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数学用語 - dizmox - 2012-09-08
I made a deck to help me with mathematics terminology in Japanese, so if anyone wants to use it, feel free. There's basically a one-to-one correspondence with English so can do this English -> Japanese output. Of course this isn't comprehensive but I think it serves as a good start. If there are any core areas I've missed out or you want me to upload it in some particular format do say.
To add it to a deck, just copy+paste this list into a .txt file and import into Anki.
Edit: realised this doesn't work when copying from this post, so I uploaded the deck here for now. http://www.2shared.com/file/U-9C3XuD/_online.html
Edit: Uploaded it as a shared deck for Anki 2.0 now!
probability space 確率空間
absolute value 絶対値
expectation 期待値
consecutive integers 連続する整数
((strict)sub)set （（狭義・真）部分）集合
(sub)group （部分）群
(sub)ring （部分）環[かん]
arithmetic mean 相加平均
median 中央値
mode 最頻値
divisibility 割り切れること
natural number 自然数
factor 因数、約数
multiple 倍数
positive/negative number (excluding 0) 正の数, 負の数
odd / even 奇数 / 偶数
prime number 素数
reciprocal 逆数、反数
sequence （数）列
nth decimal place 少数第n位
nth digit 第n桁目
tangent (trigonometry) 正接
sine 正弦
cosine 余弦
coefficient 係数
bisector 二等分線
circumference (of circle) 円周
perimeter 周
base (geometry) 底辺
area, volume 面接、体積
right angle 直角
opposite/vertical angles (are equal) 対頂角 （は等しい）
hypotenuse 斜辺
cube 立方体
cuboid 直方体
cylinder 円柱、円筒
isosceles triangle 二等辺三角形
scalene triangle 不等辺三角形
trapezium 台形
(inverse/identity) element, element of a set （逆/単位）元、要素
stochastic process 確率過程
(random) variable （確率）変数
(dis, right)continuous function （不、右）連続関数
topological space 位相空間
vector space ベクトル空間
integration, differentiation 積分法, 微分法
equation 方程式
inequality 不等式
orthonormalisation 正規直交化
projection (onto vector space) 射影
orthogonal basis 正規基底
normed linear (sub)space ノルム線型（部分）空間
relative topology 相対位相
subspace topology 部分空間位相
induced topology 誘導位相
measure (theory, space) 測度（論、空間）
generalisation 一般化
theorem 定理
proposition 命題
corollary 系
differentiable 微分可能
tangent line, tangent point 接線、接点
recurrence relation 漸化式[ぜんかしき]
expression 表現式
solution (of equation) 解
map (function) 写像
functional equation 関数等式
indefinite integral 不定積分
identity/inverse matrix （単位、逆）行列
to take the inverse, transpose (e.g. of a matrix) 逆・転置を行う
isometry 等長写像
metric (function), metric space 距離（関数）, 距離空間
ellipse, ellipsoid 楕円、楕円体
Itou isometry 伊藤の等距離性
martingale マルチンゲール
for all times n 任意の時刻 n について
measurable 可測
stopping time 停止時刻
partial differential equation 偏微分方程式
Brownian motion ブラウン運動
rational number, irrational number, rational function 有理数、 無理数、有理関数
real number 実数
imaginary number (part) 虚数（部）
complex number 複素数
third order polynomial 三次の多項式
(partial) derivative （偏）微分、（偏）導関数
real variable function 実関数
limit 極限
converge, diverge 収束・収斂[しゅうれん]、発散
series 級数
term by term integration/differentiation 項別微分、項別積分
uniqueness 一意性
taking values in X Xに値を取る
(absolute, pointwise, uniform) convergence （絶対、点別、一様）収束
manifold 多様体
curve, surface 曲線, 曲面
optimisation 最適化
convex/concave (function, set) 凸/凹 （関数、集合）
combinatorics 組合せ数学
topology (mathematical field) 位相幾何学
shape 図形
category (theory) 圏（論）
trigonometry 三角法
univariate/multivariate polynomial 一変数多項式/多変数多項式
quotient ring 剰余環、商環
invertible 可逆
independence (probability) 独立性
similar (matrices) 相似
rank (matrix) 階数
factorial 階乗
exponential function 指数関数
natural logarithm 自然対数
base of a logarithm 対数の底
satisfying (conditions) 満たす
finite 有限
field (algebra) 体
smooth 滑らか
square 正方形
cone, square pyramid 円錐, 四角錐
prism, hexagonal prism 角柱, 六角柱
local/global 局所的/大域的
polyhedron 多面体
probability measure 確率測度
symmetry 対称性
permutation 順列
axiom 公理
differential form 微分形式
diagonal matrix 対角行列
upper triangular matrix 上三角行列
transposed matrix 転置行列
eigenvalue, eigenvector 固有値、固有ベクトル
determinant 行列式
quadratic equation 二次方程式
monotonic (strictly, non-)increasing/decreasing 単調（狭義、非）増加/減少
associativity 結合法則, 結合性
commutativity 交換法則, 可交換性
transitive relation 推移関係
right(-angled) triangle 直角三角形
composition (of functions) 合成
countable, uncountable 可算, 非可算
bijection, bijective 全単射、全単射的
injection, injective 単射, 単射程
one-to-one correspondence 一対一対応
surjection, surjective 全射, 全射程
force 力
central limit theorem 中心極限定理
perturbation 摂動
(to follow a) normal distribution 正規分布(に従う)
functional 汎関数
distributivity, distributive 分配法則, 分配的
Hermitian conjugate, conjugate transpose matrix エルミート共役, 共役転置行列
self conjugate, self adjoint 自己共役、自己随伴
operator 作用素
(linear, Fourier) transform （線型、フーリエ）変換
complex conjugate 複素共役
singular matrix 特異行列
remainder 余り
transposition 移項
general (term, solution) 一般（項、解）
factorisation 因数分解
right hand limit/derivative 右方極限値, 右方微分係数
symmetric with respect to the X-axis X軸対称の
Y as a function of X Xの関数Y
derivative of n-th order ｎ次導関数
a to the power b a の b 乗
binary, hexidecimal 二進法、十六進法 [しんほう]
torus 円環体
operation 演算
circular sector 扇形 [おうぎがた]
polygonal line 折れ線
round number おおよその数、概数
polygon 多角形
approximation 概算
outer product 外積
difference 階差、 差分
circumscribed circle 外接円
estimate 概測
extraction of square/cube root 開平/開立
probability density function 確率密度関数
cumulative distribution function 累積分布関数
convert 換算
cardinal number 基数
cardinality 濃度
irreducible 既約
common factor 共通因数
collinear 共線の
polar coordinates 極座標
local minimum/maximum 極小値, 極大値
approximate value 近似値
empty set 空集合
event (probability) 事象
sample space 標本空間
coordinate origin 原点
subtraction 減法、引き算
point of intersection 交点
radian ラジアン、弧度
characteristic equation 固有方程式
the least common multiple 最小公倍数
lowest common denominator 最小公分母
Pythagorean theorem 三平方の定理
e ネイピア数
Pi 円周率
greatest common divisor 最大公約数
periodic function 周期関数
(sufficient, necessary) condition （十分、必要）条件
elimination 消去
conditional probability 条件つき確率
division 除法、割り算
addition 加法、足し算
multiplication 乗法、掛け算
proper fraction 真分数
improper fraction 仮分数
mixed fraction; compound number 帯分数
continued fraction 連分数
numerator 分子
drop a perpendicular line 垂線を引く
regular isosahedron 正２０面体
constant of integration 積分定数
asymptotic line 漸近線
segment AB 線分AB
tangent plane 接平面
be coprime to （～と互いに）素である
process with independent increments 独立増分過程
factorize into prime factors 素因数分解する
correlation 相関関係
hyperbola, Hyperbolic geometry 双曲線、双曲的幾何学
(stratified) sampling （層化）抽出法
summation 総和
belong to ～ （～に）属する
nth term 第n項
contraposition (A⇒B is equivalent to ¬B⇒¬A) 対偶
proof by contradiction 背理法
simple interest 単利
histogram ヒストグラム, 柱状グラフ
parallelogram 平行四辺形
midpoint 中点
harmonic series 調和級数
system 系
Cartesian coordinates 直交座標
reduction of a fraction (to lowest terms) 約分
reduction to common denominator 通分
(Taylor's) formula （テイラーの）公式
concentric 同心
geometic series 等比級数
open/closed interval 開区間/閉区間
simultaneous equation 連立方程式
power (root) 冪乗（根）、累乗（根）
to square ２乗する
rate of interest 利率
random numbers 乱数
complementary event 余事象
explicit function 陽関数
implicit function 陰関数
Euclidean algorithm ユークリッドの互除法
significance (level) 有意（水準）
be approximately equal to ～ 約～に等しい
infinitesimal 無限小数
random sampling, random sample 無作為抽出、無作為標本
product set, Cartesian product 直積集合、デカルト積
inclusion 包含
integration by parts 部分積分
partial fraction 部分分数
partial sum 部分和
Fermat's little theorem フェルマーの小定理
be directly proportional to ～ （～に）比例する
repeated trials 反復試行
half-plane 半平面
counter-example 反例
discriminant (polynomial) 判別式
be inversely proportional to ～ （～に）反比例する
exclusive events 排反事象
random inspection 抜き取り検査
binomial (coefficient, theorem, expansion, distribution) 二項（係数、定理、展開、分布）
inscribed circle 内接円
inner product 内積
independent (event, trial) 独立（事象、試行）
geometric mean 幾何平均
intersection 交わり、積集合
union 和集合
difference set (eg. A/B) 差集合
complementary set 補集合
symmetric difference 対称差
inclusion-exclusion principle 包除原理
(dis, simply)connected space （非、単）連結空間
null (measure) set 零集合
completeness (of measure, metric space, etc.) 完備性
linear combination 線型結合
linearly independent/dependent 線型独立、線型従属
linear span of x1,...,xn x1～xnの張る線型部分空間、線型包
closure (topology) 閉包
interior (topology) 内部
boundary (topology) 境界
locus 軌跡
accumulation point, limit point 集積点、極限点
neighbourhood 近傍
domain of a function 定義域
homomorphic, homomorphism 準同型、準同型写像
isomorphic, isomorphism 同型、同型写像
countable additivity 可算加法性
power set 冪集合
pre-measure 有限加法的測度
Jordan normal form ジョルダン標準形
gaussian quadrature ガウス求積
vector calculus ベクトル解析
curvature 曲率
gradient (vector calculus) 勾配
divergence (vector calculus) 発散
curl (vector calculus) 回転
divergence theorem (vector calculus) 発散定理
homeomorphic, homeomorphism 位相同型・同相、同相写像
separable space 可分空間
compact space コンパクト空間
bounded (operator, set, function, etc.) 有界（作用素、集合、関数）
bounded from above (below) 上（下）に有界である、上（下）から抑えられる
partially/totally ordered set 順序集合、全順序集合
AND, OR, NOT, implies, is equivalent to (logic) かつ、または、～ではない、ならば、同値である
lemma 補題
quarternion 四元数
arithmetic 算術
numerical analysis 数値解析
Newton's method ニュートン法
decimal part 小数
geometric distribution 幾何分布
joint probability 結合確率
marginal probability 周辺確率
posterior (probability, distribution) 事後（確率、分布）
prior (probability, distribution) 事前（確率、分布）
almost everywhere, almost surely, almost all ほとんど至るところで, ほとんど確実に, ほとんど全ての
Markov chain マルコフ連鎖
(angular) momentum （角）運動量
discrete mathematics 離散数学、有限数学
cofactor matrix 余因子行列
(Taylor) expansion （テイラー）展開
path integral 線積分
closed contour integral 周回積分
arc (length) 弧（長）
(infinitesimal) line element, surface element, volume element 線素、面素、体素
units digit, hundreds digit 一の位、百の位[くらい]
parabola 放物線
Möbius strip メビウスの帯
Klein bottle クラインの壺
totally bounded set 全有界集合
sigma-algebra 完全加法族、可算加法族、σ-加法族、σ-集合体、σ-代数、σ-集合族
moment (generating function) モーメント、積率（母関数）
characteristic function 特性関数
empirical distribution (function) 経験分布（関数）
analytic function 解析関数
complex analysis 複素解析
holomorphic function 正則関数
conformal map 等角写像
power series 冪級数
n-times differentiable n回微分可能
contraction mapping 収縮写像
to derive (a formula, etc.) 導く
to find (a value, etc.) 求める
fundamental group 基本群
ideal イデアル
scheme 概型
abstract algebra 抽象代数
fundamental theorem of (algebra, calculus, etc.) ～の基本定理
Abelian group アーベル群
transcendental number 超越数
Diophantine equation ディオファントス方程式
linear regression 線形回帰
queuing theory 待ち行列理論
applied, pure mathematics 応用数学、純粋数学
Galois theory ガロア理論
proof 証明
interpolation 内挿、補間
error 誤差
disjoint sets 素集合
entire function 整関数
Legendre transform ルジャンドル変換
n-dimensional n次元
数学用語 - NijiRanger - 2012-09-08
I really have to sleep now, but I just wanted to say that you are super awesome for making this, and I'll check it out properly tomorrow.
数学用語 - vileru - 2012-09-08
Thanks! I have some background in mathematical logic, so it's interesting to know the Japanese counterparts of the terms used in the field. Unfortunately, I haven't had a chance to use those terms in Japanese yet, but at least I know I have this great resource available when I do.
数学用語 - kitsu - 2012-09-09
It would be awesome to group them by similar level/field (i.e. arithmetic, algebra, trigonometry, linear algebra, calculus, formal logic, programming). Alphabetic isn't the best grouping for math topics.
It looks very thorough though, Good job!
数学用語 - dizmox - 2012-09-10
If someone volunteers to group them for me please do. (・∀・)
I don't really know much about mathematical logic I'm afraid... mostly probability/statistics/analysis/topology (+ a basic level of some other things).
数学用語 - NijiRanger - 2012-09-10
Thank you for your hard work, I'll definetly be using this.
I love the way they use kanji for almost everything, it makes it so elegant and logical. (Like math should be!)
Also, a couple I have in my math deck that I couldn't find here; 導く - to derive, and 求める - to find.
数学用語 - Irixmark - 2012-09-10
Awesome work dizmox!
This might be the only E->J cards in my deck... although I know that someone will now insist on J->J with definitions and an example sentence, as in \int_{-1}^1 f(x)\,dx \approx \sum_{i=1}^n w_i f(x_i) ですね。
数学用語 - dizmox - 2012-09-10
NijiRanger Wrote:Also, a couple I have in my math deck that I couldn't find here; 導く - to derive, and 求める - to find.Added~ I'll be updating the list as I find more.
数学用語 - imabi - 2012-09-10
I must say, this is a very great resource.
数学用語 - dizmox - 2012-09-10
I'm glad people will find it it useful. I decided I better add new words to the end of the list (instead of just inserting them in the middle) so people can update their decks more easily if they want. The list is now in order of words added, so anyone inconvenienced by this before now should be able to find the ones they're missing without any trouble.
When it reaches equilibrium I'll upload it as a shared deck I suppose.
数学用語 - CharleyGarrett - 2012-09-12
I'm a bum. I don't know how to import the text file into anki. Please post again when the deck has been shared. That'll work.
数学用語 - dizmox - 2012-09-12
Hmm, you're right it's not importing properly (pasting onto here must have altered the formatting).
Since:
Quote:As Anki 2 is due out soon, uploading of shared decks and plugins for the old version of Anki has been disabled.I uploaded the deck to here for now. http://www.2shared.com/file/U-9C3XuD/_online.html