01204211/activity7 number theory 2 - ประวัติรุ่นแก้ไข

Jittat: /* In-class activities */

2015-12-09T17:15:26Z

In-class activities

Jittat เมื่อ 17:14, 9 ธันวาคม 2558

2015-12-09T17:14:28Z

Jittat เมื่อ 02:39, 15 ตุลาคม 2558

2015-10-15T02:39:36Z

Jittat: /* In-class activities */

2015-10-14T17:48:31Z

In-class activities

Jittat: /* In-class activities */

2015-10-14T17:46:27Z

In-class activities

Jittat: /* In-class activities */

2015-10-14T17:40:35Z

In-class activities

Jittat: /* In-class activities */

2015-10-14T17:40:06Z

In-class activities

Jittat: /* In-class activities */

2015-10-14T17:38:03Z

In-class activities

Jittat: /* In-class activities */

2015-10-14T17:21:57Z

In-class activities

Jittat: /* In-class activities */

2015-10-14T17:19:18Z

In-class activities

@@ แถว 3: / แถว 3: @@
 == In-class activities ==
-: '''Due: 14 Dec 2015'''
+: '''Due date: 14 Dec 2015'''
 ''These activities require programming.  You can use any languages that you like.  Please keep the codes for these activities for the other sets of activities as well.''

@@ แถว 2: / แถว 2: @@
 == In-class activities ==
 ''These activities require programming.  You can use any languages that you like.  Please keep the codes for these activities for the other sets of activities as well.''
@@ แถว 130: / แถว 132: @@
 (b) The coefficient matrix in this question is a special one to find coefficients of a polynomial <math>F(x)=a_9x^9 + a_8x^8 + \cdots a_1x + a_0</math>.  Find <math>F(1),F(2),\ldots,F(10)</math>.  What do you see?  (Don't forget to perform every calculation modulo 17.)

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:39, 15 ตุลาคม 2558
แถว 16:		แถว 16:

	(e) <math>a = </math>your student id, <math>b = </math> the student id of another student sitting next to you. (Don't forget to write down the values of <math>a</math> and <math>b</math> as well.		(e) <math>a = </math>your student id, <math>b = </math> the student id of another student sitting next to you. (Don't forget to write down the values of <math>a</math> and <math>b</math> as well.
		+
		+
		+	'''Notes:''' The pseudo code for the Extended-GCD is as follows. (Don't forget to watch the video clips.)
		+
		+	FUNCTION ExtendedGCD(a,b)
		+	1. IF a mod b == 0 THEN
		+	2. return (b,0,1)
		+	3. ELSE
		+	4. (g,x,y) = ExtendedGCD(b, a mod b)
		+	5. return (g,y, x - y * floor(a/b))
		+	6. ENDIF
		+

@@ แถว 80: / แถว 80: @@
 Let's perform all calculations modulo 17.
-Solve for <math>a_0,a_1,\ldots,a_9</math> in this system of linear equations.
+(a) Solve for <math>a_0,a_1,\ldots,a_9</math> in this system of linear congruences.  (Don't forget that we are doing modular arithmetic modulo 17 here.)
 <math>
@@ แถว 98: / แถว 98: @@
 a_9 \\ a_8 \\ a_7 \\ a_6 \\ a_5 \\ a_4 \\ a_3 \\ a_2 \\ a_1 \\ a_0
 \end{array}\right)
+\equiv
 \left(\begin{array}{c}
 b_1 \\ b_2 \\ b_3 \\ b_4 \\ b_5 \\ b_6 \\ b_7 \\ b_8 \\ b_9 \\ b_{10}
@@ แถว 117: / แถว 117: @@
 , 16, 5, 9, 6, 4, 14, 15, 10, 1
-'''Notes:''' The coefficient matrix in this question is a special one to find coefficients of a polynomial <math>F(x)=a_9x^9 + a_8x^8 + \cdots a_1x + a_0</math>.
+(b) The coefficient matrix in this question is a special one to find coefficients of a polynomial <math>F(x)=a_9x^9 + a_8x^8 + \cdots a_1x + a_0</math>.  Find <math>F(1),F(2),\ldots,F(10)</math>.  What do you see?  (Don't forget to perform every calculation modulo 17.)
 == Homework ==

@@ แถว 116: / แถว 116: @@
 , 1, 2, 4, 8, 16, 15, 13, 9, 1
 , 16, 5, 9, 6, 4, 14, 15, 10, 1
 == Homework ==

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 17:38, 14 ตุลาคม 2558
แถว 76:		แถว 76:

	The nice thing about modular arithmetic when the modulus is a prime is that we can perform division with integers. This enables us to use methods (designed for a system of real numbers) to solve a system of linear equations.		The nice thing about modular arithmetic when the modulus is a prime is that we can perform division with integers. This enables us to use methods (designed for a system of real numbers) to solve a system of linear equations.
		+
		+	Let's take your student id and make it our constraints. Let <math>b_1,b_2,b_3,\ldots,b_{10}</math> be the digits from your student id. (E.g., if your id is 1234567890, <math>b_1=1,b_5=5,b_{10}=0</math>.)
		+
		+	Let's perform all calculations modulo 17.
		+
		+	Solve for <math>a_0,a_1,\ldots,a_9</math> in this system of linear equations.
		+
		+	<math>
		+	\left(\begin{array}{cccccccccc}
		+	1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\
		+	2 & 1 & 9 & 13 & 15 & 16 & 8 & 4 & 2 & 1 \\
		+	14 & 16 & 11 & 15 & 5 & 13 & 10 & 9 & 3 & 1 \\
		+	4 & 1 & 13 & 16 & 4 & 1 & 13 & 16 & 4 & 1 \\
		+	12 & 16 & 10 & 2 & 14 & 13 & 6 & 8 & 5 & 1 \\
		+	11 & 16 & 14 & 8 & 7 & 4 & 12 & 2 & 6 & 1 \\
		+	10 & 16 & 12 & 9 & 11 & 4 & 3 & 15 & 7 & 1 \\
		+	8 & 1 & 15 & 4 & 9 & 16 & 2 & 13 & 8 & 1 \\
		+	9 & 1 & 2 & 4 & 8 & 16 & 15 & 13 & 9 & 1 \\
		+	7 & 16 & 5 & 9 & 6 & 4 & 14 & 15 & 10 & 1
		+	\end{array}\right)
		+	\left(\begin{array}{c}
		+	a_9 \\ a_8 \\ a_7 \\ a_6 \\ a_5 \\ a_4 \\ a_3 \\ a_2 \\ a_1 \\ a_0
		+	\end{array}\right)
		+	=
		+	\left(\begin{array}{c}
		+	b_1 \\ b_2 \\ b_3 \\ b_4 \\ b_5 \\ b_6 \\ b_7 \\ b_8 \\ b_9 \\ b_{10}
		+	\end{array}\right)
		+	</math>

	== Homework ==		== Homework ==

@@ แถว 73: / แถว 73: @@
 '''A.6''' '''Gaussian Elimination.''' In this activity we will implement the Gaussian Elimination algorithm for solving systems of linear equations.
-: ''Do you remember the Gaussian Elimination algorithm?  If you don't, please read [https://en.wikipedia.org/wiki/Gaussian_elimination this wikipedia entry] first.''
+: ''Do you remember the Gaussian Elimination algorithm?  If you don't, please read [https://en.wikipedia.org/wiki/Gaussian_elimination this wikipedia entry on the Gaussian elimination algorithm] first.''
 == Homework ==

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 17:19, 14 ตุลาคม 2558
แถว 72:		แถว 72:

	'''A.6''' '''Gaussian Elimination.''' In this activity we will implement the Gaussian Elimination algorithm for solving systems of linear equations.		'''A.6''' '''Gaussian Elimination.''' In this activity we will implement the Gaussian Elimination algorithm for solving systems of linear equations.
		+
		+	: ''Do you remember the Gaussian Elimination algorithm? If you don't, please read [https://en.wikipedia.org/wiki/Gaussian_elimination this wikipedia entry] first.''

	== Homework ==		== Homework ==