2026년 02월 23일 출간 | ISBN : 1125104791 | 308쪽 | 규격外 | 1판

Ⅰ 문제를 통한 수학적 사고의 이해 수학의 어원 ·············································································· 002 수학의 7가지 속성 ·································································· 003 ① 핵심접근, 근본적 이해 ·············································· 003 쾨니히스베르크 다리 문제 ························································· 003 체스 문제 ·················································································· 005 기사의 여행 문제 ······································································ 006 오일러 그래프, 해밀턴 그래프 ···················································· 009 플뢰리 알고리즘 ········································································ 010 5개의 컵 문제 ··········································································· 011 물통 문제 ·················································································· 012 세 개의 산 문제 ········································································ 016 미로 찾기 ·················································································· 018 보드게임 SET ··········································································· 023 ② 엄밀한 논리, 논증 ······························································ 030 플라톤 ······················································································ 031 윌리엄 블레이크의 〈태고의 나날들〉 ··········································· 032 폴 에이드리언 모리스 디랙 ························································ 033 겔만과 쿼크 그리고 군 ······························································· 034 자연과학의 속성 ········································································ 036 칼 포퍼 ····················································································· 038 유클리드와 원론 ········································································ 038 ㆍ 목 차 ㆍ iv 목차 ③ 창조성, 독창성, 다양성 ····················································· 043 피타고라스 정리의 증명(가필드의 증명법) ·································· 044 피타고라스 정리의 증명(박부성의 증명법) ·································· 045 피타고라스 정리의 증명(바스카라의 증명) ·································· 046 흥미로운 평면기하 문제들 ························································· 046 수학계의 흥미로운 논문들 ························································· 047 수학계의 흥미로운 미해결 문제들 ·············································· 056 ④ 아름다움, 순수성 ································································ 059 수학의 아름다움에 대한 철학자, 수학자, 물리학자들의 주장 ······· 059 소수의 무한개수 증명 ································································ 062 테일러 전개식 ··········································································· 064 복소수의 아름다움 ···································································· 066 오일러 지표 ·············································································· 071 수학에서의 아름다움 ································································· 073 바젤 문제와 리만제타함수 ························································· 075 데자르그의 정리 ········································································ 079 파푸스 정리 ·············································································· 079 파스칼의 정리 ··········································································· 081 아름다운 수학공식 10선 ···························································· 081 ⑤ 위태로운 벽돌 쌓기 ··························································· 083 러셀의 역설 ·············································································· 084 ⑥ 무한대를 다룬다 ································································· 085 칸토어의 집합론 ········································································ 086 선택 공리 ·················································································· 089 연속체 가설 ·············································································· 090 괴델의 불완전성 정리 ································································ 091 목차 v ⑦ 유용성 ···················································································· 092 울릉도에서 독도가 보이는가? ···················································· 093 숫자 맞추기 ·············································································· 095 앨런 튜링 ·················································································· 101 루이 브라유 ·············································································· 101 모스부호 ··················································································· 103 만물은 수이다. ·········································································· 103 주민등록번호 ············································································ 105 성냥개비 게임 ··········································································· 106 아이스크림 31게임 ···································································· 107 국제수학올림피아드 ·································································· 108 게임이론 ··················································································· 110 초콜릿 게임 ·············································································· 111 신과의 치킨 게임 ······································································ 112 존 내쉬 ····················································································· 113 파푸스 정리 ·············································································· 113 몽주 ························································································· 114 수학적 모델링 ··········································································· 115 로트카-볼테라 모델 ·································································· 115 빅토리아 호수의 나일퍼치 이야기 ·············································· 117 빅토리아 호수의 부레옥잠 이야기 ·············································· 118 금융수학 ··················································································· 118 CT 사진의 원리 ········································································· 123 라돈 변환 ·················································································· 124 고속 푸리에 변환(FFT, Fast Fourier Transform) ························· 125 연습문제 ····················································································· 126 집합론 부록 ··············································································· 133 vi 목차 Ⅱ 생활속의 수학 수학과 영화 ·············································································· 144 마방진 ······················································································ 148 최석정과 라틴방진 ···································································· 154 오일러와 직교 라틴방진 ····························································· 157 지수귀문도 ················································································ 158 스도쿠 ······················································································ 159 마방진 난제 ·············································································· 162 샘 로이드 퍼즐 ·········································································· 165 미국의 3대 퍼즐 작가 ································································ 170 런던 지하철과 위상수학 ····························································· 171 회전 드럼 문제 ·········································································· 171 인간 vs 인공지능의 역사 ··························································· 171 행렬 ························································································· 178 Alpha max plus beta min algorithm ········································· 181 페이지 공식 ·············································································· 183 구글 입사 문제 ·········································································· 185 하노이의 탑 ·············································································· 192 체스판 위의 쌀 ·········································································· 194 어느 자선 사업가의 선행 ··························································· 194 케빈 베이컨의 6단계 ································································· 195 스탠리 밀그램의 실험 ································································ 196 A4 용지의 수학 ········································································· 196 빨간 풍선을 찾아라! ·································································· 202 복면산 ······················································································ 203 선교사와 식인종 문제 ································································ 208 목차 vii 필즈상(Fields Medal) ································································ 211 3대 수학상 ················································································ 213 브레이크스루상 ········································································· 214 경제학과 수학 ··········································································· 215 안정적인 결혼 문제 ··································································· 216 정보 이론 ·················································································· 220 논리 퍼즐 ·················································································· 221 부자의 유언 문제 ······································································ 229 간단한 숫자 마술 ······································································ 230 가중투표제 ················································································ 231 권력지수 ··················································································· 234 연습문제 ····················································································· 237 Ⅲ 생활속의 확률과 통계 확률이란 무엇인가 ···································································· 246 확률의 정의 ·············································································· 247 확률의 역사 ·············································································· 248 확률의 덧셈 법칙과 곱셈 법칙 ··················································· 252 확률에서 논란이 되는 문제 ························································ 253 오자의 개수 ·············································································· 257 보드게임 SET의 기댓값과 확률 ·················································· 257 확률을 이용한 정상과 비정상 구분하기 ······································ 260 1993년 LA 다저스 81승 81패 경기 결과 ······································ 261 동전 1000번 던지기 ·································································· 263 viii 목차 홀인원 확률 ·············································································· 264 남녀 폐암 발병 확률 ·································································· 266 로또 확률과 기댓값 ··································································· 266 은하계 로또 게임 ······································································ 268 자신에게는 엄격하고 남에게는 너그러운 확률 ···························· 269 이기적 유전자 ··········································································· 271 정액 베팅과 정률 베팅 ······························································· 274 베이즈 공식 ·············································································· 275 코로나의 확률 ··········································································· 277 코로나 백신의 위험성은? 278 연습문제 ····················································································· 281 참고문헌································································································ 283?