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日本代购-大学数学の根幹／IanStewart／DavidTall／蟹江幸博【3000円以上送料無料】
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日本代购-著者IanStewart(著) DavidTall(著) 蟹江幸博(訳)出版社共立出版発売日2024年02月ISBN9784320115590ページ数484Pキーワードだいがくすうがくのこんかん ダイガクスウガクノコンカン すてゆあ−と いあん STEW ステユア−ト イアン STEW9784320115590内容紹介 大学で数学の学習を始めると、初めに「数」や「集合」などといった、一見すると当たり前に思える概念があらためて広く扱われる。しかしこれらは、その先の大学数学でより高度な概念を学習していくための基盤ともなる大切な概念であり、理解が曖昧なままでは、その後いくら学習を積み重ねても「砂上の楼閣」の如くひどく頼りないものになってしまうだろう。 本書では、上記の数・集合の概念の他に、数理論理・証明・関係（順序体や同値性）・無限とその濃度・置換と群論などといった、数学における基礎的ながらも軽視されがちな概念全般を徹底的に追究していく。こうして、地中に広く深く理解の「根」を張り巡らせることで、その後に難解な数学概念に出会っても動じない「幹」の太い喬木となり、理解の枝葉を大きく茂らせることができるのである。 大学数学やその先の研究活動にも通用する、強固な「数学の根幹」をもたらすべく、詳しく解説する。[原著: The Foundations of Mathematics, 2nd Edition, Oxford University Press , 2015]※本データはこの商品が発売された時点の情報です。目次第1部 直観的背景（数学的思考/数の体系）/第2部 形式化の始まり（集合/関係/関数/数学的論理/数学的証明）/第3部 公理系の展開（自然数と帰納法による証明/実数/完備な順序体としての実数/複素数とその先）/第4部 公理系を使って（公理系、構造定理、柔軟な思考/置換と群/濃度/無限数）/第5部 基礎の強化（集合論の公理）/付録 証明の読み方：「自己説明」戦略
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