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What Is Algebra?

Algebra is one of the many branches of mathematics that deal with things like symbols, as well as the rule needed for changes those symbols. Elementary algebra, considered the introduction to algebra, uses those symbols to represent quantities that do not have fixed values, also known as variables. Words describe the relationship between different words, and algebraic equations are used to describe the relationship between different variables.

Algebra is helpful when it comes to the representation of problems or issues as math expressions. Typically, variables will be represented by letters like x,y, and z. Addition, subtraction, multiplication, and division are used to great sensical math expressions. Many other branches of mathematics use algebra as part of their own theories, such as trigonometry, geometry, calculus, etc.

Some examples of algebraic equations include the following:

  • x + y = 1,900
  • ⅔∙x – ½∙y = 500
  • (a – b)2 = a2 – 2ab + b2
  • (a + b)(a – b) = a2 – b2
  • 10x + 63 = y
  • ax + b = c

Algebra has many uses. Algebra is used to determine ranking in online search engines, as well as the testing of code for software engineering, machine learning, etc. Today, algebra is being used to solve supply chain problems in a number of countries. There are a number of different industries that use algebra regularly. Some positions include architects, economists, engineers, market research analysts, meteorologists, factory workers, and geologists. Algebra involves many different theories, from the algebraic theory to the Infinity Category Theory.

Common Subdisciplines of Algebra

  • Pre-algebra
  • Elementary algebra
  • Advanced algebra
  • Linear algebra
  • Commutative algebra
  • Abstract algebra
  • Universal algebra

How to Approach Learning Algebra

Algebra might seem a little intimidating if math isn’t your strong suit, but you need to just take a few simple steps to prepare for an algebra class.

To start, consider reviewing your basic math knowledge. In order to do well at algebra, you’ll need to be decent with basic mathematics skills and problem-solving. Review addition, subtraction, multiplication, and division before you start learning algebra. From there, revisit using exponents and parentheses.

You’ll also need to know the order of operations to excel at algebra. PEMDAS is a tool that helps:

  • Parentheses
  • Exponents
  • Multiplication
  • Division
  • Addition
  • Subtraction

This is the order in which algebraic equations are solved. A popular way to remember this order is through mnemonic expressions. We recommend memorizing the phrase “Please Excuse My Dear Aunt Sally.”

Once you have sufficiently memorized the order of operations, it’s time to approach learning algebra.

Algebra Student Curriculum FAQs

In most school systems, middle school students are taught pre-algebra and some elementary algebra. Pre-algebra will include concepts such as advanced arithmetic, fractions, spatial reasoning, basic geometry (such as the Pythagorean theorem), mathematical reasoning, etc.

From there, they will be taught some concepts from elementary algebra. Classes will usually involve teaching variables and basic operations using variables. Linear equations and some algebraic word problems may also be taught.

College algebra usually focuses on advanced algebra concepts. Typically, students will learn about radicals, quadratic equations, absolute value, and linear-quadratic systems. Some algebra classes in college, especially first-year courses, will simply revisit basic concepts from algebra. These include polynomials, factoring, functions, graphics, linear equations, and radicals.

Generally, students will be placed in the algebra class in college that suits their current understanding of algebra, based both on high school algebra grades as well as SAT and ACT scores in the mathematics section. This will be determined by introductory college testing.

For first and second-year algebra students, the following basic algebraic concepts are introduced: The formation of equations, set operations, advanced factoring, advanced linear equations, quadratic equations, exponents, radicals, polynomials, ratios, proportions, rectangular coordinates, rational expressions, and more.

When it comes to university algebra courses, specifically third and fourth-year courses, the algebra introduced is much more complex. Such courses include applied college algebra, linear algebra, abstract algebraic systems, honors algebra courses, and more.

The topics covered in university algebra courses also vary. In general, the following concepts are explored and taught for more advanced algebra students: Sequences, series, polynomial functions, conic sections, matrix transformations, semigroups, monoids, group theory, ring theory, field theory, module theory, linear transformations, euclidean vectors, and more.

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How Do I Become a Algebra Tutor?

If you have a passion for teaching others and love algebra, becoming an algebra tutor is easy. You need a minimum of a high school degree or GED to start teaching kindergarten and middle school grade levels. You may need a degree in a specialist subject for higher-level algebra courses depending on the level of practice you plan to teach. The costs of algebra tutors vary because you will set your pay rates and time schedules depending on your own experience and circumstances.

Your first step will be to decide which topics you’d like to tutor. Then choose the age groups and grade levels you want to teach. Learn the curriculum and critical concepts for those grade levels. And lastly, establish your teaching methods, tools, and eventually, you will create your own course materials over time as you get more experience working with students.

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