm is the gcd (i.e., why r_n on p.26 is the gcd of a and b.)
• Aug. 28: 2.4 The Euclidean Algorithm, Part I. 2.3 g.c.d., Part II (we have not finished this section yet.)
  homework:
  • sec 2.4 #2(a)(c)
  • sec 2.3 #13
• Aug. 26: 2.2 Division Algorithm, finished. 2.3 g.c.d., Part I.
  homework:
  • sec 2.2 #4,6
  • sec 2.3 Prove Theorem 2.2. #3,6
• Aug. 24: 2.1 Early number theory. 2.2 Division Algorithm, half way through.
  homework: sec 2.1 #1 (#5, optional if you want to try.)
• The first homework set that consists of problems from sections 1.1 and 1.2 is due this coming Monday.
• Aug. 21: 1.2 The Binomial Theorem, finished.
  homework: sec 1.2 #5
• Notice about tutoring center. Math Tutoring Center is Boyd 205, as written on the syllabus. However, there will be workers in Boyd 205 on Thursday & Friday upgrading the networking 7 wiring. Therefore the tutoring center will be temporarily relocated for those two days starting tomorrow. We will be located in Cobb Hall room 130. The building is on front campus drive. You can walk out the main Boyd doors and continue across going between calloway and college of business, then up the steps and fork left and continue over the Cobb. You can enter the right side doors and it is on that hallway, you do not need to go to the main entrance where the deck is.
• Aug. 19: 1.2 The Binomial Theorem, half way through.
  homework: sec 1.2 #1, 3(a)(b)(e).
• Aug. 17: 1.1 Mathematical Induction (First Principle).
  homework: sec 1.1 #1,5,7.
• The classroom has been changed to Boyd 206.
• Aug. 14: Background survey.