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Mathematicians

Conduct research in fundamental mathematics or in application of mathematical techniques to science, management, and other fields. Solve problems in various fields using mathematical methods.

What EWU math students are doing right now

See all 6 projects →

Avista Hydropower

2024
Partner: Avista Utilities

Dynamic power management for a hydropower facility with multiple turbines. EWU students built optimization models that balance load across turbines in real time.

Linear programming Nonlinear programming MATLAB Computational optimization
Outcome: MAA-sponsored industry partnership

Columbia Lighting LitePro

Ongoing
Partner: Columbia Lighting R&D

Custom radiosity software for computing light intensities in critical environments. Alumnus-led project that took applied mathematics from theory to shipping production code.

Radiosity theory Software engineering Numerical methods
Outcome: Production software at Columbia Lighting

What education do people in this job actually have?

O*NET incumbent survey (2024)
Bachelor's degree 10% Graduate degree 90%

How EWU courses prepare you for this work (12 of 12 O*NET tasks have course evidence)

  • Employ the appropriate numerical technique to approximate a solution of an initial value problem, boundary value problem, or partial differential equation, with careful consideration of initial or boundary data.
  • Demonstrate the ability to analyze algorithms to interpolate data with polynomials.
  • Compute local truncation error and understand its relationship to the global error in a given numerical scheme.
  • Construct finite-difference schemes in order to approximate solutions to differential equations and analyze their order of approximation

use numerical schemes to find approximate solutions to initial value problems utilizing mathematical software such as Matlab or Mathematica.

  • Compare the error from a numerical calculus approximation to the corresponding error estimate;
  • Implement a numerical approximation to a solution of an initial value problem;
  • Employ and analyze a prescribed method to find a root of a nonlinear equation (with knowledge of the strengths and weaknesses of the approach);
  • Compute volumes using a variety of methods
  • Apply differential and integral calculus techniques to trigonometric functions, exponential functions, logarithmic functions and the inverses of these functions

Apply the techniques of multiple integration and partial derivatives to applied problems

  • Utilize quantitative methods to analyze linear and non-linear systems of differential equations
  • Perform linear stability analysis
  • Utilize qualitative methods to analyze linear and non-linear systems of differential equations
  • Implement an iterative method to solve a problem (e.g. matrix decomposition, solution of a linear system of equations, determining eigenpairs of a matrix)
  • Provide details of backward stability analysis of an iterative scheme;

Model a physical signal by using mathematical functions, and solve the equations when excited by an arbitrary function.

Analyze the asymptotic performance of algorithms.

Use mathematical software to approximate solutions of biological models

Apply number theoretic techniques to cryptography

Work with the applications of geometric transformations in the sciences

  • Interpret output from statistical software correctly
  • Use the least squares method to estimate parameters

Apply iterative methods for solving systems of equations of at least two non-linear equations

Determine the big-Oh growth rate of an algorithm.

Independently research mathematical concepts

  • Compute areas under a curve
  • Demonstrate the role of continuity in evaluating limits graphically and numerically

Apply classical solution techniques to differential equation models of physical systems

Analyze a signal both in time domain and in frequency domain.

use numerical schemes to find approximate solutions to initial value problems utilizing mathematical software such as Matlab or Mathematica.

  • Employ the appropriate numerical technique to approximate a solution of an initial value problem, boundary value problem, or partial differential equation, with careful consideration of initial or boundary data.
  • Demonstrate the ability to analyze algorithms to interpolate data with polynomials.

Implement an iterative method to solve a problem (e.g. matrix decomposition, solution of a linear system of equations, determining eigenpairs of a matrix)

Apply the techniques of multiple integration and partial derivatives to applied problems

Apply group theoretic concepts to solve mathematical problems

  • Explain the relationship between matroids and different algorithms for solving problems
  • Identify the complexity class of a problem
  • Implement a program that uses an array to solve a problem.
  • Write, compile and execute a complete program for a given problem.
  • Independently research mathematical concepts
  • Synthesize pertinent mathematical background material
  • Apply differential and integral calculus techniques to trigonometric functions, exponential functions, logarithmic functions and the inverses of these functions
  • Compute volumes using a variety of methods

Use mathematical software to approximate solutions of biological models

Apply classical solution techniques to differential equation models of physical systems

Model a physical signal by using mathematical functions, and solve the equations when excited by an arbitrary function.

  • Employ and analyze a prescribed method to find a root of a nonlinear equation (with knowledge of the strengths and weaknesses of the approach);
  • Implement a numerical approximation to a solution of an initial value problem;

Work with the applications of geometric transformations in the sciences

Apply iterative methods for solving systems of equations of at least two non-linear equations

  • Utilize quantitative methods to analyze linear and non-linear systems of differential equations
  • Utilize qualitative methods to analyze linear and non-linear systems of differential equations

Apply number theoretic techniques to cryptography

  • Apply basic linear algebra to economic problems.
  • Solve simple differential equations focusing on topics in economics.

Analyze the asymptotic performance of algorithms.

  • Independently research mathematical concepts
  • Synthesize pertinent mathematical background material
  • Apply group theoretic concepts to solve mathematical problems
  • Apply group theoretic concepts to the natural sciences
  • Apply classical solution techniques to differential equation models of physical systems
  • Construct partial differential equation models for physical systems
  • Apply differential and integral calculus techniques to trigonometric functions, exponential functions, logarithmic functions and the inverses of these functions
  • Demonstrate knowledge of relationships between exponents and logarithms and their derivatives
  • Demonstrate the ability to perform integration by applying one of the following techniques: Powers of trigonometric functions, Trigonometric substitution, Algebraic substitution, Method of parts, Partial fractions for the linear and the quadratic case

Apply the techniques of multiple integration and partial derivatives to applied problems

Work with the applications of geometric transformations in the sciences

  • Solve simple differential equations focusing on topics in economics.
  • Apply basic linear algebra to economic problems.

Apply number theoretic techniques to cryptography

  • use numerical schemes to find approximate solutions to initial value problems utilizing mathematical software such as Matlab or Mathematica.
  • set up and solve second order, constant coefficient differential equations that arise from physical systems such as mass-spring systems and RLC circuits.  In addition, students will have a strong intuition of the phenomenon of resonance.

Employ the appropriate numerical technique to approximate a solution of an initial value problem, boundary value problem, or partial differential equation, with careful consideration of initial or boundary data.

Model a physical signal by using mathematical functions, and solve the equations when excited by an arbitrary function.

Employ and analyze a prescribed method to find a root of a nonlinear equation (with knowledge of the strengths and weaknesses of the approach);

  • Utilize qualitative methods to analyze linear and non-linear systems of differential equations
  • Utilize quantitative methods to analyze linear and non-linear systems of differential equations

Implement an iterative method to solve a problem (e.g. matrix decomposition, solution of a linear system of equations, determining eigenpairs of a matrix)

Use mathematical software to approximate solutions of biological models

  • Identify the complexity class of a problem
  • Explain the relationship between matroids and different algorithms for solving problems
  • Model a physical signal by using mathematical functions, and solve the equations when excited by an arbitrary function.
  • Describe each of the following system categories: Linear, nonlinear, time-invariant, time-varying, causal, noncausal, memoryless, continuous-time, discrete-time etc.

Independently research mathematical concepts

  • Apply classical solution techniques to differential equation models of physical systems
  • Construct partial differential equation models for physical systems
  • Contextualize partial differential equation models of physical systems
  • Visualize models graphically
  • Use mathematical software to approximate solutions of biological models
  • Interpret dynamics of discrete and continuous models
  • Construct model equations from a description of a biological system
  • Utilize quantitative methods to analyze linear and non-linear systems of differential equations
  • Utilize qualitative methods to analyze linear and non-linear systems of differential equations

Program a memory management simulation.

Work with the applications of geometric transformations in the sciences

  • use numerical schemes to find approximate solutions to initial value problems utilizing mathematical software such as Matlab or Mathematica.
  • set up and solve second order, constant coefficient differential equations that arise from physical systems such as mass-spring systems and RLC circuits.  In addition, students will have a strong intuition of the phenomenon of resonance.
  • Employ the appropriate numerical technique to approximate a solution of an initial value problem, boundary value problem, or partial differential equation, with careful consideration of initial or boundary data.
  • Demonstrate the ability to analyze algorithms to interpolate data with polynomials.

Analyze a communication system and measure a performance in terms of probability of

Apply the techniques of multiple integration and partial derivatives to applied problems

Apply differential and integral calculus techniques to trigonometric functions, exponential functions, logarithmic functions and the inverses of these functions

Model both open and closed-loop systems using both time and frequency domain methods.

CLO 1: Determine the value of thermodynamic function to physical situations

Evaluate systems for stability, causality, and linearity in discrete time

  • Independently research mathematical concepts
  • Synthesize pertinent mathematical background material
  • Apply group theoretic concepts to solve mathematical problems
  • Apply group theoretic concepts to the natural sciences
  • Demonstrate knowledge of relationships between exponents and logarithms and their derivatives
  • Apply differential and integral calculus techniques to trigonometric functions, exponential functions, logarithmic functions and the inverses of these functions
  • Understand the development of the natural logarithmic function

Apply number theoretic techniques to cryptography

  • set up and solve second order, constant coefficient differential equations that arise from physical systems such as mass-spring systems and RLC circuits.  In addition, students will have a strong intuition of the phenomenon of resonance.
  • use numerical schemes to find approximate solutions to initial value problems utilizing mathematical software such as Matlab or Mathematica.
  • Work with the applications of geometric transformations in the sciences
  • Explain the historical aspects of Euclidean geometry

Model a physical signal by using mathematical functions, and solve the equations when excited by an arbitrary function.

Apply classical solution techniques to differential equation models of physical systems

Demonstrate a conceptual knowledge of the derivative as a limit of slopes of secants, as the slope of non-vertical tangents and as the rate of change of one quantity with respect to another

  • Employ the appropriate numerical technique to approximate a solution of an initial value problem, boundary value problem, or partial differential equation, with careful consideration of initial or boundary data.
  • Demonstrate the ability to analyze algorithms to interpolate data with polynomials.

Employ and analyze a prescribed method to find a root of a nonlinear equation (with knowledge of the strengths and weaknesses of the approach);

Write rigorous correctness proofs for algorithms.

Utilize qualitative methods to analyze linear and non-linear systems of differential equations

Derive the implications of the principles of special relativity.

CLO 3: Explain bonding theories such as molecular orbital theory

  • Work with the applications of geometric transformations in the sciences
  • Explain the historical aspects of Euclidean geometry
  • Independently research mathematical concepts
  • Synthesize pertinent mathematical background material

Demonstrate knowledge of relationships between exponents and logarithms and their derivatives

Employ and analyze a prescribed method to find a root of a nonlinear equation (with knowledge of the strengths and weaknesses of the approach);

Provide a geometrical interpretation of the cross product, directional derivative and gradient

CLO 1: Determine the value of thermodynamic function to physical situations

Employ the appropriate numerical technique to approximate a solution of an initial value problem, boundary value problem, or partial differential equation, with careful consideration of initial or boundary data.

set up and solve second order, constant coefficient differential equations that arise from physical systems such as mass-spring systems and RLC circuits.  In addition, students will have a strong intuition of the phenomenon of resonance.

Construct model equations from a description of a biological system

Understand the mathematical definition of the five asymptotic notations: Θ, O, o, Ω, and ω.

Demonstrate a conceptual knowledge of the derivative as a limit of slopes of secants, as the slope of non-vertical tangents and as the rate of change of one quantity with respect to another

Apply basic linear algebra to economic problems.

Apply group theoretic concepts to solve mathematical problems

Utilize qualitative methods to analyze linear and non-linear systems of differential equations

Give definitions of the terms sequence and infinite series

  • Model a physical signal by using mathematical functions, and solve the equations when excited by an arbitrary function.
  • Explain the relation between the time and frequency domains, and apply techniques for converting from one domain to another.
  • Independently research mathematical concepts
  • Synthesize pertinent mathematical background material

Apply group theoretic concepts to solve mathematical problems

Demonstrate knowledge of relationships between exponents and logarithms and their derivatives

Write rigorous correctness proofs for algorithms.

Design algorithms to solve computational problems

Demonstrate the ability to analyze algorithms to interpolate data with polynomials.

Employ and analyze a prescribed method to find a root of a nonlinear equation (with knowledge of the strengths and weaknesses of the approach);

Apply number theoretic techniques to cryptography

  • Independently research mathematical concepts
  • Synthesize pertinent mathematical background material
  • Work with the applications of geometric transformations in the sciences
  • Explain the historical aspects of Euclidean geometry
  • Apply group theoretic concepts to solve mathematical problems
  • Apply group theoretic concepts to the natural sciences

Apply number theoretic techniques to cryptography

Demonstrate knowledge of relationships between exponents and logarithms and their derivatives

Interpret model assumptions

Write rigorous correctness proofs for algorithms.

  • Apply group theoretic concepts to the natural sciences
  • Apply group theoretic concepts to solve mathematical problems

Understand the foundation of AI

Apply group theoretic concepts to cryptology and coding theory

Apply number theoretic techniques to cryptography

Implement code that reads information from a file.

Identify digital modulations such as BPSK, BFSK, QPSK, MPSK, and MQAM.

  • Write a professional report adhering to scholarly standards
  • Summarize the professional report in an oral presentation
  • Independently research mathematical concepts
  • Independently research mathematical concepts
  • Write a professional report adhering to scholarly standards

Recent regional postings for this occupation

View all 45 postings from the last year →

5 most recent CareerOneStop listings for this occupation. "Live" in Quick Facts counts only postings the scraper re-confirmed in the last 7 days; older real postings still appear here until they age out.

Course evidence covers every O*NET task we tracked

Every O*NET task for this occupation has at least one candidate course match in the EWU Math BS catalog (matched at cosine similarity ≥ 0.30 against course learning outcomes). Faculty review of individual matches is ongoing. Electives extend that preparation further.

More O*NET details for this occupation (skills, knowledge, tools & technology)
Skills (42)
Basic Skills: Active Learning
Basic Skills: Active Listening
Basic Skills: Critical Thinking
Basic Skills: Learning Strategies
Basic Skills: Mathematics
Basic Skills: Monitoring
Basic Skills: Reading Comprehension
Basic Skills: Science
Basic Skills: Speaking
Basic Skills: Writing
+ 32 more on O*NET
Knowledge (5)
Computers and Electronics
Education and Training
English Language
Mathematics
Physics
Tools & technology (30)
Analytical or scientific software: AMPL
Analytical or scientific software: ARfit
Analytical or scientific software: Algae
Analytical or scientific software: Analyse-it
Analytical or scientific software: Analysis and Visualization of Time Sequences AVTS
Analytical or scientific software: Apfloat
Analytical or scientific software: Apple Shazam
Analytical or scientific software: Aptech Systems GAUSS
Analytical or scientific software: Aztec
Analytical or scientific software: Computer Algebra System for Algebraic Geometry CASA

O*NET's tools-and-technology list aggregates software encountered across the occupation's many sub-roles, so the list can be broad. Treat it as a directory of what people in this job might use, not a checklist of what every job requires.

Where this data comes from. Occupation descriptions, tasks, skills, and education-incumbents survey come from the U.S. Department of Labor's O*NET 30.2. Washington-state pay and employment projections come from WA Employment Security Department and the BLS Occupational Employment and Wage Statistics. Live job postings come from CareerOneStop, refreshed nightly from a scrape that tracks the original posting date and the date our system last saw each posting live.

How we connect courses to occupations. Course catalog descriptions and program-level learning outcomes are indexed alongside O*NET task statements. Where a course's language aligns with a task an occupation requires, we mark it as evidence of preparation. Faculty review each candidate match and either confirm or veto it; only confirmed matches surface in totals.

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