BSc: Analytic Geometry And Linear Algebra II.s23 - Revision history

Ya.kholodov at 09:57, 27 January 2023

2023-01-27T09:57:57Z

← Older revision		Revision as of 09:57, 27 January 2023
Line 99:		Line 99:
	\| Midterm \|\| 30		\| Midterm \|\| 30
	\|-		\|-
−	\| ~~Tests~~\|\| 30 (15 for each)	+	\| Two intermediate tests\|\| 30 (15 for each)
	\|-		\|-
	\| Final exam \|\| 30		\| Final exam \|\| 30
	\|-		\|-
−	\| ~~Programming~~ tasks \|\| 20	+	\| Five programming tasks \|\| 20
	\|}		\|}

Ya.kholodov at 09:56, 27 January 2023

2023-01-27T09:56:47Z

← Older revision		Revision as of 09:56, 27 January 2023
Line 99:		Line 99:
	\| Midterm \|\| 30		\| Midterm \|\| 30
	\|-		\|-
−	\| Tests\|\| 20 (15 for each)	+	\| Tests\|\| 30 (15 for each)
	\|-		\|-
	\| Final exam \|\| 30		\| Final exam \|\| 30

Ya.kholodov at 09:54, 27 January 2023

2023-01-27T09:54:48Z

← Older revision		Revision as of 09:54, 27 January 2023
Line 82:		Line 82:
	! Grade !! Range !! Description of performance		! Grade !! Range !! Description of performance
	\|-		\|-
−	\| A. Excellent \|\| 85-~~100~~ \|\| -	+	\| A. Excellent \|\| 90-110 \|\| -
	\|-		\|-
−	\| B. Good \|\| 65-84 \|\| -	+	\| B. Good \|\| 75-89 \|\| -
	\|-		\|-
−	\| C. Satisfactory \|\| 50-64 \|\| -	+	\| C. Satisfactory \|\| 60-74 \|\| -
	\|-		\|-
−	\| D. Fail \|\| 0-49 \|\| -	+	\| D. Fail \|\| 0-59 \|\| -
	\|}		\|}

Line 99:		Line 99:
	\| Midterm \|\| 30		\| Midterm \|\| 30
	\|-		\|-
−	\| Tests\|\| 20 (10 for each)	+	\| Tests\|\| 20 (15 for each)
	\|-		\|-
−	\| Final exam \|\| 50	+	\| Final exam \|\| 30
	\|-		\|-
		+	\| Programming tasks \|\| 20
−	\| In-class participation \|\| 5 extras
	\|}		\|}

I.konyukhov: /* Final assessment */

2022-06-28T08:15:57Z

Final assessment

← Older revision		Revision as of 08:15, 28 June 2022
Line 228:		Line 228:

	=== Final assessment ===		=== Final assessment ===
−	~~'''~~Section 1~~'''~~	+	==== Section 1 ====
	# Find linear independent vectors (exclude dependent): <math display="inline">\overrightarrow{a}=[4,0,3,2]^T</math>, <math display="inline">\overrightarrow{b}=[1,-7,4,5]^T</math>, <math display="inline">\overrightarrow{c}=[7,1,5,3]^T</math>, <math display="inline">\overrightarrow{d}=[-5,-3,-3,-1]^T</math>, <math display="inline">\overrightarrow{e}=[1,-5,2,3]^T</math>. Find <math display="inline">rank(A)</math> if <math display="inline">A</math> is a composition of this vectors. Find <math display="inline">rank(A^T)</math>.		# Find linear independent vectors (exclude dependent): <math display="inline">\overrightarrow{a}=[4,0,3,2]^T</math>, <math display="inline">\overrightarrow{b}=[1,-7,4,5]^T</math>, <math display="inline">\overrightarrow{c}=[7,1,5,3]^T</math>, <math display="inline">\overrightarrow{d}=[-5,-3,-3,-1]^T</math>, <math display="inline">\overrightarrow{e}=[1,-5,2,3]^T</math>. Find <math display="inline">rank(A)</math> if <math display="inline">A</math> is a composition of this vectors. Find <math display="inline">rank(A^T)</math>.
	# Find <math display="inline">E</math>: <math display="inline">EA=U</math> (<math display="inline">U</math> – upper-triangular matrix). Find <math display="inline">L=E^-1</math>, if <math display="inline">A=\left(		# Find <math display="inline">E</math>: <math display="inline">EA=U</math> (<math display="inline">U</math> – upper-triangular matrix). Find <math display="inline">L=E^-1</math>, if <math display="inline">A=\left(
Line 244:		Line 244:
	\end{array}		\end{array}
	\right)</math>. Provide an example of vector b that makes this system unsolvable.		\right)</math>. Provide an example of vector b that makes this system unsolvable.
		⚫	==== Section 2 ====
−
⚫	~~'''~~Section 2~~'''~~
	# Find the dimensions of the four fundamental subspaces associated with <math display="inline">A</math>, depending on the parameters <math display="inline">a</math> and <math display="inline">b</math>: <math display="inline">A=\left(		# Find the dimensions of the four fundamental subspaces associated with <math display="inline">A</math>, depending on the parameters <math display="inline">a</math> and <math display="inline">b</math>: <math display="inline">A=\left(
	\begin{array}{cccc}		\begin{array}{cccc}
Line 271:		Line 270:
	\right)</math>.		\right)</math>.
	# Find an orthonormal basis for the subspace spanned by the vectors: <math display="inline">\overrightarrow{a}=[-2,2,0,0]^T</math>, <math display="inline">\overrightarrow{b}=[0,1,-1,0]^T</math>, <math display="inline">\overrightarrow{c}=[0,1,0,-1]^T</math>. Then express <math display="inline">A=[a,b,c]</math> in the form of <math display="inline">A=QR</math>		# Find an orthonormal basis for the subspace spanned by the vectors: <math display="inline">\overrightarrow{a}=[-2,2,0,0]^T</math>, <math display="inline">\overrightarrow{b}=[0,1,-1,0]^T</math>, <math display="inline">\overrightarrow{c}=[0,1,0,-1]^T</math>. Then express <math display="inline">A=[a,b,c]</math> in the form of <math display="inline">A=QR</math>
		⚫	==== Section 3 ====
−
−
⚫	~~'''~~Section 3~~'''~~
	# Find eigenvector of the circulant matrix <math display="inline">C</math> for the eigenvalue = <math display="inline">{c}_1</math>+<math display="inline">{c}_2</math>+<math display="inline">{c}_3</math>+<math display="inline">{c}_4</math>: <math display="inline">C=\left(		# Find eigenvector of the circulant matrix <math display="inline">C</math> for the eigenvalue = <math display="inline">{c}_1</math>+<math display="inline">{c}_2</math>+<math display="inline">{c}_3</math>+<math display="inline">{c}_4</math>: <math display="inline">C=\left(
	\begin{array}{cccc}		\begin{array}{cccc}
Line 297:		Line 294:
	\end{array}		\end{array}
	\right)</math>.		\right)</math>.
		⚫	==== Section 4 ====
−
−
⚫	~~'''~~Section 4~~'''~~
	<ol>		<ol>
	<li><p>Find <math display="inline">det(e^A)</math> for <math display="inline">A=\left(		<li><p>Find <math display="inline">det(e^A)</math> for <math display="inline">A=\left(

I.konyukhov: /* The retake exam */

2022-06-23T21:10:39Z

The retake exam

← Older revision		Revision as of 21:10, 23 June 2022
Line 321:		Line 321:

	=== The retake exam ===		=== The retake exam ===
		+	Exams will be paper-based and will be conducted in a form of problem solving, where the problems will be similar to those mentioned above. Students will be given 1-2 hours to complete the exam.
−	Retakes will be run as a comprehensive exam, where the student will be assessed the acquired knowledge coming from the textbooks, the lectures, the labs, and the additional required reading material, as supplied by the instructor. During such comprehensive oral/written the student could be asked to solve exercises and to explain theoretical and practical aspects of the course.
		+	First retake will be conducted in the same form as the midterm and final exams. The weight of the retake exam will be the same as the all course.
		+	Second retake will be conducted in the same form as the midterm and final exams. The weight of the retake exam will be the same as the all course.

I.konyukhov: /* Final assessment */

2022-06-23T21:10:07Z

Final assessment

← Older revision		Revision as of 21:10, 23 June 2022
Line 300:		Line 300:

	'''Section 4'''		'''Section 4'''
−	ol>	+	<ol>
	<li><p>Find <math display="inline">det(e^A)</math> for <math display="inline">A=\left(		<li><p>Find <math display="inline">det(e^A)</math> for <math display="inline">A=\left(
	\begin{array}{cc}		\begin{array}{cc}

I.konyukhov: /* Final assessment */

2022-06-23T21:09:42Z

Final assessment

Show changes

I.konyukhov: /* Ongoing performance assessment */

2022-06-23T21:07:57Z

Ongoing performance assessment

@@ Line 195: / Line 195: @@
 ==== Section 1 ====
-# How to perform the shift of the vector?
+# How to perform Gauss elimination?
 ==== Section 2 ====
-# How to interpret geometrically the distance between lines?
+# How to define orthogonal complements of the space?
-# How to rewrite the equation of a plane in a vector form?
+# How to find an orthonormal basis for the subspace spanned by the given vectors?
 ==== Section 3 ====
-# How to perform a transformation of the coordinate system?
+# How to find matrix for the Fourier transform?
-# How to compose the equation of a surface of revolution?
+# How to diagonalize a square matrix?
 === Final assessment ===

I.konyukhov: /* Activities and Teaching Methods */

2022-06-23T21:05:42Z

Activities and Teaching Methods

I.konyukhov: /* Resources, literature and reference materials */

2022-06-23T21:01:13Z

Resources, literature and reference materials

← Older revision		Revision as of 21:01, 23 June 2022
Line 117:		Line 117:
	* Gilbert Strang. Introduction to Linear Algebra, 4th Edition, Wellesley, MA: Wellesley-Cambridge Press, 2009. ISBN: 9780980232714		* Gilbert Strang. Introduction to Linear Algebra, 4th Edition, Wellesley, MA: Wellesley-Cambridge Press, 2009. ISBN: 9780980232714
	* Gilbert Strang, Brett Coonley, Andrew Bulman-Fleming. Student Solutions Manual for Strang’s Linear Algebra and Its Applications, 4th Edition, Thomson Brooks, 2005. ISBN-13: 9780495013259		* Gilbert Strang, Brett Coonley, Andrew Bulman-Fleming. Student Solutions Manual for Strang’s Linear Algebra and Its Applications, 4th Edition, Thomson Brooks, 2005. ISBN-13: 9780495013259
−
−	=== Software and tools used within the course ===
−	* No.

	== Activities and Teaching Methods ==		== Activities and Teaching Methods ==

← Older revision		Revision as of 21:05, 23 June 2022
Line 122:		Line 122:
	\|+ Teaching and Learning Methods within each section		\|+ Teaching and Learning Methods within each section
	\|-		\|-
−	! Teaching Techniques !! Section 1 !! Section 2 !! Section 3	+	! Teaching Techniques !! Section 1 !! Section 2 !! Section 3 !! Section 4
	\|-		\|-
−	\| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) \|\| 1 \|\| 1 \|\| 1	+	\| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Project-based learning (students work on a project) \|\| 0 \|\| 0 \|\| 0	+	\| Project-based learning (students work on a project) \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Modular learning (facilitated self-study) \|\| 0 \|\| 0 \|\| 0	+	\| Modular learning (facilitated self-study) \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Differentiated learning (provide tasks and activities at several levels of difficulty to fit students needs and level) \|\| 1 \|\| 1 \|\| 1	+	\| Differentiated learning (provide tasks and activities at several levels of difficulty to fit students needs and level) \|\| 1 \|\| 1 \|\| 1 \|\| 1
	\|-		\|-
−	\| Contextual learning (activities and tasks are connected to the real world to make it easier for students to relate to them) \|\| 0 \|\| 0 \|\| 0	+	\| Contextual learning (activities and tasks are connected to the real world to make it easier for students to relate to them) \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Business game (learn by playing a game that incorporates the principles of the material covered within the course) \|\| 0 \|\| 0 \|\| 0	+	\| Business game (learn by playing a game that incorporates the principles of the material covered within the course) \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Inquiry-based learning \|\| 0 \|\| 0 \|\| 0	+	\| Inquiry-based learning \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Just-in-time teaching \|\| 0 \|\| 0 \|\| 0	+	\| Just-in-time teaching \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Process oriented guided inquiry learning (POGIL) \|\| 0 \|\| 0 \|\| 0	+	\| Process oriented guided inquiry learning (POGIL) \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Studio-based learning \|\| 0 \|\| 0 \|\| 0	+	\| Studio-based learning \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Universal design for learning \|\| 0 \|\| 0 \|\| 0	+	\| Universal design for learning \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Task-based learning \|\| 0 \|\| 0 \|\| 0	+	\| Task-based learning \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|}		\|}
	{\| class="wikitable"		{\| class="wikitable"
	\|+ Activities within each section		\|+ Activities within each section
	\|-		\|-
−	! Learning Activities !! Section 1 !! Section 2 !! Section 3	+	! Learning Activities !! Section 1 !! Section 2 !! Section 3 !! Section 4
	\|-		\|-
−	\| Lectures \|\| 1 \|\| 1 \|\| 1	+	\| Lectures \|\| 1 \|\| 1 \|\| 1 \|\| 1
	\|-		\|-
−	\| Interactive Lectures \|\| 1 \|\| 1 \|\| 1	+	\| Interactive Lectures \|\| 1 \|\| 1 \|\| 1 \|\| 1
	\|-		\|-
−	\| Lab exercises \|\| 1 \|\| 1 \|\| 1	+	\| Lab exercises \|\| 1 \|\| 1 \|\| 1 \|\| 1
	\|-		\|-
−	\| Experiments \|\| 0 \|\| 0 \|\| 0	+	\| Experiments \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Modeling \|\| 0 \|\| 0 \|\| 0	+	\| Modeling \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Cases studies \|\| 0 \|\| 0 \|\| 0	+	\| Cases studies \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Development of individual parts of software product code \|\| 0 \|\| 0 \|\| 0	+	\| Development of individual parts of software product code \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Individual Projects \|\| 0 \|\| 0 \|\| 0	+	\| Individual Projects \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Group projects \|\| 0 \|\| 0 \|\| 0	+	\| Group projects \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Flipped classroom \|\| 0 \|\| 0 \|\| 0	+	\| Flipped classroom \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Quizzes (written or computer based) \|\| 1 \|\| 1 \|\| 1	+	\| Quizzes (written or computer based) \|\| 1 \|\| 1 \|\| 1 \|\| 1
	\|-		\|-
−	\| Peer Review \|\| 0 \|\| 0 \|\| 0	+	\| Peer Review \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Discussions \|\| 1 \|\| 1 \|\| 1	+	\| Discussions \|\| 1 \|\| 1 \|\| 1 \|\| 1
	\|-		\|-
−	\| Presentations by students \|\| 0 \|\| 0 \|\| 0	+	\| Presentations by students \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Written reports \|\| 0 \|\| 0 \|\| 0	+	\| Written reports \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Simulations and role-plays \|\| 0 \|\| 0 \|\| 0	+	\| Simulations and role-plays \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Essays \|\| 0 \|\| 0 \|\| 0	+	\| Essays \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Oral Reports \|\| 0 \|\| 0 \|\| 0	+	\| Oral Reports \|\| 0 \|\| 0 \|\| 0 \|\| 0
	\|}		\|}