Math 341 Spring 2013 Course Schedule

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

3 Friday

April 5

1.4: The Fibonacci Numbers

1.5: Divisibility

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

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

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

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

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

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

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.

28 Monday

May 20

HW Problems Discussion

9.2: Primitive Roots for Primes

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

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 11.1: 1, 3, 5a, 11, 15, 27

Hint for #15: consider 2, 3, and 6

35 Friday

May 31

11.1: Quadratic Residues and Nonresidues 11.1: 1, 3, 5a, 11, 15, 27

Hint for #15: consider 2, 3, and 6

36 Monday

June 3

HW Problems Discussion

11.2: The Law of Quadratic Reciprocity

11.2: 1, 3, 4
37 Tuesday

June 4

RSA Public Key Cryptography Quiz 8 on 11.1, 11.2
38 Thursday

June 6

RSA Public Key Cryptography
39 Friday

June 7

Review