Algebra is a branch of mathematics that uses symbols and letters to represent numbers and quantities in equations and formulas.
Core Mathematical Branch
EN: A branch of mathematics concerning the study of symbols and the rules for manipulating them to solve equations.
翻譯: 代數學，數學的一個分支，研究符號以及操縱這些符號以解方程的規則。
Abstract Structure
EN: A mathematical structure involving operations like addition and multiplication defined on a set of elements.
翻譯: 一種數學結構，涉及在一個元素集合上定義的加法、乘法等運算。
School/University Subject
EN: A course or subject taught in schools and universities that introduces the basic concepts of algebraic manipulation.
翻譯: 在學校和大學中教授的課程或科目，介紹代數運算的基本概念。
小提醒：Remember that 'algebra' refers to the abstract system and methods, not just the simple act of solving for 'x'. It's a broad field, not a single equation.
點擊下方的 US / UK 按鈕可播放發音。
Real-life Examples of "Algebra" from YouTube Videos
Arthur Benjamin: Teach statistics before calculus!
TED
“The mathematics curriculum that we have is based on a foundation of arithmetic and algebra, And everything we learn after that is building up towards one subject, And at top of that pyramid it's calculus.”
1. a branch of mathematics that uses letters and symbols to represent numbers and quantities in formulas and equations
代數學，一門使用字母和符號來表示公式和方程式中的數字與數量的數學分支
In high school, students usually take a course in algebra.
在高中，學生通常會修一門代數課程。
Solving for 'x' is a fundamental skill in algebra.
解出 'x' 是代數中的一項基本技能。
2. a system of algebra based on a particular set of axioms or rules
基於特定公理或規則的代數體系
Boolean algebra is essential for computer science and logic circuits.
布林代數對於計算機科學和邏輯電路至關重要。
Linear algebra deals with vector spaces and linear mappings.
線性代數研究向量空間和線性映射。
3. abstract symbolic manipulation and the study of mathematical structures
抽象的符號運算及對數學結構的研究
Modern algebra explores groups, rings, and fields.
現代代數探討群、環和域。
Her research is in the field of abstract algebra.
她的研究領域是抽象代數。
| Pattern | Meaning | Example |
|---|---|---|
| algebra + of + noun | ...的運算 | The algebra of matrices is fundamental to computer graphics. (矩陣代數是電腦圖形學的基礎。) |
| study + algebra | 學習代數 | She decided to study algebra over the summer. (她決定在暑假期間學習代數。) |
| apply + algebra | 應用代數 | Engineers apply algebra to solve complex design problems. (工程師應用代數來解決複雜的設計問題。) |
| abstract algebra | 抽象代數 | Abstract algebra deals with algebraic structures like groups and rings. (抽象代數處理如群和環的代數結構。) |
| Boolean algebra | 布林代數 | Boolean algebra is essential for digital circuit design. (布林代數對於數位電路設計至關重要。) |
EN:Linear algebra and abstract algebra are two important algebras.
翻譯:線性代數和抽象代數是兩種重要的代數結構。
在大多數日常及教育情境中，將 algebra 視為不可數名詞使用即可；僅在專業數學語境下區分不同結構時，才需使用其可數形式。
algebra vs arithmetic
algebra 是使用符號和變數來研究數學結構和關係的抽象數學分支；arithmetic 則是處理數字基本運算（加減乘除）的具體計算。
algebra vs geometry
algebra 主要透過符號和方程式研究數量關係；geometry 則透過圖形、形狀和空間屬性研究結構關係。
algebra vs calculus
algebra 研究靜態的數學關係和方程式；calculus 研究變化率（微分）和累積量（積分）的動態數學。
在對話中，當引述或提及自己或他人正在學習、使用或討論代數時，會用這個詞。 EN: I was talking to my tutor, and she said, "Once you get the hang of algebra, the rest makes more sense." 翻譯: 我跟我的家教老師聊天，她說：「一旦你掌握了代數，其他部分就會更容易理解。」
EN:He looked at the problem and was like, "This isn't just algebra; it's a logic puzzle."
翻譯:他看著那道題目，然後說：「這不只是代數，這是一個邏輯謎題。」
用來強調某件事像代數一樣複雜、抽象或需要系統性思考，有時帶有誇張或幽默的語氣。 EN: Planning this family reunion is like doing advanced algebra with too many variables. 翻譯: 籌劃這次家庭聚會就像在做變數太多的進階代數題。
EN:Don't ask me to explain their relationship; it's pure emotional algebra to me.
翻譯:別叫我解釋他們的關係，對我來說那完全是情感代數。
在思考如何解釋複雜或逐步推導的事情時，可能會用「algebra」作為一個暫時的比喻或填充詞。 EN: So the process is... well, think of it as a kind of social algebra—you balance different interests. 翻譯: 所以這個過程是…嗯，把它想成一種社會代數——你要平衡不同的利益。
EN:Figuring out the bill... let's do the algebra here: you had the appetizer, I had the entrée...
翻譯:算一下帳單…我們來做個代數運算：你點了開胃菜，我點了主菜…
正式寫作注意：在學術論文或正式報告中，應避免將「algebra」用於比喻或語氣強調。正式文體中，此詞應嚴格指數學分支「代數」本身。
the basics of algebra
the basics of [noun]
代數的基礎知識
linear algebra
[adjective] algebra
線性代數
solve an algebra problem
solve an [noun] problem
解一道代數題
do algebra homework
do [noun] homework
做代數作業
abstract algebra
[adjective] algebra
抽象代數
take an algebra class
take an [noun] class
上代數課
Boolean algebra
[proper noun] algebra
布林代數
algebra textbook
[noun] textbook
代數教科書
×I need to buy an algebra.
✓I need to buy an algebra textbook.
"Algebra" is an uncountable noun referring to a branch of mathematics. You cannot buy "an algebra". You buy a book about algebra or study algebra.
×I have difficulty with the algebra.
✓I have difficulty with algebra.
When referring to the general subject or field of study, "algebra" is used without the definite article "the". Use "the" only when specifying a particular type or instance (e.g., "the algebra we learned yesterday").
×We studied many different algebras in class.
✓We studied many different algebra concepts in class.
"Algebra" is generally uncountable. To refer to different types or branches, use "types of algebra", "areas of algebra", or "algebra concepts". The plural "algebras" is highly specialized (referring to distinct algebraic structures) and not used in general learning contexts.
×I have a test on algerbra next week.
✓I have a test on algebra next week.
A common spelling mistake is swapping the "e" and "b", writing "algerbra". Remember the correct order is a-l-g-e-b-r-a.
×This is algebra's basic rule.
✓This is a basic rule of algebra.
While not grammatically incorrect, using the possessive form (algebra's) for abstract, uncountable fields like mathematics is uncommon and sounds awkward. It's more natural to use "of algebra" or "in algebra".
×I need to calculate the algebra for this problem.
✓I need to use algebra to solve this problem.
"Algebra" is not something you calculate. It is a tool or method you *use* to calculate or solve problems. Common collocations are "use algebra", "do algebra", "apply algebra", or "solve using algebra".