Is Pre Calculus Harder Than Linear Algebra?

When students first delve into higher mathematics, the initial question usually is, “Is Pre-Calculus harder than Linear Algebra?”. This question is particularly relevant for students choosing between one or the other or preparing to take both simultaneously in college.

An immediate glance at both subjects brings to mind the complexities of each course, with unfamiliar symbols and complex problems. As you may suspect, the truth is a little more contextual  and really depends upon your learning style..

In this blog, we will lay out both subjects, in order of their level of difficulty, and assist you in determining which course might be the better fit for you. Our tutors at Mathpracs will help you prepare and understand the foundational knowledge of each course, and prepare you for components that make the learning of both calculus and linear algebra easy, less intimidating, and fun to learn.

Understanding the Basics:

How is Pre-Calculus different from Linear Algebra?

Pre-Calculus

Pre-Calculus is a branch of mathematics concerned with change and motion that is taken as a prerequisite to Calculus. It builds on the algebra skills you’ve already learned and introduces new topics like exponential and logarithmic functions, trigonometry, and sequences. The focus lies in understanding the different types of functions and how they transform based on certain transformations, how they can be illustrated on a graph, analyzed, and used to model real-world situations. Pre-Calculus also helps to sharpen your skills in solving equations, working with inequalities, and mitigating complex numbers.

Students regularly learn or experience more than one type of calculus:

• Polynomial, rational, exponential, and logarithmic functions
  
• Trigonometric identities and functions
  
• Complex numbers
  
• Conic sections (parabolas, ellipses, hyperbolas)
  
• Sequences and Series
  
• Limits and applying Limits to Functions
  
• Basic Combinatorics and Probabilities

Linear Algebra

Linear algebra is a branch of mathematics that centers around vector spaces and the linear relationships between them. It involves working with vectors, matrices, systems of equations, and various transformations. 

This area of study is essential to many contemporary fields, including computer graphics, machine learning, and engineering.

Here are some key concepts in linear algebra:

• Matrices and matrix operations
• Eigenvalues and eigenvectors
• Systems of linear equations
• Vector spaces
• Linear transformations

Although the course you take depends on what suits your learning style the best, most students prefer taking Linear Algebra first. Linear Algebra as a course does an awesome job to review some of the basic algebra concepts you learnt in middle school or high school, and helps you be well-prepared for Pre calculus. 

Concepts vs. Calculations

Pre-Calculus is very procedure based. First, you generally go for a step by step approach in either differentiating or integrating functions. After you figure out the basic formulas, the process becomes more intuitive with practice. 

Linear algebra is more abstract. You need to reason about different spaces, dimensions and transformations in ways that might not always be tangible or easy to grasp. You will need to gain some conceptual clarity often without fully visualizing the actual mechanics behind it. 

For some individuals, the structure of logical rules and formulas which outline the calculations makes PreCalculus easier to understand; and for others who enjoy the puzzles and patterns, linear algebra makes more sense. 

Visual vs. Abstract

You frequently imagine curves in PreCalculus and visualize different geometric figures in mathematics and the changes occurring in those curves.

While drawing 2D or 3D vectors is possible in linear algebra, in higher dimensions concepts, it is generally not intuitive from a spatial perspective.

Use of Algebra

In most cases, algebraic manipulations require relativistic calculus. Understanding the theory over simplification is more important in linear algebra.

Real-World Applications

These disciplines are beneficial in real life for the following reasons:

Motion, heat, and growth are explained using calculus in physics, engineering, and biology.

Data science, machine learning, and 3D graphics rely heavily on concepts shadowed by linear algebra.

If you are enrolled in a STEM course, you will probably use both disciplines, but the most applied subject will depend on your academic focus and major.

How MathPracs can help you Master both

Many students will tell you that linear algebra seems easier to learn due to its abstract nature, whereas PreCalculus is built on topics from linear algebra like understanding the rate of changes, matrices and spaces with relatively little intuition.

At the same time, Linear Algebra can be overwhelming at times because it requires hefty hours of practice for you to achieve mastery and well prepare for high level courses. That’s why MathPracs has built a platform that’s all about making complex nonfiction simple and easy to grasp, by connecting you with tutors offering to help you learn and master these concepts. 

 Here’s what we offer:

• In-depth lesson plans.
• Detailed instructions on each major concept and topic.
• Real world examples and problems pertaining to the concepts being learnt.
• Explain why each topic is important in the field of mathematics.
• Personalized homework and help aiming to help you get ahead of everyone!

Conclusion

In the final analysis, the best course to take might not be reflective of everyone’s perspective, but mostly people choose to go and learn linear algebra prior to taking any calculus level classes, as it is a more systematic approach to learn the concepts in mathematics.. It all depends on your learning style, your previous background in mathematics, and current strengths.

If you prefer to solve specific problems by memorizing formulaic steps, you might find PreCalculus less challenging. If you have good facility at thinking abstractly and like to see patterns, you will probably find linear algebra to be a better suit like most people..

So don’t suffer through math on your own. Whether you are just starting to venture into the world of vectors or are moving on to integrals, tutors at MathPracs will help you learn challenging math concepts, and make them easier to grasp.

Get started right away at MathPracs, where math becomes easy..