Applied Math Vs. Pure Math: Differences And Similarities

By Indeed Editorial Team

Published 6 September 2022

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

Studying mathematics at a university might interest you if you enjoy working with numbers, statistics, physics, mechanics and geometry. As a mathematician, you can work across many industries and might concentrate on theoretical or applied mathematics. Knowing about different mathematics majors, including pure math and applied math, can help you choose the right one for your career. In this article, we discover what pure math and applied math are, review the differences and similarities between applied math vs. pure math and explore the tips for choosing the right course.

Defining Applied Math Vs. Pure Math

Before comparing applied math vs. pure math, it is essential to consider the definition of these two terms:

What is applied math?

Applied mathematics involves the application of mathematics to problems and practical usage of mathematical equations and concepts for solving real-world analytical problems in the field of technology, healthcare, science and business. The field primarily involves pattern and analysis recognition to predict trends accurately and how things might happen in the future. A career in applied math focuses on using formulas to create a solution that can benefit different areas. Applied mathematics requires a professional to know computation techniques and algorithmic applications.

Often, professionals in this field can specialise in data analytics, engineering and statistics. Interestingly, applied mathematics requires the application of mathematical and statistical evaluation. Some common industries where you can work after your applied mathematics course are:

  • Engineering

  • Research and development

  • Banking

  • Financial consulting

Related: Types Of Mathematics Courses (With How-To And Careers)

What is pure math?

Pure mathematics involves the study and research of abstract mathematical concepts and theories. Even though pure mathematics support hypothesis development and research, the concept of pure mathematics support innovation and application in applied mathematics. Professionals who study pure mathematics primarily work in research, academics and development areas rather than focusing on the practical application of mathematics. Students might study subjects like geometry, analysis and algebra during the pure math course. This course helps in increasing your problem-solving, modelling and critical thinking skills. Some industries where pure mathematicians can work are:

  • Computing

  • Insurance

  • Teaching

  • Finance

  • Medical and scientific research

Related: Important Statistics Skills And Tips To Develop Them

Differences Between Applied Math Vs. Pure Math

Although applied and pure mathematics have overlapping concepts, these two differ from one another in various aspects:

Coursework

In applied mathematics, students pursue undergraduate courses that teach physics, systems design, calculus, computational mathematics, computer science, optimisation theory, differential equations, linear algebra and numerical analysis. The coursework a student studies in applied math can help them enter the computer and data science, finance, accounting and mechanical engineering field.

In comparison, students pursuing undergraduate courses study subjects like multivariate calculus, modelling, linear algebra, discrete mathematics, differential equations, geometry, topology, nonlinear dynamics, complex variables and general relativity. These subjects help solve problems, find facts and answer questions that focus on the rule of mathematics. Typically, a career in pure mathematics requires an advanced degree as these professionals work in academics, private institutions and the research and development field.

Related: Top 15 Careers In Mathematics (And Salary Information)

Career paths

As applied mathematics focuses on practical use, a career in this field allows you to work in different roles. Some professions that depend on applied mathematics are:

  • Data analysts

  • Auditor

  • Advisor

  • Portfolio analyst

  • Engineer

A degree in pure mathematics primarily supports a career in academics and research. Some professions that depend on pure mathematics are:

  • Theoretical physicist

  • Topologist

  • Mathematics professor

  • Mathematical researcher

Related: How To Become A Data Analyst: A Complete Guide

Application

Both the fields of mathematics find their usage in various fields. Pure mathematics focuses on practical fields and helps in innovation and discovery. For instance, applied math relates to surgical procedures, medicine dosage and patient data in the medical field. Many financial processes often focus on applying mathematical equations and concepts practically. Even in the technology field, applied math helps in completing work-related projects.

Professionals studying pure mathematics help in research and theory development. Some other areas where pure mathematics finds its usage are the study of quantum theory and topology. Professionals in topology and quantum theory focuses on research findings and supports new development in technology and science.

Branches

The three significant areas of applied mathematics include statistics, optimisation and differential equations. These areas have many sub-branches, such as machine learning, optimal design, discrete mathematics and Fourier analysis. Some important branches of pure mathematics include geometry, algebra, calculus, statistics and geometry.

Use of calculus

Calculus is the fundamental component of both applied and pure mathematics. In applied mathematics, calculus helps in solving problems related to mechanics. Pure mathematics uses calculus to find tangent lines of arbitrary geometries and calculate areas of different figures.

Ease of study

Applied mathematics requires a slightly different set of capabilities and skills than pure mathematics. The former focuses on deductive reasoning but requires a broader knowledge of science and technology. In comparison, pure mathematics requires deductive reasoning and critical thinking skills.

Related: How To Use Deductive Reasoning

Similarities Between Applied And Pure Mathematics

Many overlapping concepts in applied and pure mathematics help students study modelling, theoretical application, computation and mathematical analysis. Some similarities between applied and pure mathematics are:

Concepts

When pursuing a bachelor's degree in pure or applied mathematics, you are likely to cover certain concepts that overlap with each other. Some concepts to study include differential calculus, number theory, multivariate calculus, computation, geometry and statistical analysis. When pursuing a career in pure and applied mathematics, these topics can diverge as concepts and help build on basic mathematics.

Skills

Students pursuing applied and pure mathematics require similar skill sets. To succeed in applied and pure mathematics, students require analytical, problem-solving and critical thinking skills. Both the courses require technical skills, such as statistical evaluation, arithmetic and hypothesis testing. These professionals rely heavily on technical communication methods to compute mathematical data and communicate complex topics to others.

Related: How To Improve Analytical Skills (With Steps And Benefits)

Calculations

Professionals working in the pure and applied mathematics field focus on using formulas, statistical measurements and equations that help contribute to research and application. For instance, a data scientist might rely on mathematical equations and theories to use in machine learning systems. A professional in the pure mathematics field might use similar equations and concepts to publish quantum physics and astronomy theories. While the application and use of both disciplines differ, the dependency on mathematical calculations and equations is the same.

What To Consider When Choosing Between Applied And Pure Mathematics

Use these tips to consider when choosing between two disciplines:

Research the skills you need

Both the mathematics discipline requires different skills. For example, theoretical mathematician focuses on applying their research and concepts more than mathematicians who primarily focus on accounting and financial analysis project. Knowing your current skills level can help determine which math field is ideal for your career and supports advancement in your profession.

Know your career interest

When choosing a mathematics field, consider the professional roles that might interest you. For instance, applied math is helpful in finance, business management, engineering, science and technology industries. For instance, courses in pure mathematics can help you enter the field of academics and research. Knowing your career interest can help you make an informed career decision.

Related: How To Set And Achieve Long-Term Goals (With Examples)

Consider your educational goals

Another thing to consider before choosing a career path is understanding the education you want to complete. For instance, some professionals might pursue technical certification in applied mathematics, like statistics and data science. In addition, you can pursue a bachelor's degree for continuous advancement in your field. Think about the educational budget and time you can spend studying these courses. Based on these answers, you can make an informed decision.

Take help from your professional network

Before choosing between these two courses, network with your industry professionals to understand the pros and cons of each field. Experienced statisticians, data scientists and theorists can help you answer your questions about the job, its responsibilities and employer requirement. The more you research and collect information, the easier it can become to choose a viable career option.

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