定理(Theorem)、命題(Proposition)、輔助定理(Lemma)、引申定理(Corollary)、假設(Assumption)

名詞定義：
定理(Theorem)、命題(Proposition)、輔助定理(Lemma)、引申定理(Corollary)、假設(Assumption)

名詞解釋

Theorem：就是定理，比較重要的，簡寫是 Thm。

Lemma：小小的定理，通常是為了證明後面的定理，如果證明的篇幅很長時，可能會把證明拆成幾個部分來敘述，雖然篇幅可能變多，但脈絡卻很清楚。

Corollary：推論。由定理立即可推知的結果。

Property：性質，結果雖然值得一記，卻沒定理來的深刻。

Proposition：有人翻譯為「命題」， 有些作者喜歡用，大概也可以算是比較簡單的定理的一種稱呼。

Claim：證明時先敘述一個結果，再作證明。看的人比較輕鬆。

Note：通常只是一個註解。

Remark：涉及一些結論，比較起來 "Note" 比較像說明， "remark" 則常是非正式的定理。

至於「定義」可以想成是一個若且唯若的定理,

Lehrer Tom

video: Tom Lehrer singing some math themed songs

Thomas Andrew "Tom" Lehrer (born April 9, 1928) is an American singer-songwriter, satirist, pianist, and mathematician. He also lectured on mathematics and musical theater.

Lehrer is best known for the pithy, humorous songs he recorded in the 1950s and 60s. His work often parodied popular song forms, notably in "The Elements", where he sets the names of the chemical elements to a tune from Gilbert and Sullivan. Lehrer's earlier work frequently dealt with trivial subject matter, but he also produced a number of songs dealing with the social and political issues of the day, particularly when he went on to write for the TV show That Was The Week That Was.

Lehrer earned his BA in mathematics (Magna Cum Laude) from Harvard University in 1947, when he was 18. He received his MA the next year, and was inducted into Phi Beta Kappa. He taught classes at MIT, Harvard and Wellesley. He remained in Harvard's doctoral program for several years, taking time out for his musical career and to work as a researcher at Los Alamos, New Mexico. He joined the Army from 1955 to 1957, working at the National Security Agency. (Lehrer has been rumored to have invented the Jello Shot during this time, as a means of circumventing liquor restrictions.^[3] ) All of these experiences eventually became fodder for songs: "Fight Fiercely, Harvard", "The Wild West Is Where I Want To Be" and "It Makes a Fellow Proud to Be a Soldier", respectively. There was perhaps some truth to his comment in the intro to the latter song, in which he said he had left the Army and was now in the "Radioactive Reserve".

In 1960, Lehrer returned to full-time studies at Harvard. However, he never completed his doctoral studies, and never received a PhD in mathematics (pig ah, haha~~~). In 1972, he joined the faculty of the University of California, Santa Cruz, teaching an introductory course entitled "The Nature of Mathematics" to liberal-arts majors — "Math for Tenors", according to Lehrer. He also taught a class in musical theater. He still occasionally performs songs in his lectures, primarily those relating to the topic [2].

Math jokes and videos

Math love song by the Klein Four (There are lots of puns using math terms in here: group, function, relationship, etc.

Statistics rap video!

Tom Lehrer singing some math themed songs

Math jokes

More math jokes