A Guide To Mathematics

by Charlie Snow
Depending on your goals, the type of math necessary may be different from other career fields. This article gives readers a basic overview of common STEM career fields and the mathematics required for each.
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Engineering: Despite the many different worlds of engineering (ex. Civic engineering vs chemical engineering), the math skills required are typically the same across the board. Engineering requires an understanding of algebra, linear algebra, multiple levels of calculus, and depending on what the program offers, trigonometry. Like most STEM fields, engineers also require a basic understanding of statistics and probability.

Computer Science: Computer science, like engineering, is a very broad field and mathematics requirements will depend on your specific interest or program, however, if you plan on majoring in computer science or IT or becoming a worker in the field, you should have a concrete understanding of algebra, discrete mathematics, calculus, and statistics.

Research: Research, or data science, can be done across many fields of interest and as such, the math requirements for particular jobs will be affected by what is being studied. For basic data science, however, one should familiarize themselves with algebra, calculus, and especially statistics.

STEM Careers With Basic Math:
While there are hardly any jobs out there that require absolutely no math, these next few career paths offer options for STEM oriented students who aren’t crazy about mathematics.

• Technicians: Technicians are responsible for operating machinery, such as X-Ray machines or medical equipment. While some math will be required to earn a degree or certificate, technicians’ jobs mostly operate around knowing how to work a specific machine, not crunching numbers.
• Technical Writers: Technical writers are responsible for creating tools such as tech manuals and writing directions for how to use certain technology. This job is great for students who may have an interest in technology or writing but who dislike mathematics.
• Diagnostic or Therapeutic Healthcare Careers: While this does not apply to all jobs in either field, diagnostic and therapeutic healthcare careers both deal with patient to staff interaction and directly providing medical care rather than billing for medical fees or filing medical records.
• Automotive Engineers: While these jobs do still require a substantial amount of math, it doesn’t use the more complicated mathematical concepts used by, say, aerospace engineers

STEM Careers With Advanced Math:

• Advanced Physics: Physics, which combines science with the mathematical concepts of algebra and calculus, is often thought of as one of the most difficult scientific/mathematical concepts to comprehend. Some of the most advanced mathematics being studied currently is theoretical and quantum physics.
• Data Analysts: Residing within the realm of research, data analysts require not only an in-depth understanding of statistics and probability, they also require a very deep understanding of linear algebra, as their job relies on using mathematical algorithms to find trends and similarities in the data they analyze.
• Aerospace Engineers: Aerospace engineers typically word on designing aircraft and spacecraft, a job that requires both mathematics and physics. Aerospace engineering is a very mathematically intense job that requires calculating velocities and using advanced concepts of calculus and physics.

So What are These Mathematical Concepts?

Algebra: Algebra, put simply, is mathematics that uses variables (ex. X and Y) to derive unknown variables such as proportions or percentages from mathematical equations. Algebra is divided into five subjects: Elementary Algebra, Advanced Algebra, Abstract Algebra, Linear Algebra, and Commutative Algebra. 

• Elementary Algebra: 
  • variables 
  • evaluating expressions/equations 
  • properties of equalities/inequalities, 
  • solving algebraic/linear equations with one or two variables
• Advanced Algebra:
  • Equations with inequalities
  • Matrices
  • Solving system of linear equations
  • Graphing functions and linear equations
  • Polynomial Equation
  • Quadratic Functions 
  • Polynomials 
  • Radicals
  • Sequences and series
  • Rational expressions
  • Trigonometry
  • Discrete mathematics 
  • Probability
• Abstract Algebra:
  • Sets
  • Binary Operations
  • Inverse Elements
  • Associativity
  • Identity Elements
• Linear Algebra:
  • Linear equations
  • Vector Spaces
  • Relations
  • Matrices and matrix decomposition
  • Relations and Computations

• Commutative Algebra:
  • Commutative algebra draws upon many other mathematical concepts in many different ways and is a large part of current pure mathematics

Calculus: Calculus has many applications and many branches that have either a wide or narrow application- or both.

• Standard (Infinitesimal) Calculus:

• Based on a system of derivatives and integrals
• Includes dozens of different types of calculus (vector calculus, exterior calculus)

• Real Analysis:
  • Part of ‘standard’ calculus
  • Expands off basic calculus and uses other mathematical concepts to prove formulas work
• Non-Standard Calculus:
  • Non-Newtonian Calculus
  • Stochastic Calculus

Statistics: Statistics is a method of analyzing and interpreting data in mathematical terms. Statistics can be split into two types: Descriptive and Inferential.

• Descriptive: Descriptive statistics is used to describe the data collected. This can mean describing the distribution of data, the mead, the median, the range, exct.
• Inferential: Inferential statistics is used to interpret the meaning of descriptive statistics on order to make predictions and inferences based on the data collected.

Sources:
https://www.wgu.edu/blog/how-much-math-computer-science-require2110.html#close 
https://bestaccreditedcolleges.org/articles/careers-and-education/what-math-courses-are-required-for-engineering-majors.html 
https://www.businessinsider.com/high-paying-jobs-for-people-who-dont-like-math-2016-3#2-pediatrician-21 
https://byjus.com/maths/algebra/ 
https://byjus.com/maths/types-of-statistics/ 
https://www.calculushowto.com/different-types-of-calculus/ 

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