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2013 Fiscal Year Final Research Report

Content Development for Distance Education in Advanced University Mathematics Using Mizar

Research Project

  • PDF
Project/Area Number 22300285
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Educational technology
Research InstitutionShinshu University

Principal Investigator

SHIDAMA Yasunari  信州大学, 工学部, 教授 (20226129)

Co-Investigator(Kenkyū-buntansha) WASAKI Katsumi  信州大学, 工学部, 教授 (70271492)
KPAULINE Naomi  信州大学, 工学部, 准教授 (40283238)
YAMAZAKI Hiroshi  信州大学, 工学部, 助教 (00293522)
OKAZAKI Hiroyuki  信州大学, 工学系研究科, 助教 (50432167)
Co-Investigator(Renkei-kenkyūsha) FUTA Yuichi  北陸先端科学技術大学院大学, 情報科学研究科, 准教授 (50706223)
ARAI Kenichi  東京理科大学, 理工学部, 助教 (60645290)
Project Period (FY) 2010-04-01 – 2014-03-31
Keywordseラーニング / プルーフチェッカ
Research Abstract

The Mizar system is a software program to mechanically verify the correctness of theorem proofs written in a formal mathematical language. The applicants have helped to drive an international project for pursuing research on the formalization of mathematical theorems using the Mizar system and creating an open archive of the compiled mathematical knowledge. In order to apply the results of this work to education, the members built a module for embedding the Mizar system into an e-learning CMS used in a graduate curriculum and developed contents for training students in logic and advanced university mathematics. The results of this research offer an effective solution to the serious and difficult task of "training logical thinking skills to students" in higher education.

  • Research Products

    (49 results)

All 2013 2012 2011 2010 Other

All Journal Article (46 results) (of which Peer Reviewed: 46 results) Presentation (2 results) Remarks (1 results)

  • [Journal Article] Differential Equations on Functions from R into Real Banach Space2013

    • Author(s)
      Keiko Narita, Noboru Endou,Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 21(4) Pages: 261-272

    • DOI

      10.2478/forma-2013-0028

    • Peer Reviewed
  • [Journal Article] Submodule of free Z-module2013

    • Author(s)
      Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 21(4) Pages: 273-282

    • DOI

      10.2478/forma-2013-0029

    • Peer Reviewed
  • [Journal Article] Isometric Differentiable Functions on Real Normed Space2013

    • Author(s)
      Yuichi Futa, Noboru Endou, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 21(4) Pages: 249-260

    • DOI

      10.2478/forma-2013-0027

    • Peer Reviewed
  • [Journal Article] Formulation of Cell Petri Nets2013

    • Author(s)
      Mitsuru Jitsukawa, Pauline N. Kawamoto, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 21(4) Pages: 241-247

    • DOI

      10.2478/forma-2013-0026

    • Peer Reviewed
  • [Journal Article] The Linearity of Riemann Integral on Functions from R into Real Banach Space2013

    • Author(s)
      Keiko Narita, Noboru Endou, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 21(3) Pages: 185-191

    • DOI

      10.2478/forma-2013-0020

    • Peer Reviewed
  • [Journal Article] Formalization of the Advanced Enc ryption Standard. Part I2013

    • Author(s)
      Kenichi Arai, Hiroyuki Okazaki
    • Journal Title

      Formalized Mathematics

      Volume: 21(3) Pages: 171-184

    • DOI

      10.2478/forma-2013-0019

    • Peer Reviewed
  • [Journal Article] Double Sequences and Limits2013

    • Author(s)
      Noboru Endou, Hiroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 21(3) Pages: 163-170

    • DOI

      10.2478/forma-2013-0018

    • Peer Reviewed
  • [Journal Article] Isomorphisms of Direct Products of Cyclic Groups of Prime-power Order2013

    • Author(s)
      Hiroshi Yamazaki, Hiroyuki Okazaki, Kazuhisa Nakasho , Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 21(3) Pages: 207-211

    • DOI

      10.2478/forma-2013-0022

    • Peer Reviewed
  • [Journal Article] Riemann Integral of Funtions from R into Real Banach Space2013

    • Author(s)
      Keiko Narita, Noboru Endou, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 21(2) Pages: 145-152

    • DOI

      10.2478/forma-2013-0016

    • Peer Reviewed
  • [Journal Article] Differentiation in Normed Spaces2013

    • Author(s)
      Noboru Endou, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 21(2) Pages: 95-102

    • DOI

      10.2478/forma-2013-0011

    • Peer Reviewed
  • [Journal Article] N-dimensional Binary Vector Spaces2013

    • Author(s)
      Kenichi Arai, Hiroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 21(2) Pages: 75-81

    • DOI

      10.2478/forma-2013-0008

    • Peer Reviewed
  • [Journal Article] Constructing Binary Huffman Tree2013

    • Author(s)
      Hiroyuki Okazaki, Yuichi Futa, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 21(2) Pages: 133-143

    • DOI

      10.2478/forma-2013-0015

    • Peer Reviewed
  • [Journal Article] Gaussian Integers2013

    • Author(s)
      Yuichi Futa, Hiroyuki Okazaki, Daich Mizushima, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 21(2) Pages: 115-125

    • DOI

      10.2478/forma-2013-0013

    • Peer Reviewed
  • [Journal Article] Random Variables and Product of Probability Spaces2013

    • Author(s)
      Hiroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 21(1) Pages: 33-39

    • DOI

      10.2478/forma-2013-0003

    • Peer Reviewed
  • [Journal Article] Isomorphisms of Direct Products of Finite Commutative Groups2013

    • Author(s)
      Hiroyuki Okazaki, Hiroshi Yamazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 21(1) Pages: 65-74

    • DOI

      10.2478/forma-2013-0007

    • Peer Reviewed
  • [Journal Article] The C^k Space2013

    • Author(s)
      Katuhiko Kanazashi, Hroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 21(1) Pages: 25-31

    • DOI

      10.2478/forma-2013-0002

    • Peer Reviewed
  • [Journal Article] Formal Definition of Probability on Finite and Discrete Sample Space for Proving Security of Cryptographic Systems Using Mizar2013

    • Author(s)
      Hiroyuki Okazaki, Yuichi Futa, Yasunari Shidama
    • Journal Title

      Artificial Intelligence Research

      Volume: 2(4) Pages: 37-48

    • DOI

      10.5430/air.v2n4p37

    • Peer Reviewed
  • [Journal Article] Formalization of Definitions and Theorems Related to an Elliptic Curve Over a Finite Prime Field by Using Mizar2013

    • Author(s)
      Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Journal of Automated Reasoning

      Volume: 50(2) Pages: 161-172

    • DOI

      10.1007/s10817-012-9265-2

    • Peer Reviewed
  • [Journal Article] On L1 Space Formed by Complex-Valued Partial Functions2012

    • Author(s)
      Yasushige Watase, Noboru Endou, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(4) Pages: 349-357

    • DOI

      10.2478/v10037-012-0039-4

    • Peer Reviewed
  • [Journal Article] Isomorphisms of Direct Product of Finite Cyclic Groups2012

    • Author(s)
      Kenichi Arai, Hiroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(4) Pages: 343-347

    • DOI

      10.2478/v10037-012-0038-5

    • Peer Reviewed
  • [Journal Article] Contracting Mapping on Normed Linear Space2012

    • Author(s)
      Keiichi Miyajima, Artur Kornilowicz, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(4) Pages: 291-301

    • DOI

      10.2478/v10037-012-0035-8

    • Peer Reviewed
  • [Journal Article] Free Z-module2012

    • Author(s)
      Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(4) Pages: 257-280

    • DOI

      10.2478/v10037-012-0033-x

    • Peer Reviewed
  • [Journal Article] Banach's Continuous Inverse Theorem and Closed Graph Theorem2012

    • Author(s)
      Hideki Sakurai, Hiroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(4) Pages: 271-274

    • DOI

      10.2478/v10037-012-0032-y

    • Peer Reviewed
  • [Journal Article] Quotient Module of Z-module2012

    • Author(s)
      Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(3) Pages: 205-214

    • DOI

      10.2478/v10037-012-0024-y

    • Peer Reviewed
  • [Journal Article] Extended Euclidean Algorithm and CRT Algorithm2012

    • Author(s)
      Hiroyuki Okazaki, Yosiki Aoki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(2) Pages: 175-179

    • DOI

      10.2478/v10037-012-0020-2

    • Peer Reviewed
  • [Journal Article] Formalization of the Data Encryption Standard2012

    • Author(s)
      Hiroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(2) Pages: 125-146

    • DOI

      10.2478/v10037-012-0016-y

    • Peer Reviewed
  • [Journal Article] Higher Order Partial Differentiation2012

    • Author(s)
      Noboru Endou, Hiroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(2) Pages: 113-124

    • DOI

      10.2478/v10037-012-0015-z

    • Peer Reviewed
  • [Journal Article] Operations of Points on Elliptic Curve in Projective Coordinates2012

    • Author(s)
      Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(1) Pages: 87-95

    • DOI

      10.2478/v10037-012-0012-2

    • Peer Reviewed
  • [Journal Article] Riemann Integral of Functions from R into n-dimensional Real Normed Space2012

    • Author(s)
      Keiichi Miyajima, Artur Kornilowicz, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(1) Pages: 79-86

    • DOI

      10.2478/v10037-012

    • Peer Reviewed
  • [Journal Article] The Differentiable Functions from R into Rn2012

    • Author(s)
      Keiko Narita, Artur Kornilowicz, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(1) Pages: 65-71

    • DOI

      10.2478/v10037-012-0009-x

    • Peer Reviewed
  • [Journal Article] Morphology for Image Processing. Part I2012

    • Author(s)
      Hiroshi Yamazaki, Czeslaw Bylinski, Katsumi Wasaki
    • Journal Title

      Formalized Mathematics

      Volume: 20(1) Pages: 61-63

    • DOI

      10.2478/v10037-012-0008-y

    • Peer Reviewed
  • [Journal Article] Z-modules2012

    • Author(s)
      Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(1) Pages: 47-59

    • DOI

      10.2478/v10037-012-0007-z

    • Peer Reviewed
  • [Journal Article] Differentiable Functions on Normed Linear Spaces2012

    • Author(s)
      Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(1) Pages: 31-40

    • DOI

      10.2478/v10037-012-0005-1

    • Peer Reviewed
  • [Journal Article] Functional SpaceC(Ω), C_0(Ω)2012

    • Author(s)
      Katuhiko Kanazashi, Hiroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(1) Pages: 15-22

    • DOI

      10.2478/v10037-012-0003-3

    • Peer Reviewed
  • [Journal Article] The Differentiable Functions from R into R^n2012

    • Author(s)
      Keiko Narita, Artur Kornilowic, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 20(1) Pages: 65-71

    • DOI

      10.2478/v10037-012-0009-x

    • Peer Reviewed
  • [Journal Article] More on the Cont inuity of Real Functions2012

    • Author(s)
      Keiko Narita, Artur Kornilowicz, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 19(4) Pages: 233-239

    • DOI

      10.2478/v10037-011-0032-3

    • Peer Reviewed
  • [Journal Article] Partial Differentiation, Differentiation and Continuity on n-Dimensional Real Normed Linear Spaces2011

    • Author(s)
      Takao Inoue, Adam Naumowicz, Noboru Endou, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 19(2) Pages: 65-68

    • DOI

      10.2478/v10037-011-0011-8

    • Peer Reviewed
  • [Journal Article] Banach Algebra of Bounded Complex-Valued Functionals2011

    • Author(s)
      Katuhiko Kanazashi, Hiroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 19(2) Pages: 121-126

    • DOI

      10.2478/v10037-011-0019-0

    • Peer Reviewed
  • [Journal Article] Differentiable Functions into Real Normed Spaces2011

    • Author(s)
      Hiroyuki Okazaki, Noboru Endou, Keiko Narita, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 19(2) Pages: 69-72

    • DOI

      10.2478/v10037-011-0012-7

    • Peer Reviewed
  • [Journal Article] Riemann Integral of Functions from R into Real Normed Space2011

    • Author(s)
      Keiichi Miyajima, Takahiro Kato, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 19(1) Pages: 17-22

    • DOI

      10.2478/v10037-011-0003-8

    • Peer Reviewed
  • [Journal Article] Cartesian Products of Family of Real Linear Spaces2011

    • Author(s)
      Hiroyuki Okazaki, Noboru Endou, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 19(1) Pages: 51-59

    • DOI

      10.2478/v10037-011-0009-2

    • Peer Reviewed
  • [Journal Article] Formalization of Integral Linear Space2011

    • Author(s)
      Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 19(1) Pages: 61-64

    • DOI

      10.2478/v10037-011-0010-9

    • Peer Reviewed
  • [Journal Article] Moreon Continuous Functions on Normed Linear Spaces2011

    • Author(s)
      Hiroyuki Okazaki, Noboru Endou, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 19(1) Pages: 45-49

    • DOI

      10.2478/v10037-011-0008-3

    • Peer Reviewed
  • [Journal Article] Riemann Integral of Functions R into C2010

    • Author(s)
      Keiichi Miyajima, Takahiro Kato, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 18(4) Pages: 201-206

    • DOI

      10.2478/v10037-010-0024-8

    • Peer Reviewed
  • [Journal Article] Differentiation of Vector-Valued Functions on n-Dimensional Real Normed Linear Spaces2010

    • Author(s)
      Takao Inoue, Noboru Endou, Yasunari Shidama
    • Journal Title

      Formalized Mathematics

      Volume: 18(4) Pages: 207-212

    • DOI

      10.2478/v10037-010-0025-7

    • Peer Reviewed
  • [Journal Article] 電子テキストを利用した情報リテラシ教育の実施結果収集を行う大規模工-ジェントベースシステムの開発と評価2010

    • Author(s)
      田中敬一, 和崎克己
    • Journal Title

      教育システム情報学会誌

      Volume: 27(3) Pages: 267-279

    • Peer Reviewed
  • [Presentation] Content Development for Distance Education in Advanced University Mathematics Using Mizar2013

    • Author(s)
      Takaya IDO, Hiroyuki OKAZAKI, Hiroshi YAMAZAKI, Pauline Naomi, KAWAMOTO, Katsumi WASAKI, Yasunari SHIDAMA
    • Organizer
      Proceedings of the 2013 International Conference on e-Learning,e-Business, Enterprise Information Systems, and e-Government(EEE'13)
    • Place of Presentation
      Las Vegas, Nevada, USA
    • Year and Date
      20130722-25
  • [Presentation] Development and Evaluation of a Large-Scale Agent-Based System for Information Literacy Education-Improving the Automatic Collection of Learning Results through Template Matching2011

    • Author(s)
      Keiichi TANAKA, Katsumi WASAKI
    • Organizer
      The 8th International Conference on Information Technology : New Generations(ITNG2011)
    • Place of Presentation
      Las Vegas, Nevada, USA (DOI : 10.1109/ITNG.2011.8)
    • Year and Date
      20110411-13
  • [Remarks]

    • URL

      http://shirodanuki.cs.shinshu-u.ac.jp/mizar/moodle/

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Published: 2015-06-25  

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