Job Duties Custom List 15-2021.00 — Mathematicians
- Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
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- Apply research or simulation results to extend biological theory or recommend new research projects.
- Develop or use mathematical models to track changes in biological phenomena, such as the spread of infectious diseases.
- Draw conclusions or make predictions, based on data summaries or statistical analyses.
- Develop or implement data analysis algorithms.
- Prepare statistical data for inclusion in reports to data monitoring committees, federal regulatory agencies, managers, or clients.
- Analyze clinical or survey data, using statistical approaches such as longitudinal analysis, mixed-effect modeling, logistic regression analyses, and model-building techniques.
- Write detailed analysis plans and descriptions of analyses and findings for research protocols or reports.
- Calculate sample size requirements for clinical studies.
- Read current literature, attend meetings or conferences, and talk with colleagues to keep abreast of methodological or conceptual developments in fields such as biostatistics, pharmacology, life sciences, and social sciences.
- Design research studies in collaboration with physicians, life scientists, or other professionals.
- Prepare tables and graphs to present clinical data or results.
- Write program code to analyze data with statistical analysis software.
- Provide biostatistical consultation to clients or colleagues.
- Review clinical or other medical research protocols and recommend appropriate statistical analyses.
- Determine project plans, timelines, or technical objectives for statistical aspects of biological research studies.
- Plan or direct research studies related to life sciences.
- Prepare articles for publication or presentation at professional conferences.
- Monitor clinical trials or experiments to ensure adherence to established procedures or to verify the quality of data collected.
- Write research proposals or grant applications for submission to external bodies.
- Design or maintain databases of biological data.
- Collect data through surveys or experimentation.
- Assign work to biostatistical assistants or programmers.
- Analyze archival data, such as birth, death, and disease records.
- Design surveys to assess health issues.
- Teach graduate or continuing education courses or seminars in biostatistics.
- Apply research or simulation results to extend biological theory or recommend new research projects.
- Develop or use mathematical models to track changes in biological phenomena, such as the spread of infectious diseases.
- Draw conclusions or make predictions, based on data summaries or statistical analyses.
- Develop or implement data analysis algorithms.
- Prepare statistical data for inclusion in reports to data monitoring committees, federal regulatory agencies, managers, or clients.
- Compare models using statistical performance metrics, such as loss functions or proportion of explained variance.
- Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
- Identify relationships and trends or any factors that could affect the results of research.
- Analyze, manipulate, or process large sets of data using statistical software.
- Apply feature selection algorithms to models predicting outcomes of interest, such as sales, attrition, and healthcare use.
- Apply sampling techniques to determine groups to be surveyed or use complete enumeration methods.
- Clean and manipulate raw data using statistical software.
- Create graphs, charts, or other visualizations to convey the results of data analysis using specialized software.
- Deliver oral or written presentations of the results of mathematical modeling and data analysis to management or other end users.
- Design surveys, opinion polls, or other instruments to collect data.
- Identify business problems or management objectives that can be addressed through data analysis.
- Identify solutions to business problems, such as budgeting, staffing, and marketing decisions, using the results of data analysis.
- Read scientific articles, conference papers, or other sources of research to identify emerging analytic trends and technologies.
- Recommend data-driven solutions to key stakeholders.
- Test, validate, and reformulate models to ensure accurate prediction of outcomes of interest.
- Write new functions or applications in programming languages to conduct analyses.
- Compare models using statistical performance metrics, such as loss functions or proportion of explained variance.
- Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
- Identify relationships and trends or any factors that could affect the results of research.
- Define data requirements, and gather and validate information, applying judgment and statistical tests.
- Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
- Present the results of mathematical modeling and data analysis to management or other end users.
- Perform validation and testing of models to ensure adequacy, and reformulate models, as necessary.
- Prepare management reports defining and evaluating problems and recommending solutions.
- Collaborate with others in the organization to ensure successful implementation of chosen problem solutions.
- Formulate mathematical or simulation models of problems, relating constants and variables, restrictions, alternatives, conflicting objectives, and their numerical parameters.
- Observe the current system in operation, and gather and analyze information about each of the component problems, using a variety of sources.
- Analyze information obtained from management to conceptualize and define operational problems.
- Study and analyze information about alternative courses of action to determine which plan will offer the best outcomes.
- Collaborate with senior managers and decision makers to identify and solve a variety of problems and to clarify management objectives.
- Specify manipulative or computational methods to be applied to models.
- Design, conduct, and evaluate experimental operational models in cases where models cannot be developed from existing data.
- Develop and apply time and cost networks to plan, control, and review large projects.
- Educate staff in the use of mathematical models.
- Develop business methods and procedures, including accounting systems, file systems, office systems, logistics systems, and production schedules.
- Review research literature.
- Define data requirements, and gather and validate information, applying judgment and statistical tests.
- Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
- Adapt statistical methods to solve specific problems in many fields, such as economics, biology, and engineering.
- Analyze and interpret statistical data to identify significant differences in relationships among sources of information.
- Identify relationships and trends in data, as well as any factors that could affect the results of research.
- Evaluate the statistical methods and procedures used to obtain data to ensure validity, applicability, efficiency, and accuracy.
- Report results of statistical analyses, including information in the form of graphs, charts, and tables.
- Determine whether statistical methods are appropriate, based on user needs or research questions of interest.
- Prepare data for processing by organizing information, checking for inaccuracies, and adjusting and weighting the raw data.
- Develop and test experimental designs, sampling techniques, and analytical methods.
- Present statistical and nonstatistical results, using charts, bullets, and graphs, in meetings or conferences to audiences such as clients, peers, and students.
- Design research projects that apply valid scientific techniques, and use information obtained from baselines or historical data to structure uncompromised and efficient analyses.
- Evaluate sources of information to determine any limitations, in terms of reliability or usability.
- Process large amounts of data for statistical modeling and graphic analysis, using computers.
- Develop software applications or programming for statistical modeling and graphic analysis.
- Report results of statistical analyses in peer-reviewed papers and technical manuals.
- Plan data collection methods for specific projects, and determine the types and sizes of sample groups to be used.
- Apply sampling techniques, or use complete enumeration bases to determine and define groups to be surveyed.
- Examine theories, such as those of probability and inference, to discover mathematical bases for new or improved methods of obtaining and evaluating numerical data.
- Supervise and provide instructions for workers collecting and tabulating data.
- Prepare and structure data warehouses for storing data.
- Adapt statistical methods to solve specific problems in many fields, such as economics, biology, and engineering.
- Analyze and interpret statistical data to identify significant differences in relationships among sources of information.
- Identify relationships and trends in data, as well as any factors that could affect the results of research.
- Perform complex calculations as part of the analysis and evaluation of data, using computers.
- Analyze data from research conducted to detect and measure physical phenomena.
- Design computer simulations to model physical data so that it can be better understood.
- Write research proposals to receive funding.
- Teach physics to students.
- Report experimental results by writing papers for scientific journals or by presenting information at scientific conferences.
- Observe the structure and properties of matter, and the transformation and propagation of energy, using equipment such as masers, lasers, and telescopes, to explore and identify the basic principles governing these phenomena.
- Develop theories and laws on the basis of observation and experiments, and apply these theories and laws to problems in areas such as nuclear energy, optics, and aerospace technology.
- Collaborate with other scientists in the design, development, and testing of experimental, industrial, or medical equipment, instrumentation, and procedures.
- Describe and express observations and conclusions in mathematical terms.
- Perform complex calculations as part of the analysis and evaluation of data, using computers.
- Design, develop and modify software systems, using scientific analysis and mathematical models to predict and measure outcomes and consequences of design.
- Analyze information to determine, recommend, and plan installation of a new system or modification of an existing system.
- Analyze user needs and software requirements to determine feasibility of design within time and cost constraints.
- Confer with data processing or project managers to obtain information on limitations or capabilities for data processing projects.
- Confer with systems analysts, engineers, programmers and others to design systems and to obtain information on project limitations and capabilities, performance requirements and interfaces.
- Consult with customers or other departments on project status, proposals, or technical issues, such as software system design or maintenance.
- Coordinate installation of software system.
- Determine system performance standards.
- Develop or direct software system testing or validation procedures, programming, or documentation.
- Modify existing software to correct errors, adapt it to new hardware, or upgrade interfaces and improve performance.
- Monitor functioning of equipment to ensure system operates in conformance with specifications.
- Obtain and evaluate information on factors such as reporting formats required, costs, or security needs to determine hardware configuration.
- Prepare reports or correspondence concerning project specifications, activities, or status.
- Recommend purchase of equipment to control dust, temperature, or humidity in area of system installation.
- Specify power supply requirements and configuration.
- Store, retrieve, and manipulate data for analysis of system capabilities and requirements.
- Supervise and assign work to programmers, designers, technologists, technicians, or other engineering or scientific personnel.
- Supervise the work of programmers, technologists and technicians and other engineering and scientific personnel.
- Train users to use new or modified equipment.
- Design, develop and modify software systems, using scientific analysis and mathematical models to predict and measure outcomes and consequences of design.
- Compile laboratory test data and perform appropriate analyses.
- Conduct routine and non-routine analyses of in-process materials, raw materials, environmental samples, finished goods, or stability samples.
- Interpret test results, compare them to established specifications and control limits, and make recommendations on appropriateness of data for release.
- Calibrate, validate, or maintain laboratory equipment.
- Ensure that lab cleanliness and safety standards are maintained.
- Perform visual inspections of finished products.
- Complete documentation needed to support testing procedures, including data capture forms, equipment logbooks, or inventory forms.
- Identify and troubleshoot equipment problems.
- Write technical reports or documentation, such as deviation reports, testing protocols, and trend analyses.
- Investigate or report questionable test results.
- Monitor testing procedures to ensure that all tests are performed according to established item specifications, standard test methods, or protocols.
- Identify quality problems and recommend solutions.
- Participate in out-of-specification and failure investigations and recommend corrective actions.
- Receive and inspect raw materials.
- Train other analysts to perform laboratory procedures and assays.
- Supply quality control data necessary for regulatory submissions.
- Serve as a technical liaison between quality control and other departments, vendors, or contractors.
- Write or revise standard quality control operating procedures.
- Participate in internal assessments and audits as required.
- Perform validations or transfers of analytical methods in accordance with applicable policies or guidelines.
- Evaluate analytical methods and procedures to determine how they might be improved.
- Prepare or review required method transfer documentation including technical transfer protocols or reports.
- Review data from contract laboratories to ensure accuracy and regulatory compliance.
- Develop and qualify new testing methods.
- Coordinate testing with contract laboratories and vendors.
- Evaluate new technologies and methods to make recommendations regarding their use.
- Compile laboratory test data and perform appropriate analyses.
