…How do mathematicians solve problems? There have been few rigorous scientific studies of this question. Modern educational research, based on cognitive science, largely focuses on education up to high school level. Some studies address the teaching of undergraduate mathematics, but those are relatively few. There are significant differences between learning and teaching existing mathematics and creating new mathematics. Many of us can play a musical instrument, but far fewer can compose a concerto or even write a pop song. (more…)
2014/07/20
reading
廣告
2014/07/19
舊物: 1981 GCE AL Math 2
其實找到很多舊卷,希望有時間掃瞄多些。今天只貼 1981 年的
University of Cambridge
Local Examinations Syndicate
General Certificate of Education (Advanced Level)
Higher School Certificate (Overseas Centres Only)
Mathematics 2 (Syllabus A)
當中的 Q.16, (more…)
2014/07/18
2014/07/14
2014/07/12
[FW] 微積分的宗教秘史
微積分的宗教秘史
今日的積分學源自17世紀兩位數學家的爭辯,他們背後的動機究竟是數學還是宗教呢?
撰文/亞歷山大(Amir Alexander)
翻譯/鍾樹人
重點提要
■17世紀,義大利數學家卡瓦列里提出:任何平面都是由無窮多個線條構成,而任何立體則由無窮多個平面組成。他說,我們可以利用這些「不可分量」來計算長度、面積和體積──這是邁向現代微積分重要的一步。
■和卡瓦列里同時代的瑞士數學家古爾丁對此非常不認同,他批評不可分量不合邏輯,但這兩人的爭論並非全是出於數學理由。
■他們分屬兩個不同教派,雖然名稱類似,但兩方教派的哲學大不相同:古爾丁屬於耶穌會,而卡瓦列里則屬於耶穌教團。前者相信可利用數學把嚴密的邏輯結構強加在混亂的宇宙之上,後者則比較想順從直覺去了解複雜的世界。 (more…)