College Math vs. Algebra: The Differences Explained
Sometimes in college, you will choose between a few classes to complete a requirement for your degree program. Unless you are studying math or a math-based major like engineering, you will likely have some flexibility to choose the math courses you take. One of the most common choices that schools offer is between college math and algebra, but what are the differences?
College math differs from college algebra in that the math course covers a wide range of math concepts, including algebra, geometry, trigonometry, and precalculus. In comparison, an algebra course will cover topics like functions, systems, exponents, inequalities, graphing, and logarithms.
This article will explain the differences between college math and algebra and cover topics in each class. Then, we explain what other math courses colleges offer and what math courses are required for math majors. Finally, we have some resources that you can use to learn more about college math, college algebra, and other college math courses.
College Math vs. Algebra
College math and algebra may sound like they are the same classes, but there are a few differences between the two. In the most general sense, algebra is a specific type of math, whereas a “math” class will cover a wide variety of math topics, including algebra.
First, let’s compare the general definitions of math and algebra.
Merriam-Webster defines mathematics as:
The science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.
On the other hand, Merriam-Webster defines algebra as:
A generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic.
So, algebra is a branch of mathematics, and mathematics covers much more than just algebra. Colleges decide which math classes they will offer to students, whether it be general math, algebra, or both.
You Might Have a Choice Between the Two Classes
Depending on your major, you may have a choice in which math class or classes you take, or you may be required to take specific ones. In general, math-focused majors require higher-level classes like calculus and differential equations.
Most other students will just have to take a math or algebra course and may have a choice in the matter.
Compared to an algebra class, the general math class will likely be easier since it covers a wider range of topics. On the other hand, the algebra class will dive deeper into algebra topics specifically.
There are also two CLEP, or college level examination programs, exams covering college math and college algebra. The algebra exam is harder and more in-depth, and there are four topics covered on the exam.
As for the math exam, it is broader and covers seven topics, with twenty percent of the exam covering algebra.
College Math: Topics Covered
If you’re taking a general math course in college, it will cover a wide variety of topics, depending on what level you are studying and what the college’s mathematics department decides is most important.
A basic math class is generally meant for students who do not need anything more than a general math class to complete their degree requirements. If you do not need to take a calculus class for your major, there is little reason to take one. This class will cover your math requirement without having to enroll in anything too specific or advanced.
Students can also take a class like this as a refresher or prerequisite to higher-level math classes.
Here is an example of the topics covered in a college math course, from a Math 100 syllabus (source):
- Whole Numbers
- Signed Numbers
- Basic Algebra
- Proportion and Percentages
- Formula and Application Problems
- Powers and Roots
As you can see, algebra is part of the curriculum for a college math class, but instead of being the only topic covered as it would be in an algebra class, it is 10% of the math class. But, remember that this is only an example of what a college math class might cover.
Every school will have a slightly different curriculum.
Furthermore, some colleges skip over algebra and basic math concepts because they expect students to study these in high school and not relearn them in college.
For example, Harvard’s first math class offered to students is an introduction to calculus. The requirement for the class is an understanding of precalculus, which students should learn in high school (source).
College Algebra: Topics Covered
Knowing basic, college-level algebra concepts is important if you are taking more advanced math courses.
The beginning of an algebra course teaches students how to solve algebraic equations, including variables, systems, and inequalities. Word problems sometimes require students to determine which algebraic equations they need to solve a problem or graph the equations to visually represent the problem.
Furthermore, algebra classes require students to use logs and exponential functions to solve problems.
Let’s look at an example of what topics a college algebra course might cover (source).
- Basic Equations and Inequalities
- Graphs, Lines, and Functions
- Integer Exponents and Polynomials
- Rational Expressions
- Fractional Exponents and Radicals
- Functions, Exponential Functions, and Logarithms
These topics will vary slightly depending on the college and whether or not the algebra class is meant as a prerequisite for another course or to fill a math requirement for non-math majors.
Let’s look at an example of a college that offers multiple algebra courses.
First, there is a lower-level algebra class designed for liberal arts and science students, which covers the most basic algebra topics like:
These are topics that are crucial to understanding for anyone going into another math course.
Then, students can take the second level of college algebra once they complete the one above or prove proficiency in the topics covered in that class.
This second algebra class covers:
- Coordinate geometry
- Rational expressions and equations
- Linear and quadratic equations
- Nonlinear inequalities
The first algebra class is meant as a course for non-math majors that will fill a math requirement. The second course is meant as an algebra basis for math, science, engineering, and other math-related majors (source).
Other Math Courses
College math and algebra are not the only math courses that colleges offer. As with anything that universities offer, there will be variations of what colleges offer, but colleges will generally offer similar classes.
Let’s look at the math classes offered by a certain college as an example (source):
- Topics for mathematical literacy
- College algebra
- Trigonometry and analytical geometry
- Calculus I
- Calculus II
- Calculus III
- Differential Equations
- Concepts of Real Analysis
- Linear Algebra
- Algebraic Structures
- Complex Analysis
The first two classes listed are the college math and algebra classes discussed in this article.
All the other classes listed cover other topics, and most of them require algebra as a prerequisite, or they are taken as an alternative to algebra.
The first class listed is the basic math class made for students who need to complete a general math requirement but do not need anything specific or anything too advanced. The college algebra class can also fulfill a requirement or prerequisite to more advanced math classes like calculus.
Most majors are fine to just take college algebra or math, but others will need to take other, more advanced classes like calculus.
Let’s look at what majors are typically required to take calculus classes (source):
- Engineering majors
- Business majors
- Math majors
- Computer science
- Environmental science
- Public Health
Most other majors will not need to take calculus, but just a general math class, which can be college math, algebra, calculus, or any other math course that the student is interested in.
If you enjoy math enough, you can study mathematics as your degree program.
In this case, you will likely skip over the basic college math and algebra courses that we have been discussing thus far. Instead, you will start in a higher-level math course because you should have a background in algebra, precalculus, and other basic math topics before enrolling in a mathematics program.
Let’s look at what being a math major entails.
At Yale, students majoring in math have to take 10 advanced math courses, some of which are electives, and some are required for all math students.
The required math courses are linear algebra, analysis, and multivariate calculus. There are also seminars and essay classes required for math majors, typically taken senior year after you have a foundation of the other classes you must take.
Then, there are seven other math classes that you must take, and you can choose these seven classes.
Here are the five categories of math classes that you can choose from:
- Algebra, combinatorics, and number theory
- Logic and foundations
- Geometry and topology
- Applied mathematics
There are also other classes that do not fit into these categories that will count for your math electives.
Some of these classes are listed below:
- Optimization techniques
- Computer programming courses, like algorithms
- Mathematical economics classes, like game theory
- Information theory
- Statistical inference
There are other classes and requirements that you need to complete as a math major. These requirements usually depend on what type of math degree you are working towards.
Here are the common variations of math degrees:
- Bachelor of Science in Mathematics
- Bachelor of Arts in Mathematics
- Bachelor of Science in Applied Mathematics
- Mathematics Minor
Sources: Yale and North Central College
College Math and Algebra Resources
If you are studying math, algebra, or both at a college level, you need to study hard to understand the topics. Math builds on itself, so if you don’t understand the most basic concepts, you will not be able to study more advanced topics. The resources in this section will help you learn and practice college math and algebra.
Intro to College Math (link to Amazon) is a great book for anyone taking college math. It covers arithmetic, geometry, algebra, and statistics with examples, practice problems, and complete solutions.
There are also great resources for college math students on YouTube, like the full, basic college mathematics playlist from Dana Mosely. More than sixty videos in this series cover topics like:
- Whole numbers
- Financial math
- Science-based math
Algebra I For Dummies and Algebra II For Dummies is a book series, found on Amazon.com, that teaches you the most important concepts in algebra in an easy-to-understand way. Both books have practice problems, and examples taught using methods similar to those used in a college algebra course.
Another great resource for learning algebra is the full algebra course on YouTube from freeCodeCamp.org. This course has more than 6 ½ hours of content and is taught by Dr. Linda Green, a professor at the University of North Carolina.
Finally, if you are taking college algebra or need to brush up on your algebra skills before taking other math classes, there is an online course offered by Study.com.
The course covers graphs, linear equations, systems and includes practice problems.
College math covers a wide range of math topics, including:
- Algebra and Trigonometry
On the other hand, college algebra covers algebra topics solely, like:
- Systems at an in-depth level
Lower-level classes can be used as a prerequisite for more advanced math courses like calculus or taken by non-math and science majors to fill a general education requirement. No matter why you are taking either course, know that math is typically a little easier than algebra since it is a broader range of topics.