마스터제목스타일편집 - Prof. Sang-Gu Lee Homepagematrix.skku.ac.kr/2012-Album/2012-JMMSPF/2012-JMM-Mobile...마스터제목스타일편집 마스터부제목스타일편집

마스터 제목 스타일 편집

마스터 부제목 스타일 편집

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We show that the Smartphone and Sage-Math have features that can be

effectively used for learning of the second course of linear algebra.

A mobile contents and smartphone App was developed. It has all lecture notes,

video lectures, solutions of problems, computational tools and social

networking features for the second course of linear algebra. Now

students can have a whole process of learning linear algebra in their

hand. This shows a potential to possible changes in an effective learning of linear

algebra.

In this talk, we present this new android App and contents. Further, we

introduce how it was made and used for students' learning of the 2nd course of

linear algebra.



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I. System of Linear EquationsII. Linear Transformation and Matrix III. Vector Space IV. Determinant V. Eigenvalues and Eigenvector VI. Inner Product

Linear Algebra with Sage

Sections

1. Inner product2. Vector equation of line

and plane

VectorVector

Example Exercise

Combination: LA + Sage + Smartphone

LA with Sage.wmv avi file (Movie)

<Motivation : computations in LA>



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Cover

Combination: Smartphone Apps

Linear Algebra with Sage

· LSE

· Matrix

· L. T.

· Diagonalization

All could download this free Android Smartphone Appin https://market.android.com/ Search : SKKU matrix or

‘LA with Sage’

Vector operations

Sage-Math Tutorial

Inner product and projection

https://market.android.com






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(Main)



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Web Contents (web version) and Smartphone Apphttp://matrix.skku.ac.kr/2011-sage/sage/skkula.html

Work for i-phone as well



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Smartphone AppMatrix Theory Contents (Lecture Note)

1

Textbook: Kwak, Hong (2004). Linear Algebra: Second Edition, Birkhauser.

Lecture: 2011 SKKU Matrix Theory Lectures given by Sang-Gu Lee

App



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Textbook: Kwak, Hong (2004). Linear Algebra: Second Ediition, Birkhauser.

Lecture: 2011 SKKU Matrix Theory Lectures of Prof. Sang-Gu Leehttp://www.youtube.com/results?search_query=SKKU+math

KOCW (http://www.kocw.or.kr)Youtube (http://www.youtube.com)

Matrix Theory Contents (Lecture Movies)2

http://www.kocw.Youtube





http://www.youtube.com




http://www.youtube.com/results?search_query=SKKU+math











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Textbook: Kwak, Hong (2004). Linear Algebra: Second Ediition, Birkhauser.

Solution: Linear Algebra Exercise Solution Book

http://matrix.skku.ac.kr/2010-Album/2010-MT-all-Solution-v1-sglee/2010-MT-all-Solution-v1-sglee.html

Matrix Theory Contents (Problems and Solutions)3























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0. Click address Mobile Sage Server (or Published)① (Cut and Paste)② Revise3. Click [Evaluate]

How to use

Mobile Sage Matrix Tool for Computation (1)4



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Computing…

Mobile Sage Matrix Tool for Computation (2)5



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①

②

④

③

Mobile Sage Matrix Tool for Computation(with SNS)6

0. Click address Mobile Sage Server (or Published)① (Cut and Paste)② Revise3. Click [Evaluate]4. Use (or Publish)



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Matrix Theory Computation Tool (Sage with SNS)7

5. tweet (or use facebook or Me2Day etc)



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Contents Sharing SystemSNS for HW : send all HW answers,

Then collect and submit.)

Contents Sharing System using SNS

E-mail Twitter Facebook

Matrix Theory Computation Tool (Sage with SNS)8

http://www.facebook.com/search/results.php?q=mobile%20math&init=quick&tas=0.8210595338745295

















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free Android Smartphone App

This application supports followings:

1. All Lecture Notes (PPT)2. All Lectures (Movies, You-Tube)3. Solutions for all Problems4. Mobile Sage tools to Compute

Lecture Note + Lecture Movie+ Problems & Solutions + Computation tool (Sage)

+ SNS

Mobile Matrix Theory with Sagehttps://market.android.com/details?id=skku.la.sol

https://market.android.com/details?id=skku.la.sol











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Sage: Sage Calculator for Matrix

http://matrix.skku.ac.kr/2011-Sage/2011-Mobile-Math/MobileMath.html

Matrix Theory Computational Tool (Sage)9

MT with Sage.avi

avi file (Movie)

http://matrix.skku.ac.kr/2011-sage/sage/skkula.html

New free Android Smartphone App‘ with Sage’

https://market.android.com/ Search : SKKU matrix , MT







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Anytime Anywhere



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http://matrix.skku.ac.kr/newMT/index.html

Matrix Theory Web Contents1

Lecture Note











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http://www.youtube.com/results?search_query=skku+matrix

Matrix Theory Youtube Lectures2

Lecture

Spring 2011 (all lectures were recorded)












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Matrix Theory Problems and Solutions3

Problems and Solutions











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http://matrix.skku.ac.kr/2011-Sage/2011-Mobile-Math/MobileMath.html

Sage Calculator for Matrix4

http://galois09.skku.ac.kr/sage/scm-help.html

Computational Tool (no need to login)












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2011 KSME Fall Meeting

Linear Transformation

• x축, y축, 원점, 직선에대한 대칭을 시각화 하였다.• x축, y축 방향으로의 층밀림을 시각화 하였다.• 기본적인 대칭행렬의 표준행렬에 대해 알 수 있다.<직선에 의한 대칭 이동>

<X축 대칭> <오른쪽 층밀림>

http://math1.skku.ac.kr/pub/

http://math1.skku.ac.kr/pub








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(Android Linux Based System

(Android 2.0/2.1 Eclair Linux Kernel 2.6.29)

Java Application(JIT Compilation)

XML Treating Library(SAX Parser)

SQLite DBMS(with Java Library)

OpenGL ES 2.0(3D Engine Library)

SGL Graphic EngineOpenCore Media Frameworks

Phone Contacts Browser ......

Smartphone OS using Java

"Google released most of the Android code under the Apache License,

a free software and open source license."



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http://developer.android.com

1. Based Java (Open sources)2. Software Development Kit for Windows / Linux / MacOS

3. Embedding Eclipse IDE Environment4. XML, Java program language are usable.

Eclipse (with ADT) Emulator (with SDK)

Eclipse







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<Free> Search in Apple App store :

Korean mathematicians

All others can be downloaded from Android Market https://market.android.com/ by typing

SKKU matrix or Matrix Theory







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In 2005, Bill Gates of MS mentioned the 2nd IT Boom.Bill Gates expected it will be a ‘Mobile revolution’.

We're also thinking about providing affordable and inspiringsolutions on effective teaching and learning of Linear Algebra.

In this talk, we introduced a model of smartphoneApp that contains Lecture PPT, Lecture movies, Solutionson Problems, and Computational tools with most ofcommands for the 2nd course of LA.

It provided all possible resources for students not only tostudy the contents but also to deal with large sizecomputations and visualizations that can be used for theirown research problems with no cost and time to learnprograming language.

Our faculties and students told us that they learned more andthink these kind of tools may lead us to more

.



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• Teresa Franklin and Li-Wei Peng, Mobile math: math educators and students engage in mobile learning, J. Comput. High. Educ. 20. (2008)• Duk-Sun Kim, Sang-Gu Lee*, Greg Markowsky, Mobile Sage-Math for Linear Algebra and its Application, Electronic Journal of Mathematics & Technology (eJMT) V.4, No. 3, p.1-13, (2010)• Sang-Gu Lee, Contemporary Linear Algebra (3rd Ed.), KyungmoonPub. (2009)• Sang-Gu Lee, Duk-Sun Kim, MathML and JAVA Implementation in Linear Algebra, The Electronic Journal of Mathematics and Technology, Volume 3, Number 1, 1-11, ISSN 1933-2823 (2009)• Sang-Gu Lee, Rae-Young Ko, Duk-Sun Kim, Jin-Yeong Bak,Development of Mobile Sage-math and its use in Linear Algebra, J. Korea Soc. Math. Ed. Ser. E: Communications of Mathematical Education, Vol. 23, No. 4, 483-506 (2009)



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July 8~15, 2012Seoul, KOREA

http://icme12.org/

2014

2012

http://icme12.org

http://icme12.org

http://icme12.org

Sage Calculator for Matrix

Lecture Notes

Lectures

Problems

Sage

Q/A

http://matrix.skku.ac.kr/2011-sage/sage/skkula.html (1 / 2)2012-01-27 오전 11:39:29

http://matrix.skku.ac.kr/2011-sage/sage/lecturenotes.html

http://matrix.skku.ac.kr/2011-sage/sage/lectures.html

http://matrix.skku.ac.kr/2011-sage/sage/problems.html

http://matrix.skku.ac.kr/2011-sage/sage/scm.html

http://115.145.139.39/?mid=sagematrixsns


http://matrix.skku.ac.kr/2011-sage/sage/skkula.html (2 / 2)2012-01-27 오전 11:39:29



- Free Worksheet -

Matrices(행렬생성)

Matrix Operations(행렬연산)

Matrix Spaces(행렬공간)

Row Operations(행연산)

Echelon Form(행사다리꼴)

Constructing Subspaces(부분행렬)

Combining Matrices(행렬결합)

Matrix Decomposition(행렬분해)

copyrights ⓒ 2011. Made by [email protected] and

[email protected]. All rights reserved.

http://matrix.skku.ac.kr/2011-Sage/2011-Mobile-Math/MobileMath.html2012-01-27 오전 11:40:19

http://math3.skku.ac.kr/spla/freeworksheet

http://math3.skku.ac.kr/spla/Operation_Matrix1








Documents

마스터제목스타일편집 - Prof. Sang-Gu Lee Homepagematrix.skku.ac.kr/2012-Album/2012-JMMSPF/2012-JMM-Mobile...마스터제목스타일편집 마스터부제목스타일편집