What is Algebra?

Mastering algebra is crucial for high school students as it prepares them for college-level math courses. (Jason Snipes & Neal Finkelstein, WestEd). 

But what is Algebra? And, why is it such a crucial stepping stone in your mathematical education?

Algebra is the branch of mathematics that expresses problems through numbers, letters, and symbols. The numerical values in algebra are not constant. So, you need to assign a constant symbol (x,y, or z) to the changing numerical values for their identification. The symbols do not have a fixed numerical value and are called variables. 

The given numbers, letters, and symbols undergo various mathematical operations to determine the missing values.

But that’s not all about Algebra. In this article, we will discuss:

• Algebra topics
• Resources to learn Algebra
• What are the 5 types of Algebra
• Importance of learning Algebra

Looking to Learn Algebra? Book a Free Trial Lesson and match with top Algebra Tutors for Concepts, Homework Help, and Test Prep.

Algebra topics

Think of Algebra like a big tree with many branches (types of courses). Each branch has smaller branches (topics) and leaves (subtopics).

As you progress academically, you learn about different branches and topics of Algebra. Here’s a list of the main topics you’ll learn about:

Symbols and Algebraic Expressions

• Polynomial Expressions
• Rational Expressions
• Arithmetic and Finite Geometric Series

Linear Equations

• Real numbers as points on the number line
• Integers
• Linear equations and their graphs
• Solving problems with linear equations
• Linear inequalities and their graphs
• Graphing and solving systems of simultaneous linear equations

Quadratic Equations

• Factors and factoring of quadratic polynomials with integer coefficients
• Completing the square in quadratic expressions
• Quadratic formula and factoring of general quadratic polynomials
• Using the quadratic formula to solve equations

Cubic Equations

• 3D Geometry

Sequence and Series

• Arithmetic progression
• Geometric progression

Exponents

• Rational exponents
• Radical expressions
• Exponential functions

Functions

• Linear functions
• Quadratic functions – word problems involving quadratic functions
• Graphs of quadratic functions and completing the square
• Polynomial functions (including graphs of basic functions)
• Simple nonlinear functions (e.g. – square and cube root functions; absolute value; rational functions; step functions)
• Logarithmic functions
• Trigonometric functions
• Fitting simple mathematical models to data

Algebra of Polynomials

• Roots and factorization of polynomials
• Complex numbers and operations
• Fundamental theorem of algebra
• Binomial coefficients (and Pascal’s triangle)
• Mathematical induction and the binomial theorem

Combinatorics and Finite Probability

• Combinations and permutations as applications of the binomial theorem and Pascal’s Triangle 

What are the 5 types of algebra?

Based on the complexity and use of expressions Algebra can be divided into five major types, as given below:

• Elementary Algebra
• Advanced Algebra
• Abstract Algebra
• Commutative Algebra
• Linear Algebra

Elementary Algebra

Elementary Algebra is a basic level of algebra that focuses on the fundamental concepts. Think of it as the first chapter of the algebra journey, where you learn the basics before tackling the complex stuff. 

In elementary algebra, you will come across essential topics such as variables, constants, and basic operations. You learn simple formulas and concepts like a+b=b+a.

These topics form the groundwork for students to build a solid understanding of algebraic principles and problem-solving techniques.

📖Recommended Reading: What is Pre-Algebra?

Advanced Algebra

Advanced algebra, also known as intermediate algebra, increases the complexity of concepts. This level of algebra delves into more abstract ideas. 

Within this advanced algebra framework, you will practice topics like quadratic equations, polynomials, functions, matrices, and systems of equations. 

Abstract Algebra 

Abstract Algebra is a branch of algebra that deals with the most advanced concepts. It involves an algebraic system with groups, rings, fields, and other abstract algebraic structures. 

In Abstract Algebra, we move beyond specific numbers and equations, focusing on broader structures and patterns. The subjects covered in Abstract Algebra are Sets, Operations in Binary, Inverse Elements Identify Elements, and Associativity.

💡Wondering when to take Algebra 1 and Algebra 2? In What Grade Should You Take Algebra 1 and Algebra 2?

Commutative Algebra

Commutative Algebra focuses on a specific type of algebraic structure. In this field, we explore commutative rings and their properties. These rings adhere to the commutativity rule, meaning the order of multiplying elements doesn’t alter the outcome.

Commutative algebra delves into these structures, ideals, and modules, providing a deeper grasp of the connections between algebraic elements. 

Linear Algebra

Linear Algebra focuses on linear equations and their connections. It also considers how things change in linear ways between different sets of numbers. It also explores planes and lines as part of the deal.  

In linear algebra, the key concepts covered are linear equations in vector space, matrix decomposition and matrices, computations, relationships, and relations.

📖Recommended Reading: What is Linear Algebra?

Resources to learn algebra

Learning algebra is tricky, and having the right resources can make it less challenging for you. You can get help from various online resources such as lessons, Web Tutorials, and YouTube videos. The resources help you: 

1. Revise an Algebra lesson.
2. Assess your Algebra skills.
3. Learn a specific Algebra topic in depth.

Here are the reliable resources to help you learn Algebra. Make sure to choose a resource that best suits your learning style.

Free algebra worksheets

Math worksheets allow you to practice and improve your math skills. The questions in the math worksheet are based on important formulas from the specific lesson.

Here are popular websites for free Algebra worksheets:

1. Math Drills 
2. Math Worksheets for Kids
3. Algebra Worksheets

Free online lessons for algebra 

You can find free online lessons on certain YouTube and Edtech platforms like Khan Academy. They help you explore and dig deeper into the lessons anytime, anywhere. 

1. Khan Academy:  For course-specific audio and video lessons.
2. YouTube: For exploring the course in detail with math experts.

The popular YouTube channels that provide Algebra lessons are:

• MIT OpenCourseWare

• 3Blue1Brown

• Math is Fun

Algebra books 

If you grasp your lessons best when learning from books, here are the top Algebra books you can choose from:

1. Spectrum Algebra by Carson-Dellosa Publising LLC.  
2. Introduction to Algebra by Richard Rusczyk 
3. Practical Algebra by Stephen L. Slavin and Peter H. Selby 

Algebra tutoring

Sometimes, learning Algebra on your own can be a tough challenge, and you may need expert help. You can find online platforms that offer personalized help with concepts, homework, and test preparation for Algebra:

1. Wiingy: For quality and affordable 1-on-1 tutoring, homework help and test-prep with Algebra tutors.
2. Chegg: For homework help.
3. The Princeton Review: For test prep.

💡Wondering if Algebra is a hard math course? Read – Is Algebra Hard?

Importance of Algebra in education and career

The benefits of learning Algebra go beyond mere mathematical proficiency. It equips you to navigate various academic and professional challenges. It enhances logical reasoning. Learning Algebra is important because it can help you in the following ways:

Lay a strong foundation for advanced math

Algebra serves as the foundation for understanding advanced math subjects like statistics and calculus.

Statistics is essential for analyzing data. Data analysis plays a crucial role in business, science, and social sciences.

Similarly, Calculus is used by scientists and engineers. It helps them describe complex processes and develop new technologies and medical treatments.

Build STEM career opportunities 

According to the U.S. Bureau of Labor Statistics, employment in STEM occupations is projected to grow by 8% from 2020 to 2030.  To secure a good future in the STEM field with competitive salaries, you must do well in math and sciences. 

Algebra is a valuable math skill that can open doors to various job opportunities in STEM fields. Many careers, including those in business, science, engineering, and technology, require a strong understanding of algebra. 

Enhance logical thinking

The process of simplifying and solving algebraic equations can be intellectually rewarding. Algebra reinforces logical thinking and problem-solving skills. 

It challenges individuals to break down complex problems into manageable steps. Practicing Algebra also develops your critical thinking and problem-solving skills.

🥇Looking for the best tips to learn Algebra? Read: How to Learn Algebra?

Key takeaways on “What is Algebra?”

Algebra is a type of math that uses symbols, letters, and numbers to solve math problems. In Algebra, variables are used to identify changing values (numbers). These variables are represented by symbols like x, y, or z.

Algebra has five branches:

Elementary Algebra, Advanced Algebra, Abstract Algebra, Linear Algebra, and Commutative Algebra.

To improve at Algebra, you can find many helpful resources like worksheets, books, and online videos.

If you need extra help, you can also get one-on-one tutoring from experienced Algebra tutors. They can help you with personalized homework, study materials, and test prep.

Algebra is an important subject for middle and high school students because it lays the foundation for learning other advanced math courses like Calculus, Trigonometry, and Geometry. So, if you’re interested in STEM courses, learning Algebra is important!

📖Recommended Reading:

• What is Algebra 1?
• What is Algebra 2?

Looking to Learn Algebra? Book a Free Trial Lesson and match with top Algebra Tutors for Concepts, Homework Help, and Test Prep.

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