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수학이 없는 세상

  • 임선주
  • |
  • 형설출판사
  • |
  • 2013-09-03 출간
  • |
  • 230페이지
  • |
  • 188 X 257 mm
  • |
  • ISBN 9788947274166
★★★★★ 평점(10/10) | 리뷰(1)
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북스크린영상으로 만나보는 한 권의 책 이야기

출판사서평

수학이 현실과 동떨어진 비실용적인 학문이라고 여기는 이들이 적지 않다. 수학공부에 대한 일반적인 생각은 다음과 같다. 좋은 대학에 입학하기 위해 좋은 성적을 얻어야하기 때문에, 또한 좋은 성적을 얻기 위해서는 수학성적이 좋아야하므로 수학공부는 해야 하고 수학은 중요한 과목이라는 생각이 만연하다. 이런 부담감 때문인지 학생들은 수학 자체를 즐기기보다는 대학에 가기 위한 수단으로 수학 공부를 한다. 이런 이유 때문인지 개중의 학생들은 대학에 들어가면 수학 공부는 더 이상 하지 않으려고 한다. 그러나 대학의 전공학과에 따라서는 전공 책이 거의 수학 책과 같음에 놀라고 당황하는 학생들도 있다. 또한 수학 공부가 어려워 수학이 없는 세상을 꿈꾸는 학생들도 있다.

사실 이런 꿈은 꾸는 사람들이 상당히 많다. 어떤 이들은 돈 계산할 때의 사칙연산만 있으면 되지 더 이상의 수학은 필요하지 않음을 이야기하기도 한다. 수학이없는 세상은 과연 어떤 세상일까? 수학이 없는 세상에서도 지금과 같은 문명의 발달을 이루어냈을까? 그러나 수학 활동은 우리 인류에게는 자연스러운 활동이다. 고도의 수학적 지식을 배우지 않은 인류는 만물의 영장인지라 자신의 주변에서 생기는 문제를 해결하는 수단으로 수학을 활용해 왔다. 고대 그리스 시대의 호메로스의 걸작인 『오디세이아』에 다음과 같은 내용이 있다. 오디세이아에 의해 장님이 된 외눈박이 거인 폴리페모스는 동굴에서 양떼를 키운다. 폴리페모스는 동굴 밖으로 나오고 들어가는 양들의 수를 셀 때 조약돌을 이용한다. 아침에 양이 한 마리씩 동굴 밖으로 나올 때마다 조약돌을 한 개씩 밖으로 옮겨 놓고 저녁에는 양이 한 마리씩 동굴로 들어갈 때마다 조약돌을 한 개씩 밖에서 안으로 옮겼다. 이 내용의 외눈박이 거인인 폴리페모스는 수학을 배운 적도 없는데 일대일대응으로 수를 세고 있다. 자신의 양들과 조약돌들을 일대일 대응시켜 잃어버린 양이 있는지를 확인하고 있는 것이다.
호로메스의 작품 『오디세이아』는 기원전 700년 전의 작품으로 구전이 아닌 최초의 기록물로 평가 받는다. 이런 작품에서 우리는 수학적 지식이 없는 폴리페모스의 수 세기 모습을 엿보았다. 이렇듯 수학 활동은 개개인에게 있어서 조금씩의 차이는 있지만 인류사회에서 수학은 대기의 공기처럼 인류와 함께 해 왔음을 어느 누구도 부인하지 못한다. 이 책을 통하여 기대하는 몇 가지를 적어본다.

첫 번째 기대하는 바는 한 번이라도 수학이 없는 세상을 생각해 본 이들에게 인류의 수학 활동이 매우 지극히 자연스러운 행위이며 다양한 분야에서 진행되었던 수학 활동에 대하여 생각해 볼 계기를 마련하고자 한다. 세상에 영향을 미친 각 분야의 거장들은 진정한 수학 활동으로 자신이 속한 분야를 발전시켰다. 수학은 다양한 분야에 큰 영향을 미쳤다. 과학, 금융, 현대의 정보 보호 기술 등의 분야뿐만이 아니라 철학, 음악, 미술, 스포츠, 영화, 문학, 건축 등의 인문학, 예술 분야에까지 영향을 미쳤다. 전혀 무관해 보이는 예술 분야까지 수학과 밀접한 관련이 있음은 바로 우리 인류가 높은 지능을 지니고 있기에 수학활동이 매우 자연스러운 행위임을 증명하는 것이다.

두 번째는 수학이 신기하면서도 재미있는 공부임을 알았으면 한다. 과거의 수학 교육은 다른 교과와 완전히 분리되어 진행되었다. 요즘 스토리텔링의 수학 교육이 서서히 진행되고 있다. 이런 수학교육에 발맞추어 더 이상 수학은 어려운 과목이 아니라 실생활의 문제 해결에 도움이 되는 재미난 과목임을 알리고자 한다.

세 번째는 수학을 삶의 지혜로 활용하기를 바란다. 수학이 단순히 계산을 이용하여 문제를 푸는 학문이 아니라, 개인의 주변에서 발생하는 문제를 합리적으로 최대한 잘 해결하기 위하여 논리 정연함과 바르게 생각하는 법을 배우는 학문임을 알리고자 한다. 개인은 삶을 영위하는 과정에서 여러 번의 선택과 갈등의 자리에 선다. 이럴 때 마다 바른 생각과 논리 정연함으로 최상의 결정을 내린다면 이것이야말로 진정한 수학 활동이다.

목차

제1장 수학은 자연을 설명하는 언어
1. 피보나치수열 ·············································································································· 11
2. 황금비 ························································································································· 18
3. 피보나치수열과 황금비의 관계－황금비는 피보나치수열의 또 다른 이름이다 ···· 23
4. 생활 속의 황금비－신용카드, 담배 갑, 엽서, 명함의 비율 ··································· 26
5. 꿀벌의 집은 왜 정육각형일까? ················································································· 26
6. 프랙탈 이론 ················································································································ 29
7. 매미와 소수 ················································································································ 32

제 2장 음악 속의 수학
1. 음악과 수학의 관계 ··································································································· 36
2. 소리란 무엇인가? ······································································································· 37
3. 피타고라스 음계 ········································································································· 38
4. 순정조(純正調, just intonation), 순정률(純正律, pure temperament) ·················· 43
5. 평균율(equal temperment) ························································································· 46
6. 황금비를 이용한 음악들 ···························································································· 50
7. 악기(樂器)에 숨겨진 수학적 원리 ············································································ 51

제 3장 미술 속의 수학
1. 황금비를 이용한 미술 작품 ······················································································ 59
2. 원근법 ························································································································· 62
3. 마방진을 이용한 회화 작품 ······················································································ 73
4. 기하학을 이용한 회화 작품 ······················································································ 75
5. 행렬을 이용한 회화 작품－워홀의 『캠벨 수프 깡통』과 『마릴린』 ······················· 78
6. 테셀레이션이란? ········································································································· 80

제4장 스포츠 속의 수학
1. 스포츠란? ···················································································································· 86
2. 자전거 속의 수학 ······································································································· 87
3. 축구 속의 수학 ·········································································································· 89
4. 야구 속의 수학 ·········································································································· 94
5. 경기에서 등위결정방법 ······························································································ 99
6. 경기 운용계획 ·········································································································· 106

제5장 건축 속의 수학
1. 건축이란? ················································································································· 112
2. 유클리드 기하학의 요소를 반영한 건축물 ····························································· 113
3. 극소곡면(비누 막의 원리)을 이용한 건축물 ·························································· 123
4. 지오데식 돔 형태의 건축물 ···················································································· 124
5. 비유클리드 기하학과 프랙탈 요소를 반영한 건축물－해체주의 ·························· 125

제6장 수학과 금융
1. 나와 금융 ················································································································· 132
2. 금융 속의 수학 ········································································································ 136
3. 금융수학이란? ·········································································································· 152
4. 금융공학이란? ·········································································································· 153

제7장 수학과 과학
1. 미분과 과학 ·············································································································· 161
2. 적분과 과학 ·············································································································· 167
3. 이산수학 ··················································································································· 171
4. 인버터 에어컨 ·········································································································· 178
5. 퍼지 이론(Fuzzy Theory) ······················································································· 180

제8장 수학과 암호
1. 암호란 무엇인가? ····································································································· 189
2. 암호의 역사 ·············································································································· 189
3. 패러티 검사(Parity Check)의 응용 ········································································ 202

제9장 수학과 나의 생활
1. 머피의 법칙 ·············································································································· 210
2. 어느 대기업의 면접시험 ·························································································· 214
3. 나의 하루 ················································································································· 215
4. 영화에 숨겨진 수학적 원리를 찾아라 ···································································· 222

저자소개

저자 임선주는 숙명여대에서 수학과를 졸업하고 동 대학교 대학원에서 대수학의 순서구조로 석사와 박사 학위를 취득한 후에 암호론과 디자인 이론 등에 관심을 갖고 연구 활동을 하였다. 숙명여대, 서울과학대, 세종대, 한성대 등에서 강사를 역임한 바 있다. 현재 동양미래 대학교 교양과 교수로 재직하고 있는 저자는 입시로 인하여 수학에 지친 학생들이 수학을 친근하게 접할 수 있는 방법에 대하여 고민한 결과, 이 책을 집필하게 되었다. 이 책에는 수학이 기계적인 계산만을 다루는 학문이 아니라 예술, 과학과 실생활 속에서 수학이 어떤 역할을 하는지에 대하여 다루고 있다. 저자는 학생들이 이 책을 통하여 수학 활동이 자연스러운 생활의 일부였음을 깨닫고 진정한 수학 활동으로부터 삶의 지혜를 얻기를 바란다.

도서소개

호로메스의 작품 『오디세이아』는 기원전 700년 전의 작품으로 구전이 아닌 최초의 기록물로 평가 받는다. 이런 작품에서 우리는 수학적 지식이 없는 폴리페모스의 수 세기 모습을 엿보았다. 이렇듯 수학 활동은 개개인에게 있어서 조금씩의 차이는 있지만 인류사회에서 수학은 대기의 공기처럼 인류와 함께 해 왔음을 어느 누구도 부인하지 못한다. 이 책을 통하여 기대하는 몇 가지를 적어본다.
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도서교환 및 환불
  • ㆍ배송기간은 평일 기준 1~3일 정도 소요됩니다.(스프링 분철은 1일 정도 시간이 더 소요됩니다.)
  • ㆍ상품불량 및 오배송등의 이유로 반품하실 경우, 반품배송비는 무료입니다.
  • ㆍ고객님의 변심에 의한 반품,환불,교환시 택배비는 본인 부담입니다.
  • ㆍ상담원과의 상담없이 교환 및 반품으로 반송된 물품은 책임지지 않습니다.
  • ㆍ이미 발송된 상품의 취소 및 반품, 교환요청시 배송비가 발생할 수 있습니다.
  • ㆍ반품신청시 반송된 상품의 수령후 환불처리됩니다.(카드사 사정에 따라 카드취소는 시일이 3~5일이 소요될 수 있습니다.)
  • ㆍ주문하신 상품의 반품,교환은 상품수령일로 부터 7일이내에 신청하실 수 있습니다.
  • ㆍ상품이 훼손된 경우 반품 및 교환,환불이 불가능합니다.
  • ㆍ반품/교환시 고객님 귀책사유로 인해 수거가 지연될 경우에는 반품이 제한될 수 있습니다.
  • ㆍ스프링제본 상품은 교환 및 환불이 불가능 합니다.
  • ㆍ군부대(사서함) 및 해외배송은 불가능합니다.
  • ㆍ오후 3시 이후 상담원과 통화되지 않은 취소건에 대해서는 고객 반품비용이 발생할 수 있습니다.
반품안내
  • 마이페이지 > 나의상담 > 1 : 1 문의하기 게시판 또는 고객센터 1800-7327
교환/반품주소
  • 경기도 파주시 문발로 211 1층 / (주)북채널 / 전화 : 1800-7327
  • 택배안내 : CJ대한통운(1588-1255)
  • 고객님 변심으로 인한 교환 또는 반품시 왕복 배송비 5,000원을 부담하셔야 하며, 제품 불량 또는 오 배송시에는 전액을 당사에서부담 합니다.