There are other options for graduate study in mathematics besides the most lucrative master’s degree, the master’s in applied mathematics. A different field of study and profession exists for applied math than for pure math. Work in applied math emphasizes the application of mathematical principles for real-world problems, while pure math explores mathematical knowledge for its own sake. The curricula for these two math-focused programs of study differ significantly from one another.
What is pure mathematics?
The study and investigation of theories and abstract mathematical concepts are included in pure mathematics. In this field of inquiry, experts frequently work in academic, research, and development settings rather than in practical ones. Although theory research and hypothesis development are supported by pure math, new applications for applied math are frequently supported by this math field’s concepts. A theoretical mathematician, for instance, might find a novel equation that has applications in the technology field. Due to this, careers in fields like information theory, quantum theory, and topology are more relevant to pure math majors.
What is applied mathematics?
In fields like science, technology, health care, and business, applying mathematical equations, concepts, and theories to solve analytical problems that arise in the real world is known as “applied math.” Applying analysis and practical formulas to develop solutions that advance various fields is the focus of a career in applied mathematics. For instance, applied mathematics is frequently required for finance and accounting procedures as the application of mathematical and statistical analysis is required for the calculations for various financial metrics. As a result, many students majoring in this field have the option of specializing in statistics, data analytics, or engineering.
Applied math vs. pure math
Although there are many ideas that are similar in both applied and pure mathematics, there are a number of differences that set them apart.
Coursework
A degree in either area of mathematics can support a wide range of career opportunities, but the program’s main areas of study are slightly different. Undergraduate students majoring in applied mathematics frequently take courses in topics like computational analysis, scientific and numerical computing, mathematical modeling, and applied algebra and probability. Many students can enter practical fields like computer and data science, mechanical engineering, or finance and accounting thanks to the coursework for applied math focuses.
The coursework for a degree in pure mathematics, however, frequently focuses on subjects in abstract algebra, discrete mathematics, complex variables, nonlinear dynamics, and general relativity. Additionally typical to many pure math degree programs are theoretical study and finishing of research projects. Additionally, a career in mathematics or pure math can frequently necessitate more advanced degrees because specialists in this field frequently hold academic positions, roles in research and development, and work for private institutions.
Applications
The applications of applied math are numerous, with a wide variety of uses for its ideas. For instance, in the medical industry, applied math is used to calculate patient data, complex surgical procedures, and medication dosage. The use of mathematical calculations in practice is essential to financial processes. Professionals in the field of technology also rely on applied math operations to finish tasks.
Pure mathematics and theoretical research have more applications in innovation and discovery than in practical fields. Mathematics-trained professionals frequently use their abilities in research, inquiry, and theory development. Topology and the study of quantum theory are two additional applications of pure mathematics where experts may contribute research findings and study results to support new developments in science and technology.
Career paths
Careers in applied math can be found across a wide range of industries because it places a strong emphasis on practical use. Consider a few occupations that require knowledge of applied mathematics:
On the other hand, careers in research inquiry are typically supported by degrees in mathematics or pure math. The roles listed below can shed light on the various pure math careers that set them apart from applied math careers:
Similarities between applied and pure mathematics
The intersection of each mathematical area of study offers opportunities to hone computation, analysis, modeling, and theoretical application skills. Other similarities between the two mathematicians are as follows:
Concepts
Both applied and pure mathematics undergraduate degree programs cover many of the same topics. For instance, a large number of undergraduate students study geometry, statistics, differential and multivariate calculus, number theory, and computation concepts. Topics can start to diverge when pursuing a graduate degree in either pure or applied mathematics as ideas build upon the fundamental mathematics covered in undergraduate coursework.
Skills
Many of the same skill sets are necessary for both mathematics disciplines, including analytical abilities, critical thinking, and problem-solving. Both pure and applied math require a variety of technical skill sets, including computational analysis, arithmetic, statistical analysis, and hypothesis testing. Both professionals in these fields use technical communication techniques to compute mathematical data and explain difficult concepts to others.
Modeling
Another overlapping application in both pure and applied mathematics is mathematical modeling. This is due to modeling requiring computational techniques, many of which have their roots in recently developed mathematical theories. Statistical analysis can be used in conjunction with theory evaluation in models that use mathematical computation. As a result, obtaining a degree in either field frequently necessitates the ability to organize and compute mathematical data into practical models.
Calculations
Both math fields depend on formulas, equations, and statistical measurement as calculations to contribute to both research and practical applications. For instance, a data scientist uses calculations in mathematics to choose the best algorithms to use in machine learning systems. A pure mathematics expert may use comparable calculations to create and publish research theories in astronomy or quantum physics. Despite the differences between the two professions, both disciplines rely heavily on mathematical calculations.
Tips to consider when choosing your math specialty
Consider the following advice as you examine your career options in mathematics to determine which field is best for achieving your objectives:
Consider your career interests
Think about the types of professional roles that interest you. Finance, business management, manufacturing, technology, engineering, and the sciences, including health care and medicine, frequently use applied math. For instance, a career in software development can frequently benefit more from a degree or certification with an applied math focus.
Research the skills you need
Additionally, both math fields call for particular skill sets for regular job duties. Theoretical mathematicians, for instance, might use their research and inquiry abilities more so than a mathematician whose career focus is on accounting and financial analysis projects. Knowing your current capabilities will enable you to choose the mathematical area that will best support your career advancement.
Think about your educational goals
Decide what you hope to achieve with your education and experience. For instance, some students opt to complete shorter technical certification programs in applied math disciplines like statistics and data science. On the other hand, a graduate or undergraduate degree might be better suited to supporting your ongoing mathematical advancement. It’s also crucial to think about your ideal timeframe for pursuing your credentials and the amount of money you can set aside for your educational objectives.
Talk with professionals in the field
Think about connecting with others in related fields of business and networking with mathematicians who can help you better understand your career options in both math fields. Expert data scientists, statisticians, theorists, and analysts are frequently able to respond to inquiries regarding job roles, typical responsibilities, and employer requirements. Finding the best career options for you can be aided by evaluating your options using primary sources and feedback.
Pure vs Applied Maths | MathsForUni
FAQ
Which is better applied or pure mathematics?
Research in pure mathematics is closely related to the practice of applied mathematics. It is superior to pure mathematics because it applies pure mathematics’ formulas to real-world situations. The goal of applied mathematics is to predict, model, and explain events in the real world.
Which is easier applied maths or pure maths?
Pure math is much more difficult. In applied math classes, students must memorize the steps to solve problems. However, proofs are a requirement for pure math classes, so knowledge of the subject is assumed.
Is algebra pure or applied math?
Analysis, which deals with continuous aspects of mathematics, algebra, which deals with discrete aspects, and geometry are the three main fields that make up pure mathematics. The undergraduate curriculum is structured so that students can become knowledgeable in each of these fields.
