- The textbook for this course is Kenneth Rosen, Elementary Number Theory and Its Applications, 6th edition. You may use either the printed textbook or the electronic version of the text.
- You should check this page frequently (i.e. daily) for updated information.
- All lecture notes, quizzes, homework assignments, and exam information are posted on PolyLearn.
- Each week, there will be a set of homework problems (take-home quizzes) to be turned in. The homework assignments will be posted on the Math 341 Homework page and in the Homework Assignments section in PolyLearn.
- I will post daily practice problems on this Course Schedule page that are not to be turned in. Although these problems will not be collected or graded, I strongly recommend that you work on these problems as soon as possible after lecture.
- Each week (typically on Tuesdays), there will be an in-class quiz. The in-class quizzes will often contain problems that are similar to the previous week's daily practice problems.
- This schedule may be adjusted as necessary!
| Class | Date | Topic | Quiz/Test/Assignment Due | Daily Practice Problems (not to be turned in) |
| 1 | Tuesday April 2 |
Welcome to Math 341! Introduction to Number Theory |
HW 1 due on Thursday April 11 | Read Sections 1.1 and 1.2 Review sums and products notation |
| 2 | Thursday April 4 |
1.3: Mathematical Induction 1.4: The Fibonacci Numbers |
1.3: 1, 3, 7, 21 1.4: 1, 3 |
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| 3 | Friday April 5 |
1.4: The Fibonacci Numbers 1.5: Divisibility |
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| 4 | Monday April 8 |
1.5: Divisibility HW Problems Discussion |
HW 2 due on Tuesday April 16 | 1.5: 1, 3, 5, 9, 11, 14, 15, 16, 19 21, 31, 37 |
| 5 | Tuesday April 9 |
3.1: Prime Numbers 3.2: The Distribution of Primes |
Read Sections 3.1 and 3.2 3.1: 5, 19 3.2: 2, 3, 14 |
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| 6 | Thursday April 11 |
3.2: The Distribution of Primes 3.4: The Euclidean Algorithm |
HW 1 Due Quiz 1 on 1.3, 1.4, 1.5 |
3.4: 1, 3 |
| 7 | Friday April 12 |
3.3: Greatest Common Divisors and Their Properties | 3.3: 1, 5, 7, 13, 15, 17, 23, 25, 27 | |
| 8 | Monday April 15 |
HW Problems Discussion 3.5: The Fundamental Theorem of Arithmetic |
HW 3 due on Tuesday April 23 | 3.5: 7, 38, 39 |
| 9 | Tuesday April 16 |
3.5: The Fundamental Theorem of Arithmetic | HW 2 Due Quiz 2 on 3.1, 3.3, 3.4 |
3.5: 42a |
| 10 | Thursday April 18 |
3.5: The Fundamental Theorem of Arithmetic 4.1: Introduction to Congruences |
3.5: 19 4.1: 1, 3 |
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| 11 | Friday April 19 |
4.1: Introduction to Congruences Applications of Congruences |
4.1: 5, 17, 22, 31, 34, 36, 41 | |
| 12 | Monday April 22 |
HW Problems Discussion Applications of Congruences |
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| 13 | Tuesday April 23 |
4.2: Linear Congruences | HW 3 Due Quiz 3 on 3.5, 4.1, Applications of Congruences |
4.2: 1a, 1c, 1d, 1e, 2a, 2c, 2d, 2e, 8a, 8b, 8c, 8d, 12 |
| 14 | Thursday April 25 |
Review for Exam 1 | ||
| 15 | Friday April 26 |
Exam 1 Quiz 4: Take-home quiz due on Friday, May 3 |
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| 16 | Monday April 29 |
4.2: Linear Congruences, continued 4.3: The Chinese Remainder Theorem |
4.2: 1b, 1f, 9, 11 | |
| 17 | Tuesday April 30 |
4.3: The Chinese Remainder Theorem | 4.3: 1, 3, 4a, 4c, 5 | |
| 18 | Thursday May 2 |
6.1: Wilson's Theorem and Fermat's Little Theorem | 6.1 Worskheet (in class) Due on Friday | |
| 19 | Friday May 3 |
6.1: Wilson's Theorem and Fermat's Little Theorem | 6.1 Worksheet Due Quiz 4 due |
6.1: 1, 3, 11, 13, 17, 19, 21 |
| 20 | Monday May 6 |
HW Problems Discussion 6.3: Euler's Theorem |
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| 21 | Tuesday May 7 |
6.3: Euler's Theorem | HW 4 Due Quiz 5 on 4.2, 4.3, 6.1 |
6.3: 1, 2, 3, 5, 11 |
| 22 | Thursday May 9 |
6.3: Euler's Theorem 7.1: The Euler-Phi Function |
7.1: 1, 2c, 11 | |
| 23 | Friday May 10 |
7.1: The Euler-Phi Function 7.2: The Sum and Number of Divisors |
7.2: 1, 2, 5a, 15, 39 | |
| 24 | Monday May 13 |
HW Problems Discussion 7.2: The Sum and Number of Divisors |
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| 25 | Tuesday May 14 |
9.1: The Order of an Integer and Primitive Roots | HW 5 Due Quiz 6 on 6.3, 7.1, 7.2 |
9.1: 1, 3, 5, 6 |
| 26 | Thursday May 16 |
9.1: The Order of an Integer and Primitive Roots | 9.1: 7, 8, 9, 11, 14, 24 | |
| 27 | Friday May 17 |
9.2: Primitive Roots for Primes | 9.2: 1, 3, 5, 9, 10, 12, 16 Additional problem: Given that 3 is a primitive root modulo 43, find all positive integers less than 43 that have order 21 modulo 43. |
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| 28 | Monday May 20 |
HW Problems Discussion 9.2: Primitive Roots for Primes |
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| 29 | Tuesday May 21 |
9.3: The Existence of Primitive Roots Note: Theorem 9.9, Example 9.13 only |
Quiz 7 on 9.1, 9.2 | 9.3: 3, 4 |
| 30 | Thursday May 23 |
9.3: The Existence of Primitive Roots Review for Exam 2 |
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| 31 | Friday May 24 |
Exam 2 | ||
| 32 | Monday May 27 |
NO CLASS: MEMORIAL DAY | ||
| 33 | Tuesday May 28 |
11.1: Quadratic Residues and Nonresidues | ||
| 34 | Thursday May 30 |
11.1: Quadratic Residues and Nonresidues 11.2: The Law of Quadratic Reciprocity |
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| 35 | Friday May 31 |
11.2: The Law of Quadratic Reciprocity 11.3: The Jacobi Symbol |
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| 36 | Monday June 3 |
HW Problems Discussion 11.3: The Jacobi Symbol |
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| 37 | Tuesday June 4 |
RSA Public Key Cryptography | HW 6 Due Quiz 8 on 11.1, 11.2, 11.3 |
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| 38 | Thursday June 6 |
RSA Public Key Cryptography | ||
| 39 | Friday June 7 |
Review |