Mathematicians
15-2021.00
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.
Sample of reported job titles: Computational Mathematician, Computational Scientist, Cryptographer, Cryptographic Vulnerability Analyst, Image Scientist, Knowledge Engineer, Mathematician, Research Computing Specialist, Research Scientist, Researcher
Occupation-Specific Information
Tasks
- Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
- Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
- Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
- Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
- Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
- Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
- Perform computations and apply methods of numerical analysis to data.
- Assemble sets of assumptions, and explore the consequences of each set.
- Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
- Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
- Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
Technology Skills
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Analytical or scientific software -
Algae; AMPL; Analyse-it; Analysis and Visualization of Time Sequences AVTS; Apfloat; Apple Shazam; Aptech Systems GAUSS; ARfit; Aztec; Computer Algebra System for Algebraic Geometry CASA; Data visualization software; DataDescription DataDesk; DifEqu; Discrete Dynamics Lab DDLab; DSP Development DADiSP; EleSoft Research; Geomview; GNU Octave; Graphics Programming Environment GRAPE; GraphPad Software GraphPad Prism; IBM SPSS Amos; IBM SPSS Statistics π₯; Insightful S-PLUS; Interactive Mathematical Proof System IMPS; JACAL; KANT; KSEG; LINDO Systems LINDO API; MacKichan Software Scientific WorkPlace; Magma Design Automation software; Maplesoft Maple; Mathsoft Mathcad; Maxima Software; Maximal Software MPL Modeling System; Minitab; ModelKinetix ModelMaker; Multipath Corporation Fast Matrix Solver FMS; Numeritek NUMERICA; PARI/GP; Polymath Software POLYMATH; Provalis Research Simstat; Sage Accounting Software; SAS π₯; StataCorp Stata; STATISTICA; SuperANOVA; Symmetrica; Systat Software SigmaPlot; The MathWizards MathViews; The MathWorks MATLAB
; UNISTAT Statistical Package; Wolfram Research Mathematica
- Business intelligence and data analysis software - Tableau π₯
- Customer relationship management CRM software - Salesforce software π₯
- Data base management system software - MySQL π₯
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Data base user interface and query software -
Microsoft Access π₯; Structured query language SQL
- Desktop publishing software - MicroPress VTeX
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Development environment software -
C ; Formula translation/translator FORTRAN; Microsoft Visual Basic π₯; Microsoft Visual Studio π₯
- Electronic mail software - Microsoft Outlook π₯
- Enterprise application integration software - Extensible markup language XML π₯
- Graphics or photo imaging software - Adobe Photoshop π₯
- Internet browser software - Web browser software
- Network security or virtual private network VPN management software - Vormetric Application Encryption
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Object or component oriented development software -
C# π₯; C++ ; Object oriented development environment software; Oracle Java π₯; Perl π₯; Python ; R π₯
- Office suite software - Microsoft Office software π₯
- Operating system software - Apple macOS π₯; Bash π₯; Linux π₯; Microsoft operating system; Microsoft Windows π₯; UNIX π₯
- Presentation software - Microsoft PowerPoint π₯
- Program testing software - User interface design software
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Spreadsheet software -
Microsoft Excel
- Transaction server software - Web server software
- Web platform development software - Cascading style sheets CSS π₯; Hypertext markup language HTML π₯; JavaScript π₯; PHP π₯
- Word processing software - Microsoft Word π₯
Occupational Requirements
Work Activities
- Getting Information - Observing, receiving, and otherwise obtaining information from all relevant sources.
- Monitoring Processes, Materials, or Surroundings - Monitoring and reviewing information from materials, events, or the environment, to detect or assess problems.
- Identifying Objects, Actions, and Events - Identifying information by categorizing, estimating, recognizing differences or similarities, and detecting changes in circumstances or events.
- Inspecting Equipment, Structures, or Materials - Inspecting equipment, structures, or materials to identify the cause of errors or other problems or defects.
- Estimating the Quantifiable Characteristics of Products, Events, or Information - Estimating sizes, distances, and quantities; or determining time, costs, resources, or materials needed to perform a work activity.
- Judging the Qualities of Objects, Services, or People - Assessing the value, importance, or quality of things or people.
- Processing Information - Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.
- Evaluating Information to Determine Compliance with Standards - Using relevant information and individual judgment to determine whether events or processes comply with laws, regulations, or standards.
- Analyzing Data or Information - Identifying the underlying principles, reasons, or facts of information by breaking down information or data into separate parts.
- Making Decisions and Solving Problems - Analyzing information and evaluating results to choose the best solution and solve problems.
- Thinking Creatively - Developing, designing, or creating new applications, ideas, relationships, systems, or products, including artistic contributions.
- Updating and Using Relevant Knowledge - Keeping up-to-date technically and applying new knowledge to your job.
- Developing Objectives and Strategies - Establishing long-range objectives and specifying the strategies and actions to achieve them.
- Scheduling Work and Activities - Scheduling events, programs, and activities, as well as the work of others.
- Organizing, Planning, and Prioritizing Work - Developing specific goals and plans to prioritize, organize, and accomplish your work.
- Performing General Physical Activities - Performing physical activities that require considerable use of your arms and legs and moving your whole body, such as climbing, lifting, balancing, walking, stooping, and handling materials.
- Handling and Moving Objects - Using hands and arms in handling, installing, positioning, and moving materials, and manipulating things.
- Controlling Machines and Processes - Using either control mechanisms or direct physical activity to operate machines or processes (not including computers or vehicles).
- Operating Vehicles, Mechanized Devices, or Equipment - Running, maneuvering, navigating, or driving vehicles or mechanized equipment, such as forklifts, passenger vehicles, aircraft, or watercraft.
- Working with Computers - Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.
- Drafting, Laying Out, and Specifying Technical Devices, Parts, and Equipment - Providing documentation, detailed instructions, drawings, or specifications to tell others about how devices, parts, equipment, or structures are to be fabricated, constructed, assembled, modified, maintained, or used.
- Repairing and Maintaining Mechanical Equipment - Servicing, repairing, adjusting, and testing machines, devices, moving parts, and equipment that operate primarily on the basis of mechanical (not electronic) principles.
- Repairing and Maintaining Electronic Equipment - Servicing, repairing, calibrating, regulating, fine-tuning, or testing machines, devices, and equipment that operate primarily on the basis of electrical or electronic (not mechanical) principles.
- Documenting/Recording Information - Entering, transcribing, recording, storing, or maintaining information in written or electronic/magnetic form.
- Interpreting the Meaning of Information for Others - Translating or explaining what information means and how it can be used.
- Communicating with Supervisors, Peers, or Subordinates - Providing information to supervisors, co-workers, and subordinates by telephone, in written form, e-mail, or in person.
- Communicating with People Outside the Organization - Communicating with people outside the organization, representing the organization to customers, the public, government, and other external sources. This information can be exchanged in person, in writing, or by telephone or e-mail.
- Establishing and Maintaining Interpersonal Relationships - Developing constructive and cooperative working relationships with others, and maintaining them over time.
- Assisting and Caring for Others - Providing personal assistance, medical attention, emotional support, or other personal care to others such as coworkers, customers, or patients.
- Selling or Influencing Others - Convincing others to buy merchandise/goods or to otherwise change their minds or actions.
- Resolving Conflicts and Negotiating with Others - Handling complaints, settling disputes, and resolving grievances and conflicts, or otherwise negotiating with others.
- Performing for or Working Directly with the Public - Performing for people or dealing directly with the public. This includes serving customers in restaurants and stores, and receiving clients or guests.
- Coordinating the Work and Activities of Others - Getting members of a group to work together to accomplish tasks.
- Developing and Building Teams - Encouraging and building mutual trust, respect, and cooperation among team members.
- Training and Teaching Others - Identifying the educational needs of others, developing formal educational or training programs or classes, and teaching or instructing others.
- Guiding, Directing, and Motivating Subordinates - Providing guidance and direction to subordinates, including setting performance standards and monitoring performance.
- Coaching and Developing Others - Identifying the developmental needs of others and coaching, mentoring, or otherwise helping others to improve their knowledge or skills.
- Providing Consultation and Advice to Others - Providing guidance and expert advice to management or other groups on technical, systems-, or process-related topics.
- Performing Administrative Activities - Performing day-to-day administrative tasks such as maintaining information files and processing paperwork.
- Staffing Organizational Units - Recruiting, interviewing, selecting, hiring, and promoting employees in an organization.
- Monitoring and Controlling Resources - Monitoring and controlling resources and overseeing the spending of money.
Detailed Work Activities
- Analyze data to identify trends or relationships among variables.
- Present research results to others.
- Prepare analytical reports.
- Update knowledge about emerging industry or technology trends.
- Apply mathematical principles or statistical approaches to solve problems in scientific or applied fields.
- Design computer modeling or simulation programs.
- Develop scientific or mathematical models.
- Determine appropriate methods for data analysis.
- Analyze security of systems, network, or data.
- Develop computer or information security policies or procedures.