Title
沖縄高専における数学通論の取り組み
Author(s)
吉居, 啓輔; 渡利, 正弘; 山本, 寛
Citation
沖縄工業高等専門学校紀要 = Bulletin of National Institute
of Technology, Okinawa College, 10: 77-84
Issue Date
2016-03-30
URL
http://hdl.handle.net/20.500.12001/19384
Ἀ⦖㧗ᑓ࠾ࡅࡿᩘᏛ㏻ㄽࡢྲྀࡾ⤌ࡳ
Ώṇᘯ, ᒣᮏᐶ㸪㸨ྜྷᒃၨ㍜ ⥲ྜ⛉Ꮫ⛉ せ᪨ ᖹᡂ 27 ᖺᗘ๓Ꮫᮇ࠾࠸࡚, ⴭ⪅ࡽࡀ⾜ࡗࡓᩘᏛ㏻ㄽࡢㅮ⩏ࡢᐇ㊶ࡘ࠸࡚ሗ࿌ࡍࡿࠋ ᖹᡂ 27 ᖺᗘࡣ, ᒣᮏ, ྜྷᒃ, Ώࡀ, ࡑࢀࡒࢀ」⣲㛵ᩘㄽ, ㄽ⌮ࣃࢬࣝ, ⥺ᙧ➢ྕ⌮ㄽࡘ ࠸࡚ㅮ⩏ࢆ⾜ࡗࡓࠋᩘᏛ㏻ㄽ࡛ࡣ, ᑓᨷ⛉ࡢᏛ⏕ࢆᑐ㇟ࡋ, ࡑࢀࡒࢀࡢᩍဨࡀ⮬㌟ࡢ◊✲ ศ㔝㏆࠸ࢸ࣮࣐ࡢ୰ࡽ, ᭷┈࡛ࡘ⯆῝࠸ࢸ࣮࣐ࢆ㑅ᐃࡋㅮ⩏ࢆ⾜࠺ࠋᮏ✏࡛ࡣ, ࡑ ࢀࡒࢀࡢᩍဨࡢᑓ㛛ᛶࢆ⏕ࡋࡓࣘࢽ࣮ࢡ࡞ᩘᏛᩍ⫱ᑐࡍࡿྲྀࡾ⤌ࡳࡢᐇ㊶ࡘ࠸࡚ሗ ࿌ࢆ⾜࠺ࠋ ࣮࣮࢟࣡ࢻ㸸」⣲㛵ᩘ, ㄽ⌮ࣃࢬࣝ, ㄗࡾゞṇ➢ྕ 1㸬ࡣࡌࡵ ⥲ྜ⛉Ꮫ⛉ᡤᒓࡍࡿᩘᏛᩍဨࡣ㏻ᖖపᏛᖺࡢᏛ⏕ࢆᑐ㇟ᇶ♏ᩘᏛᚤ✚ศ⥺ ᙧ௦ᩘ࡞ࡢㅮ⩏ࢆᢸᙜࡍࡿࠋࡋࡋᩘᏛ㏻ㄽ࡛ࡣᑓᨷ⛉ࡢᑡேᩘࡢᏛ⏕ࢆᑐ㇟ࡋ ࡚ࡑࢀࡒࢀࡢᩍဨࡢ◊✲ᑐ㇟ࡘ࠸࡚ㅮ⩏ࢆࡍࡿࡇࡀ࡛ࡁࡿࠋᖹᡂ27 ᖺᗘࡣ㸪ᒣᮏࡀ ᕤᏛ࠾࠸࡚ᵝࠎ࡞ศ㔝࡛ᚲせ࡞ࡿ」⣲㛵ᩘㄽࡢᇶ♏ࢆ㸪ྜྷᒃࡀㄽ⌮ࣃࢬࣝࢆࢸ࣮࣐ ၥ㢟ゎỴᆺᏛ⩦ࢆ㸪Ώࡀሗ㏻ಙ࡞ᵝࠎ࡞㠃ᛂ⏝ࡉࢀ࡚࠸ࡿ⥺ᙧ➢ྕ⌮ㄽࡘ࠸࡚ ᭷㝈యࡢᇶᮏⓗ࡞ᛶ㉁ࡽㅮ⩏ࢆ⾜ࡗࡓࠋᮏ✏࡛ࡣ㸪ᖹᡂ27 ᖺᗘࡢᩘᏛ㏻ㄽ࠾ࡅࡿ㸪ྛ ᩍဨࡢᩍ⫱ᐇ㊶㸪ᚋࡢྲྀࡾ⤌ࡳᑐࡋ࡚ሗ࿌ࢆ⾜࠺ࠋ 㸬⥺ᙧ➢ྕࡘ࠸࡚㸦Ώᢸᙜ㸧 ᩘᏛ㏻ㄽࡢึᅇࡽ➨ ᅇࡲ࡛ࡢᤵᴗࢆΏࡀᢸᙜࡋ㸪௦ᩘᏛධ㛛㢟ࡋ࡚ㄗࡾゞṇ➢ ྜࡢධ㛛ㅮ⩏ࢆ⾜ࡗࡓࠋ➨ ❶࡛ࡣ㸪ࡑࡢᐇ㊶ሗ࿌ࢆ⾜࠺ࠋ 㧗ᗘሗ♫࠾ࡅࡿᩘᏛࡢᚲせᛶ 㧗ᗘሗࡉࢀࡓ⌧௦♫࠾࠸࡚ࡢᩘᏛࡢ㔜せᛶࡘ࠸࡚ࡣ㸪࠸ࡢవᆅࡀ࡞࠸ࠋ ᐇ㝿㸪ᩥ㒊⛉Ꮫ┬࡛ࡣࠕ⛉Ꮫᢏ⾡࣭Ꮫ⾡ᑂ㆟ ඛ➃◊✲ᇶ┙㒊ࠖࡀ㛤ദࡉࢀ㸪ࠕᩘᏛ ࣀ࣮࣋ࢩࣙࣥᡓ␎ࠖࡀᑂ㆟࣭ᢎࡉࢀ࡚࠸ࡿZ ࠋࡇࡢሗ࿌᭩ࡢෑ㢌㒊ศ࡛ࡣ㸪ḟࡢࡼ࠺ ㏙ࡽࢀ࡚࠸ࡿࠋࠗ♫ࡢ」㞧ࡸ㧗ᗘሗ♫ࡢ㐍ᒎక࠸㸪◊✲ࡸ⏘ᴗࡢᵝࠎ࡞ሙ㠃࠾࠸࡚㸪 ⮬↛⌧㇟ࡸே㛫ࡢάື㛵ࡍࡿ」㞧࡛㔞ࡢሗࡽ㸪᭷┈࡞ሗࢆᢳฟࡋά⏝ࡍࡿ ࡇࡀࡼࡾ୍ᒙᚲせ࡞ࡗ࡚ࡁ࡚࠸ࡿࠋࡇࡢࡓࡵ㸪ࡇࢀࡽࡢㅖ⌧㇟ࡢ⫼ᚋ₯ࡴཎ⌮ ࡸἲ๎ᛶࢆぢฟࡍ➼ࡢ᪂ࡓ࡞ࠕࡶࡢࡢぢ᪉ࠖࡀᚲせ࡛࠶ࡾ㸪ࡑࢀࢆྍ⬟ࡍࡿᩘᏛⓗ ࣉ࣮ࣟࢳࡀྍḞ࡛࠶ࡿࡢㄆ㆑ࡀ㸪ㅖ⛉Ꮫ㸪⏘ᴗ࡛ࡶ㧗ࡲࡗ࡚࠸ࡿࠋࡲࡓ㸪ᬯྕ ࡼࡿሗࢭ࢟ࣗࣜࢸࡢᙉ㸪ࢥࣥࣆ࣮ࣗࢱ࣭ࢢࣛࣇࢵࢡࢫࡼࡿᫎീ⾲⌧ࡢ㧗 ᗘࡸࡇࢀࡲ࡛⾲⌧࡛ࡁ࡞ࡗࡓࡶࡢࡢྍど➼㸪ᩘᏛࡀ⏝࠸ࡽࢀࡿศ㔝ࡢ♫ⓗ ࣥࣃࢡࢺࡀቑࡋ࡚࠸ࡿࠋ࠘ ᭦ࡇࡢሗ࿌᭩ࡢ୰࡛ࡣ㸪ᩘᏛㅖ⛉Ꮫࡢᯫࡅᶫ࡞ࡿ͆ᩘᏛࣀ࣮࣋ࢱ࣮͇⫱ᡂࡢ㔜せ ᛶࡘ࠸࡚ࡶゝཬࡉࢀ࡚࠸ࡿࠋ㧗➼ᑓ㛛ᏛᰯࡢᏛ⏕ࡣࡑࢀࡒࢀࡀ⮬ศࡢᑓ㛛ࢆᣢࡕ㸪ࡘ ᩘᏛࡶᚓព࡛࠶ࡿሙྜࡀከ࠸ࠋΏࡣ㸪㧗ᑓ⏕ᑗ᮶ࢆᢸ࠺ᩘᏛࣀ࣮࣋ࢱ࣮ࡋ࡚ࡢྍ ⬟ᛶࢆឤࡌ࡚࠸ࡿࠋࡋࡋ㧗ᑓࡢ㏻ᖖᤵᴗ࡛ᢅࢃࢀ࡚࠸ࡿ⣧⢋ᩘᏛࡢෆᐜࡣ㸪Ꮫ㒊ᖺ⏕⛬ ᗘࡢࡶࡢ࡛࠶ࡾ㸪ṧᛕ࡞ࡀࡽࡑࡢඛࡢᩘᏛࡣయ⣔ⓗࡣᩍ࠼ࡽࢀ࡚࠸࡞࠸ࡢࡀ⌧≧࡛࠶ࡿࠋ ࡑࡇ࡛ᑓᨷ⛉ᖺ⏕ྥࡅࡢᩘᏛ㏻ㄽࢆ㏻ࡌ࡚㸪ᢳ㇟௦ᩘᏛࡢึṌࢆᢅ࠺ࡇࡋࡓࠋ ᤵᴗෆᐜࡑࡢ≺࠸ࡘ࠸࡚ ᩘᏛⓗ⥺ᙧ➢ྕࡣ㸪᭷㝈యୖࡢࣇࣥ✵㛫ࡢ㒊ศ✵㛫ࡢࡇ࡛࠶ࡿࠋ≉㔜せ࡞ ㄗࡾ➢ྜ࡛࠶ࡿ⥺ᙧ➢ྕࡣ㸪㐃❧ḟ᪉⛬ᘧ࡛ᐃ⩏ࡉࢀࡿ㒊ศ✵㛫㸦ゎ✵㛫㸧࡛࠶ࡿࠋㄗࡾ ゞṇ➢ྜࢆᏛ⩦ࡍࡿୖ࡛࣋ࢡࢺࣝ✵㛫ࡸ᭷㝈య࡞ࡀษ࡞࣮࣮࢟࣡ࢻ࡛࠶ࡿࡀ㸪ṧᛕ࡞ ࡀࡽ㧗ᑓࡢᶆ‽ⓗ࡞⥺ᙧ௦ᩘࡢ࣒࡛࢝ࣜ࢟ࣗࣛ㸪࣋ࢡࢺࣝ✵㛫ࡸࡑࡢ㒊ศ✵㛫ࡀᢅࢃࢀࡿ ࡇࡣᑡ࡞࠸ࠋᐇ㝿㸪Ἀ⦖㧗ᑓ࡛⏝ࡉࢀ࡚࠸ࡿᩍ⛉᭩: ࡸࡑࡢࡢ௦⾲ⓗ࡞⥺ᙧ௦ᩘࡢᩍ ⛉᭩: ࡶ࣋ࢡࢺࣝ✵㛫㛵ࡍࡿグ㏙ࡣぢᙜࡓࡽ࡞࠸ࠋᤵᴗᅇᩘࡀᅇࡋ࡞࠸ࡇࢆ⪃៖ ࡋ࡚㸪ᛮ࠸ษࡗ࡚࣋ࢡࢺࣝ✵㛫ࡢෆᐜࡣឡࡍࡿࡇࡋࡓࠋࡑࡢ௦ࢃࡾ➢ྕࡀ࠶ࡿ௦ ᩘⓗ㛵ಀࢆ‶ࡓࡍ࣋ࢡࢺࣝࡢ㞟ྜ࡛࠶ࡿࡇࢆ⌮ゎࡋ࡚ࡶࡽ࠸㸪ࡇࡢᅇࡢᤵᴗࢆ㏻ࡌ࡚⮬ ศ㐩࡛᪂ࡋ࠸⤖ᯝࢆᚓࡿࡇࢆ┠ᶆࡋ࡚ᤣ࠼ࡿࡇࡋࡓࠋ ௨ୗ㸪ᐇࡋࡓྛᤵᴗࡢෆᐜࢆㄝ᫂ࡍࡿࠋ ➨ ᅇ㸦 ᭶ ᪥㸧༙⩌㸪⩌ࡘ࠸࡚㸸௦ᩘ⣔ࡋ࡚㸪༙⩌ཬࡧ⩌ࡢᐃ⩏ࢆ⾜ࡗࡓࠋࡑࡋ ࡚⩌ࡢලయࡋ࡚㸪Q ḟᑐ⛠⩌ࢆᢅࡗࡓࠋ ➨ ᅇ㸦 ᭶ ᪥㸧⎔㸪యࡘ࠸࡚㸸ࡣࡌࡵ⎔యࢆᐃ⩏ࡋ㸪ྠ್㛵ಀࢆᑟධࡋ࡚᭷㝈 యࢆᐃ⩏ࡋࡓࠋ≉₇⩦ࡋ࡚㸪᭷㝈యୖࡢຍἲἲࡢ₇⟬⾲ࢆィ⟬ࡉࡏࡓࠋ ➨ ᅇ㸦 ᭶ ᪥㸧ㄗࡾゞṇ➢ྕձ㸸᭷㝈య Fୖ࡛⥺ᙧ➢ྕࢆᐃ⩏ࡋ㸪ࣃࣜࢸ᳨ᰝ⾜ิ ࡞ࡶᑟධࡋࡓࠋ ➨ ᅇ㸦 ᭶ ᪥㸧ㄗࡾゞṇ➢ྕղ㸸ࣃࣜࢸ᳨ᰝ➢ྕࢆࡗ࡚࡞ࡐ⥺ᙧ➢ྕ࠾࠸࡚㸪ㄗ ࡾ᳨ฟゞṇࡀྍ⬟࡞ࡢ㸪ࡑࡢ⤌ࡳࢆゎㄝࡋࡓࠋᅇ㸦 ᭶ ᪥㸧ǻ༙⩌ࡘ࠸࡚㸸༙ ⩌ǻᑐࡋ࡚ǻ༙⩌ࢆᐃ⩏ࡋࡓࠋ₇⩦ㄢ㢟ࡋ࡚㸪ḟࡢၥ㢟 $ ࢆฟ㢟ࡋࡓࠋ ၥ㢟$ ༙ຍ⩌ǻ ࠑࠒ ^ ࣭࣭࣭`ᑐࡋ࡚㸪ǻѼ^
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78
Bulletin of National Institute of Technology, Okinawa College, No.10 (2016)=^
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࣭࣭࣭, a
l`
ࡢ௦ᩘⓗ࡞ᵓ㐀ࡽ㸪࣋ࢡࢺࣝ✵㛫ࡀỴࡲࡗࡓࡇࢆពࡍࡿࠋࡇࡢࢹࣝࢆࣉࣜࣗࢵ ࣮࢝ᇙࡵ㎸ࡳ࡛㐺ᙜ࡞ḟඖࡢᑕᙳ✵㛫ᇙࡵ㎸ࡴࡇࡼࡾ㸪௦ᩘከᵝయࡢᵓ㐀ࢆᣢࡘࡇ ࡀ▱ࡽࢀ࡚࠸ࡿ: ࠋ ᚋࡘ࠸࡚ ṧᛕ࡞ࡀࡽୖグ࡛ゎㄝࡋࡓෆᐜࡣ㸪㛫ࡢ㛵ಀ࡛༑ศᏛ⏕㐩ゎㄝࡍࡿࡇࡣ࡛ࡁ࡞ ࡗࡓࠋࡋࡋࡇࡢᅇࡢㅮ⩏ࢆ㏻ࡌ࡚㸪Ꮫ⏕㐩ࡣ᭷㝈య࡞ࡢᴫᛕࡩࢀ᪂ࡋ࠸ᩘᏛࡢୡ ⏺ࢆయ㦂ࡋ࡚ࡃࢀࡓᛮ࠺ࠋㄢ㢟ࡋ࡚ฟ㢟ࡋࡓၥ㢟 $ ࡽࢇ࡞➢ྕࡀὴ⏕ࡍࡿࡢ㸪 Ώࡀ▱ࡿ㝈ࡾࡲࡔ᫂ࡽ࡛ࡣ࡞࠸ࠋᚋࡣᏛ⏕ࡀィ⟬ࡋ࡚ࡃࢀࡓㄢ㢟ࡢ⤖ᯝࢆࡶ㸪 ࡑࡇࡽⓎ⏕ࡍࡿ➢ྜࢆ◊✲ㄽᩥࡋ࡚ࡲࡵࡿணᐃ࡛࠶ࡿ㸦᪤ᩘᏛ㏻ㄽࡢཷㅮ⪅ဨ ࡽ㸪ඹⴭ⪅࡞ࡗ࡚ࡶࡽ࠺ࡇࢆゎࡋ࡚ࡶࡽࡗ࡚࠸ࡿ㸧ࠋᅇࡢᩘᏛ㏻ㄽࡢཷㅮ⪅ࡢ୰ ࡽ㸪ᑗ᮶ᩘᏛࣀ࣮࣋ࢱ࣮ࡋ࡚ά㌍ࡋ࡚ࡃࢀࡿேᮦࡀ࠶ࡽࢃࢀࡿࡇࢆᮇᚅࡋ࡚࠸ࡿࠋ 」⣲ᩘࡑࡢ㛵ᩘ㸦ᒣᮏᢸᙜ㸧 ᩘᏛ㏻ㄽࡣ㸪ᮏᰯࡢᑓᨷ⛉ᖺḟࢆᑐ㇟ࡋࡓ༙ᮇ㸦 ศᅇ㸧ࡢ㑅ᢥ⛉┠࡛࠶ࡿࠋࡑ ࡢ࠺ࡕ㸪ࠕ」⣲ᩘࡑࡢ㛵ᩘࠖ㢟ࡋ࡚㸪 ศᅇࡢㅮ⩏ࢆᢸᙜࡋࡓࠋ ㅮ⩏ෆᐜ ㅮ⩏ෆᐜࡢࡲࡲࡾࢆ⪃࠼ࡿ㸪」⣲㛵ᩘࡢᚤศ㸪ࢥ࣮ࢩ࣮࣭࣮࣐ࣜࣥࡢ㛵ಀᘧ㸪」⣲ 㛵ᩘࡢ✚ศ㸪ࢥ࣮ࢩ࣮ࡢ✚ศᐃ⌮࡞ࢆ୍㏻ࡾゎㄝࡋࡓ࠶㸪ࢥ࣮ࢩ࣮ࡢ✚ศබᘧ㸪࣮ࣟ ࣛࣥᒎ㛤㸪␃ᩘᐃ⌮ࡲ࡛ゎㄝࡋࡓ࠸ࡇࢁ࡛࠶ࡿࡀ㸪ᮏㅮࡣᅇ࡛࠶ࡾ㸪ࢥ࣮ࢩ࣮ࡢ✚ศ බᘧ㸪࣮ࣟࣛࣥᒎ㛤㸪␃ᩘᐃ⌮ࡲ࡛ゎㄝࡍࡿၥ㢟₇⩦ࡀࢇ࡛ࡁࡎ㸪ㄝ᫂ࡀ᪩ࡃ࡞ ࡿ࠸ࡗࡓၥ㢟Ⅼࡀฟ࡚ࡃࡿࠋᮏㅮࡢཷㅮ⏕ࡣᕤᏛࢆᏛࡪᏛ⏕࡛࠶ࡾ㸪ᩘᏛࢆᑓ㛛ࡋ࡚ ࠸ࡿࢃࡅ࡛࡞࠸ࠋࡲࡓ㸪ྛཷㅮ⏕ࡀᡤᒓࡍࡿࢥ࣮ࢫࡼࡗ࡚㸪ᑓ㛛ࡅࡿᩘᏛࡢ⏝ࡢ ᗘྜ࠸㐪࠸ࡀ࠶ࡾ㸪」⣲ᩘ㛵ࡍࡿᇶ♏▱㆑ࡸィ⟬ຊࡶᕪࡀࡁ࠸ࠋࡇࢀࡽࢆ຺ࡋ㸪 ᮏㅮࡣ㸪ၥ㢟₇⩦ࡢ㛫ࢆከࡃࡿࡇ㸪ၥ㢟₇⩦ࡶྵࡵ࡚࡞ࡿࡃᤵᴗ㛫ෆ࡛⤖ࡉ ࡏࡿࡇࢆඃඛࡋ㸪௨ୗࡢ᪉㔪࡛ᐇࡋࡓࠋࢥ࣮ࢩ࣮ࡢ✚ศබᘧ㸪࣮ࣟࣛࣥᒎ㛤㸪␃ᩘᐃ⌮ࡣ㋃ࡳ㎸ࡲ࡞࠸ࠋ 」⣲ึ➼㛵ᩘࢆ⏝࠸ࡓලయⓗ࡞ィ⟬ࢆฟ᮶ࡿࡔࡅከࡃ⾜࠺ࠋ ᑗ᮶㸪␃ᩘᐃ⌮ࢆᏛࡪ㝿ࡢ⌮ゎࡢຓࡅ࡞ࡿࡼ࠺㸪]Qࡢ」⣲✚ศࡅࡿ Q ࡢሙྜࡢ≉Ṧᛶࢆ㸪ORJ] ࡢከ౯ᛶࡶ㛵㐃ࡉࡏ࡚ㄝ᫂ࡍࡿࠋ ゎㄝࡣ㸪௨ୗࡢ㡰␒࡛⾜ࡗࡓ 」⣲ᩘࡢᇶᮏᛶ㉁」⣲㛵ᩘࡢᚤศ 」⣲ᩘࡣ」⣲㛵ᩘࡢᴟ㝈್ 」⣲ᩘࡢィ⟬」⣲㛵ᩘࡢᚤศ 」⣲ᩘᖹ㠃」⣲㛵ᩘࡢ✚ศ ࣮࢜ࣛࡢබᘧ」⣲ᩘᖹ㠃ࡢ᭤⥺ ᴟᙧᘧ」⣲✚ศ 」⣲ᩘࡢ Q ᰿]Qࡢ」⣲✚ศ 」⣲㛵ᩘࢥ࣮ࢩ࣮ࡢ✚ศᐃ⌮ 」⣲㛵ᩘ 」⣲㛵ᩘ I ] ࡢᐇ㒊㒊 」⣲ᩘᖹ㠃㛫ࡢീࡋ࡚ࡢ」⣲㛵ᩘ Z I ] H]ࡢᐃ⩏ ORJ] D]ࡢᐃ⩏ VLQ]FRV] ࡢᐃ⩏ ㅮ⩏㈨ᩱ ᕷ㈍ࡢㅮ⩏⏝ࡢ᭩⡠ࡣ༙ᮇ㸦 ศᅇ㸧㸪㏻ᖺ㸦 ศᅇ㸧㸪ࡲࡓࡣࡑࢀ௨ୖࡢㅮ⩏ ᅇᩘࡀᐃࡉࢀ࡚࠸ࡿࡀ㸪ᮏㅮ⩏ࡢࠕ」⣲ᩘࡑࡢ㛵ᩘࠖࡣ ศᅇ࡛࠶ࡿࠋࡼࡗ࡚ᮏㅮ ࡛ࡣ㸪ᕷ㈍ࡢ᭩⡠ࢆᩍ⛉᭩ࡋ࡚ࡑࡢࡲࡲ࠺ࡇࡣࡏࡎ㸪ᕷ㈍ࡢ᭩⡠ࡢᵓᡂࢆཧ⪃ࡋ ࡞ࡀࡽㅮ⩏ෆᐜࢆ⟇ᐃࡋࡓࠋᩍ⛉᭩ࡢ௦ࢃࡾ࠺㈨ᩱࡋ࡚㸪ᐃ⩏㸪ᐃ⌮➼ࡢゎㄝ㸪 㢟㸪⦎⩦ၥ㢟ࡽ࡞ࡿㅮ⩏㈨ᩱࢆసᡂࡋࡓࠋㅮ⩏㈨ᩱࡣ㸪⦎⩦ၥ㢟ࡶྵࡵ࡚࡚ゎㄝ ࢆࡘࡅ㸪ㅮ⩏ࡢ㝿ࣉࣟࢪ࢙ࢡࢱᢞᙳࡋ࡚ゎㄝ⏝ࡍࡿࡶ㸪ㅮ⩏୰ࡢၥ㢟₇⩦ ࡸㅮ⩏እ࡛ࡢ⊂⩦ࡢ㝿ࡢཧ⪃ᩥ᭩ࡋ࡚ࡶ⏝࡛ࡁࡿࡼ࠺ࡋࡓࠋ ㅮ⩏᪉ἲ ㅮ⩏୰㸪๓᪉ࡢࣉࣟࢪ࢙ࢡࢱᏛ⏕ࡢᣢࡘࣀ࣮ࢺ 3& ࡢ୧᪉࡛ྠࡌㅮ⩏㈨ᩱࢆ㜀ぴ࡛ࡁࡿ ࡼ࠺㸪ணࡵᏛ⏕㟁Ꮚࣇࣝ㸦3') ᙧᘧ㸧࡛ㅮ⩏㈨ᩱࢆ㓄ᕸࡋࡓࠋㅮ⩏㈨ᩱࢆ⣬༳ๅࡋ ࡚㓄ᕸࡍࡿࡣࡋ࡞ࡗࡓࠋゎㄝࡣ㸪ࣉࣟࢪ࢙ࢡࢱᢞᙳࡉࢀࡓ㈨ᩱࡢ㸪㐺ᐅ㸪㯮ᯈࢆ ⏝࠸࡚ゎㄝࢆ⾜ࡗࡓࠋ
ホ౯᪉ἲ ศᅇࡢㅮ⩏࡛㸪࣏࣮ࣞࢺࢆᅇㄢࡋ㸪ࡑࡢྜィᚓⅬࢆᩘᏛ㏻ㄽࡢࠕ」⣲ᩘࡑࡢ㛵 ᩘࠖࡅࡿᡂ⦼ࡋࡓࠋ ᐇࡋࡓ⤖ᯝ ཷㅮ⪅ྡ ࣏࣮ࣞࢺࡢᥦฟ⋡ 㸪 ᖹᆒᚓⅬ㸦‶Ⅼ㸧㸬᭱㧗Ⅼ 㸪᭱పⅬ ฟᖍ⋡ ➨ᅇ㸸 ➨ᅇ㸸 ➨ᅇ㸸 ➨ᅇ㸸 ➨ᅇ㸸 ᮏᰯࡢᮏ⛉పᏛᖺ㸦ᖺ௨ୗ㸧ẚ࡚㸪ᑓᨷ⛉ࡢᏛ⏕ࡣ⊂⩦័ࢀ࡚࠸ࡿᵝᏊ࡛࠶ࡗࡓࠋ ゎㄝ୰㸪ၥ㢟₇⩦୰㸪ࡶ㸪㉁ၥࡣࢇฟ࡞ࡗࡓࠋࡇࡢࡇࡽ㸪ㅮ⩏ෆᐜࡀ⡆ ༢ࡍࡂࡓྍ⬟ᛶࡀᠱᛕࡉࢀࡿࡀ㸪ࣥࢣ࣮ࢺ࡛ᚓࡽࢀࡓᏛ⏕ࡢពぢࡣ㸪ㅮ⩏ෆᐜࡀ⡆༢ ࡍࡂࡿㄞࡳྲྀࢀࡿࡶࡢࡣ࡞ࡃ㸪ࡴࡋࢁࡢᩍဨࡢᢸᙜ⟠ᡤࡘ࠸࡚ࡶ㸪ᇶ♏ࢆࡁࡕࢇ ㄝ᫂ࡋ࡚࠸ࡿࡇࡘ࠸࡚ホ౯ࡍࡿពぢࡀ࠶ࡗࡓࠋࡓࡔࡋ㸪ࣥࢣ࣮ࢺࡢᅇ⟅ᩘࡣከࡃ࡞ ࠸ࠋࡲࡓ㸪ᩍဨ㐲៖ࡋ࡚ࢿ࢞ࢸࣈ࡞ホ౯ࢆ᭩࡞ࡗࡓྍ⬟ᛶࡶ࠶ࡿࠋ ᚋࡢྲྀࡾ⤌ࡳ ᚋࡣ㸪ࢢ࣮ࣝࣉᏛ⩦ࡢᙧᘧࢆྲྀࡾධࢀ㸪Ꮫ⏕ࡀࡼࡾ✚ᴟⓗᏛ⩦ྲྀࡾ⤌ࡵࡿ⎔ቃࢆ సࡿࡇࢆ᳨ウࡋ࡚࠸ࡿࠋ 3㸬ㄽ⌮ࣃࢬࣝࡘ࠸࡚㸦ྜྷᒃࡀᢸᙜ㸧 ᖹᡂ㸰㸵ᖺᗘࡢᩘᏛ㏻ㄽ࡛ࡣ 㞴᫆ᗘࡢ␗࡞ࡿㄽ⌮ࣃࢬࣝ㸷ၥࢆฟ㢟ࡋࡓࠋᮏㅮ⩏࡛ࡣᩘ ࠶ࡿㄽ⌮ࣃࢬࣝࡢ୰ࡽ,ࠕᖗᏊࡢⰍࢆᙜ࡚ࡿၥ㢟ࠖࢆ୰ᚰᢅࡗࡓࠋࡇࡢᖗᏊࡢⰍࢆᙜ࡚ ࡿၥ㢟ࡣ୍⯡ࡶࡼࡃ▱ࡽࢀࡓࡶࡢࡢࡼ࠺࡛࠶ࡿࠋࡲࡓ, ㏆ᖺ࡞ࡾࢽ࣮࣮ࣗࣚࢡࢱ࣒ࢫ ࡀWhy mathematicians care about their hat color (New York Times, April 10th, 2001)
࠸࠺グࢆᥖ㍕ࡋࡓࡇ࡛ὀ┠ࢆ㞟ࡵࡓࠋࡇࡢグࡣ, ᖗᏊࡢⰍࢆᙜ࡚ࡿၥ㢟ࡢᛂ⏝ࡀࣁ࣑ ࣥࢢࢥ࣮ࢻࡤࢀࡿ➢ྕ⌮ㄽ㸦ሗ㏻ಙࡢຠ⋡ಙ㢗ᛶ㛵ࡍࡿ⌮ㄽ㸧ࡢពእ࡞⤖ࡧ ࡘࡁࢆ♧ࡋ, “ࡓࡔࡢㄽ⌮ࣃࢬࣝ”ࡽ᪂ࡓ࡞ᩘᏛࡢᐃ⌮ࡀ⏕ࡲࢀ࡚࠸ࡿ࠸࠺ࡶࡢ࡛࠶ࡿࠋ
ࡇࡢࡶ, ㄽ⌮ࣃࢬࣝࡣ⣧⢋ᴦࡋ࠸ࡔࡅࡲࡽࡎ, ᕤᏛࡢศ㔝ࡶᵝࠎ࡞ᙧ࡛ᛂ ⏝ࡉࢀ࡚࠸ࡿࠋࡑࡢࡓࡵ, ࡇࡢࢸ࣮࣐࡛࠶ࢀࡤ, Ꮫ⏕ࡗ࡚ࡶ⯆῝ࡃ, ᩘᏛⓗෆᐜࡋ ࡚ࡶ༑ศ࡞῝ࡳࢆᣢࡕ, ྠၥ㢟ゎỴ⬟ຊࡸㄽ⌮ⓗ࡞ᛮ⪃ຊࢆ㣴࠺ࡇ᭱㐺࡛࠶ࡿ ⪃࠼, ᮏㅮ⩏࡛ྲྀࡾୖࡆࡿࡇࡋࡓࠋࡲࡓ, ᮏㅮ⩏࡛ᢅࡗࡓၥ㢟ࡢ༙ࡣ, ྜྷᒃࡢᜠᖌ࡛ ࠶ࡿ⏣୰୍அẶ㸦ᮾᏛ㸧ࡼࡿⴭ᭩”ࢳ࣮ࣗࣜࣥࢢ㉸㸦࣓ࢱ㸧ࣃࢬࣝ”ࡽฟ㢟ࡋࡓࠋ 3.1 ㅮ⩏ࡢ┠ⓗᑟධ㸦ືᶵࡅ㸧 ᮏㅮ⩏ࡢ࡞ពᅗࡣḟࡢࡼ࠺タᐃࡋࡓ: 1. ணഛ▱㆑ࢆ௬ᐃࡏࡎ, ᩘᏛⓗ⯆῝࠸ࣃࢬࣝࡢၥ㢟ࢆ㑅ࡪࡇ࡛, ࢢ࣮ࣝࣉᏛ⩦ࡼ ࡿᏛ⏕ࡢၥ㢟ゎỴ⬟ຊཬࡧ, ㄽ⌮ⓗᛮ⪃ຊࡢ㣴ᡂࢆ⾜࠺ࠋ 2㸬ゎࡅ࡞࠸ㄽ⌮ࣃࢬࣝࡢࢆ♧ࡍࡇ࡛, ᩘᏛᇶ♏ㄽࡢせ࡞ࢸ࣮࣐ࡢ୍ࡘ࡛࠶ࡿド᫂ ྍ⬟࡞ၥ㢟ࡢ⧅ࡀࡾࢆᴫほࡍࡿࠋ 3. ⴭ⪅ࡀᚋࢢ࣮ࣝࣉᏛ⩦ࢆᑟධࡍࡿ࠶ࡓࡾ, ヨ㦂ⓗ࡞ྲྀࡾ⤌ࡳࡋ࡚ࢢ࣮ࣝࣉᏛ⩦ࡢ ᭷ຠ࡞㐍ࡵ᪉ཬࡧ࣓ࣜࢵࢺࢹ࣓ࣜࢵࢺࢆ᥈ࡿࠋ 5 ᅇࡢㅮ⩏ࡣึ᪥ࡢᑟධ᭱⤊᪥ࢆ㝖ࡁ, 㛗㛫㞟୰ࡋ୍࡚ࡘࡢၥ㢟ྲྀࡾ⤌ࡴࡇ ࢆయ㦂ࡋ࡚ࡶࡽ࠸ࡓ࠸࠸࠺ពᅗࡽ, ၥ㢟₇⩦ࢆ୰ᚰࡋࡓࠋᑟධ࡛ࡣ, ㄽ⌮ࣃࢬࣝࡀࡓ ࡔࡢ㢌ࡢయ᧯࡛ࡣ࡞ࡃ, ࣡ࣥࢱࣝ, ࣮࣌ࣥࣟࢬࢱࣝ࡞ࡢࢱࣝᩜࡁワࡵၥ㢟ࢆ⤂ ࡋ, ࡑࢀࡀ㟁Ẽࢩ࢙࣮ࣂ࣮ࡢล࡞ᕤᏛⓗ㌟㏆࡞ᛂ⏝ࢆᣢࡗ࡚࠸ࡿࡇࡸ, ࡉࡽࡣ ‽⤖ᬗᵓ㐀Ⓨぢࡶࡘ࡞ࡀࡗࡓࡇ㸦2011 ᖺࣀ࣮࣋ࣝ㈹㸧࡞ࢆ⤂ࡋ, Ꮫ⩦ࡢືᶵࡅ ࢆᅗࡗࡓࠋ 3.2 ᤵᴗࡢᙧᘧၥ㢟 ᐇ㝿ࡢㅮ⩏ࡢ࣓࣮ࢪࢆᣢࡕ᫆ࡃࡍࡿࡓࡵ௨ୗฟ㢟ࡋࡓၥ㢟ࡢࢆ♧ࡍࠋ᭱ึࡢ ၥ㢟ࡣึ⣭⛬ᗘ ၥ┠ࡣ୰⛬ᗘࡢ㞴᫆ᗘࡢၥ㢟ࡋ࡚ฟ㢟ࡋࡓࠋᑡࡋ㛫ࢆྲྀࡗ࡚⪃࠼࡚ ࡶࡽ࠼ࢀࡤ㠃ⓑ࠸ၥ㢟࡛࠶ࡿࡇࡀゎࡗ࡚ࡶࡽ࠼ࡿᛮ࠺ࠋ ➨ ၥ㸦ࢳ࣮ࣗࣜࣥࢢ㉸㸦࣓ࢱ㸧ࣃࢬࣝ< ࡼࡾฟ㢟㸧 㸱ேࡢᅃேྥ࠸ࠊ┳Ᏺࡀḟࡢࡼ࠺ఏ࠼ࡓࠋࠕࡇࡇ㸱ࡘࡢ㟷࠸ᖗᏊࠊ㸰ࡘࡢ㉥࠸ ᖗᏊࡀ࠶ࡿࠋ࠾ࡲ࠼㐩ࠊࡇࡢ࠺ࡕ㸱ࡘࡢᖗᏊࢆ⿕ࡏࡿࠋ⮬ศࡢᖗᏊࡢⰍࡀ㟷ࡔ☜ಙ࡛ ࡁࡓࡽ㏨ࡆࡿࡀ࠸࠸ࠋࡋࡋࠊࡶࡋ㉥࡞ࡢ㏨ࡆࡓࡽࡑࡢሙ࡛ᑕẅࡍࡿ㸟ࠖ㸱ேࡣࠊࡋࡤ ࡽࡃࡋ࡚ဨ㏨ࡆฟࡋࡓࠋ࡞ࡐ㸽 ➨ ၥ ࠶ࡿᮧࠊே㛫ே⊋ࡢᮎ⿰ࡀఫࢇ࡛࠸ࡿࠋᮧࡢྛࠎࡣㄡࡀே⊋ࡢᮎ⿰㸦௨ୗ༢ே⊋ ࡪ㸧࡛࠶ࡿࡣࠊᮏேࢆ㝖࠸࡚ဨࡀุ᩿࡛ࡁࡿࠋࡋࡋࠊࡇࡢᮧ࡛ࡣࠊ͆⮬ศࡀே⊋
࡛࠶ࡿࡇ͇ࡀࢃࡗ࡚ࡋࡲ࠺ࠊࡑࡢ᪥ࡢኪࡢෆᮧࢆ㞳ࢀ࡞ࡅࢀࡤ࡞ࡽ࡞࠸ࠊ࠸࠺ ᥅ࡀ࠶ࡿࠋࡑࡢⅭࠊᮧே㐩ࡣࠊே⊋ᙼࡀ㸦ࡲࡓࡣᙼࡽࡀ㸧ே⊋࡛࠶ࡿࡇࢆỴࡋ࡚ᩍ࠼ ࡚ࡣ࡞ࡽ࡞࠸ࠊ࠸࠺ࡇࡶࡲࡓᬯ㯲ࡢ᥅࡛࠶ࡿࠋࡋࡋ୍ேࡢᩘᏛ⪅ࡀࠊᮧே㐩ࡢ๓ ࡛ࠕࡇࡢᮧࡣே⊋ࡀ࠸ࡲࡍࡡࠖゝࡗ࡚ࡋࡲ࠺ࠋ ᮧࡣ Q ேࡢே⊋ࡀᒃࡓࡍࡿࠋே⊋ࡢᩘࡣ᪥ࡀ⤒ࡘࡘࢀࡢࡼ࠺᥎⛣ࡍࡿ㸽 ୖࡢၥ㢟ࡣᮏ㉁ⓗࡃྠࡌၥ㢟࡛࠶ࡿࠋ➨ ၥࡣ࣓ࣜ࢝ࡢⴭྡ࡞ᩘᏛ⪅ࡀ⮬㌟ࡢࣈࣟ ࢢ⤂ࡋࡓၥ㢟ࡋ࡚ᩘᖺ๓▱ேࡽཱྀ㢌࡛⪺࠸ࡓࡶࡢࢆඖస〇ࡋࡓࠋグ᠈ࡀ᭕ ࡛࠶ࡗࡓࡓࡵၥ㢟ࡢ⣽࠸タᐃࡣసࡾኚ࠼ࡓࠋ 3.3 ⪃ᐹᚋࡢྲྀࡾ⤌ࡳ ୖࡣ ၥࡶ㸪ࡋࡤࡽࡃࡢ㛫ㄡࡶ⟅࠼ࡽࢀ࡞࠸ ⟅࠼࡞࠸ ࠸࠺ሗࢆဨࡀඹ᭷ࡍࡿ ࡇ࡛ゎỴ⮳ࡿ࠸࠺✀ࡢၥ㢟࡛࠶ࡿࠋఱࡶ㛝࡞ࡅࢀࡤ 㛫ࡓࡗ࡚ࡶṇゎࡣ㎺ࡾ ╔ࡅ࡞࠸ࡶࡋࢀ࡞࠸ࠋࡋࡋࡇࢀࡽࡢၥ㢟ᑐࡋ࡚ࡶᏛ⏕㐩ࡣࡇࡕࡽࡀᮇᚅࡍࡿ௨ ୖࡢṇ⟅⋡ࢆฟࡋ࡚ࡃࢀࡓࠋヲ⣽ࡣ⣬㠃ࡢ㒔ྜୖឡࡋูࡢ✏ㆡࡾࡓ࠸ᛮ࠺ࠋࡋࡋ㸪 ᅇࡢㅮ⩏ࢆ㏻ࡋ࡚ᑓᨷ⛉ࡢᏛ⏕ࡣ, ୍ᐃࡢㄽ⌮ⓗᛮ⪃ຊࡸၥ㢟ゎỴ⬟ຊࢆᬑẁࡢㅮ⩏ࡢ ୰࡛㌟ࡘࡅ࡚࠸ࡿࡶࡢᛮࢃࢀࡿࠋᏛ⏕ࡢண௨ୖࡢࣃࣇ࢛࣮࣐ࣥࢫࢆぢࡿࡇࡀ࡛ࡁ ࡓࡇࡣ, ᬑẁࡢపᏛᖺࡢᤵᴗࡢ㝿ࠕᩘᏐࡀኚࢃࡗࡓࡔࡅ࡛ࡃྠࡌၥ㢟࡞ࡢ࡞ࡐゎࡅ ࡞࠸ࡢࡔࢁ࠺ࠖឤࡌࡿࡀከ࠸⚾ࡗ࡚ࡣ᪂㩭࡞㦫ࡁ࡛࠶ࡗࡓࠋࡇࡢㄽ⌮ⓗᛮ⪃ຊࡸ ၥ㢟ゎỴ⬟ຊࢆ㏻ᖖࡢᩘᏛࡢၥ㢟ࢆゎࡃ㝿, ࡦ࠸࡚ࡣᵝࠎ࡞ၥ㢟ࢆゎỴࡍࡿ㝿Ⓨࡍࡿ ࡓࡵࡣ, 㐣ཤᏛ⩦ࡋࡓ▱㆑ྠኈࡢ㛵㐃ࢆ㔜どࡋࡓᵓ㐀ⓗ࡞グ᠈ࡢᩚ⌮ࡢ᪉ἲࢆ㌟ ࡅࡿࡼ࠺ᣦᑟࡍࡿࡇࡀㄢ㢟࡛࠶ࡿᛮࢃࢀࡿࠋࡑࡢྲྀࡾ⤌ࡳࡢ୍⎔ࡋ࡚, ᮏㅮ⩏ࡢ࣏ࣞ ࣮ࢺ࡛ࡣ, ࠕၥ㢟ࡢᮏ㉁ࢆ⡆₩ㄝ᫂ࡍࡿࡇࠖࠕၥ㢟ࡢཎ⌮ࢆᛂ⏝ࡋู࡚ࡢၥ㢟ࢆస〇ࡍ ࡿࡇ, ࡲࡓఝ࡚࠸ࡿၥ㢟ࢆ⟅࠼ࡿࡇࠖ࡞ࢆㄢࡋࡓࠋ๓⪅ࡣ, ឤぬࡋ࡚㌟ࡘࡅࡓ▱ ㆑ࢆゝㄒ㸦ព㆑㸧ࡍࡿࡇ, ᚋ⪅ࡣ༢ၥ㢟ࢆゎࡃࡇ⤊ጞࡍࡿࡢ࡛ࡣ࡞ࡃ㸪ၥ㢟ࢆ ᢳ㇟㸦ࡲࡓࡣ୍⯡㸧ࡍࡿ⬟ຊࢆ㣴࠺ࡓࡵࡢពᅗࡀ࠶ࡗࡓࠋᥦฟࡉࢀࡓᗄࡘࡢ⯆῝ ࠸ၥ㢟ࡘ࠸࡚ࡣ㸪ูࡢ✏࡛ሗ࿌ࡋࡓ࠸ࠋ ࠾ࢃࡾ ᩘᏛ㏻ㄽࡣ⥲ྜ⛉Ꮫ⛉ᒓࡍࡿᩍဨࡗ࡚ࡣ, ᑡேᩘࡢᩍ⫱ࢆᐇ㊶ࡍࡿࡇࡀ࡛ࡁࡿ ᩘᑡ࡞࠸ᶵࡢ୍ࡘ࡛࠶ࡿࠋ㏻ᖖࡢேᩘᑐࡍࡿㅮ⩏࡛ࡣᐇ㊶ࡍࡿࡇࡀ㞴ࡋ࠸᪂ࡋ࠸ ヨࡳࡶ✚ᴟⓗᣮᡓࡍࡿࡇ࡛, ᤵᴗຊࡢྥୖⓎᒎࡉࡏ࡚࠸ࡁࡓ࠸⪃࠼࡚࠸ࡿࠋ ᘬ⏝ᩥ⊩ : ᩥ㒊⛉Ꮫ┬㸪⛉Ꮫᢏ⾡࣭Ꮫ⾡ᑂ㆟ ඛ➃◊✲ᇶ┙㒊㸪ࠕᩘᏛពࣀ࣮࣋ࢩࣙࣥᡓ␎ࠖ㸪
ᖹᡂ ᖺ ᭶ ᪥ : ⏣௦ᏹ㸪㞴Ἴⳏ∞⦅㸪᪂⦅ 㧗ᑓࡢᩘᏛ >➨ ∧࣭᪂∧@㸪᳃ฟ∧ᰴᘧ♫㸪 : 㧗㐲 ⠇ኵ㸪᪂ゞ⥺ᙧ௦ᩘ㸪᪥ᮏฟ∧ᰴᘧ♫㸪㸦㸧 : *3ILVWHU-+06WHHQEULQN5HGXFHG+LOEHUWVFKHPHVIRULUUHGXFLEOHFXUYH VLQJXODULWLHV-3XUHDQG$SSOLHG$OJHEUDSS < ⏣୰୍அࢳ࣮ࣗࣜࣥࢢ㉸ ࣓ࢱ ࣃࢬࣝᮾிᏛฟ∧
An approach to educating mathematical innovators
in Okinawa Kosen
Masahiro Watari, Hiroshi Yamamoto, 䠆Keisuke YoshiiDepartment of integrated Arts and Science
We had a sequential lectures for advanced course students in 2015 spring. Although we are mainly teaching general education such as calculus or a basic course of linear algebra, it is a great opportunity and even fun for us to have such an advanced course because we can choose topics which we are really interested in. Thus, we, as pure mathematicians, choose each topic which must be mathematically interesting and, hopefully, worth learning for students who are majoring engineering. In this paper, we would like to share our unique approaches to engineering education at NIT, Okinawa college.
Keywords: Complex analysis, Logic puzzle, Error correcting code
