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.
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
- Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
- Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
- Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
- Perform computations and apply methods of numerical analysis to data.
- Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
Technology Skills
- 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,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 statistical software,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
- Customer relationship management CRM software:Salesforce software
- Data base management system software:MySQL
- Data base user interface and query software:Microsoft Access,Structured query language SQL
Occupational Requirements
Work Activities
- 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.
- Processing Information:Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.
- Getting Information:Observing, receiving, and otherwise obtaining information from all relevant sources.
- Thinking Creatively:Developing, designing, or creating new applications, ideas, relationships, systems, or products, including artistic contributions.
Detailed Work Activities
- Analyze data to identify trends or relationships among variables.
- Analyze security of systems, network, or data.
- Apply mathematical principles or statistical approaches to solve problems in scientific or applied fields.
- Design computer modeling or simulation programs.
- Determine appropriate methods for data analysis.
Work Context
- Electronic Mail:92% responded"Every day"
- Importance of Being Exact or Accurate:79% responded"Extremely important"
- Indoors, Environmentally Controlled:63% responded"Every day"
- Structured versus Unstructured Work:58% responded"A lot of freedom"
- Face-to-Face Discussions:57% responded"Once a week or more but not every day"
Worker Requirements
Skills
- Mathematics:Using mathematics to solve problems.
- Critical Thinking:Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions, or approaches to problems.
- Complex Problem Solving:Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.
- Active Learning:Understanding the implications of new information for both current and future problem-solving and decision-making.
- Reading Comprehension:Understanding written sentences and paragraphs in work-related documents.
Knowledge
- Mathematics:Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.
- English Language:Knowledge of the structure and content of the English language including the meaning and spelling of words, rules of composition, and grammar.
- Computers and Electronics:Knowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming.
- Education and Training:Knowledge of principles and methods for curriculum and training design, teaching and instruction for individuals and groups, and the measurement of training effects.
Education
How much education does a new hire need to perform a job in this occupation? Respondents said:
- 50%Doctoral Degree
- 25%Master's Degree
- 8%Bachelor's Degree
- 8%Post-Baccalaureate Certificate - awarded for completion of an organized program of study; designed for people who have completed a Baccalaureate degree but do not meet the requirements of academic degrees carrying the title of Master.
- 8%Post-Doctoral Training
Worker Characteristics
Abilities
- Mathematical Reasoning:The ability to choose the right mathematical methods or formulas to solve a problem.
- Number Facility:The ability to add, subtract, multiply, or divide quickly and correctly.
- Deductive Reasoning:The ability to apply general rules to specific problems to produce answers that make sense.
- Inductive Reasoning:The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events).
- Information Ordering:The ability to arrange things or actions in a certain order or pattern according to a specific rule or set of rules (e.g., patterns of numbers, letters, words, pictures, mathematical operations).
Interests
- Investigative:Investigative occupations frequently involve working with ideas, and require an extensive amount of thinking. These occupations can involve searching for facts and figuring out problems mentally.
- Conventional:Conventional occupations frequently involve following set procedures and routines. These occupations can include working with data and details more than with ideas. Usually there is a clear line of authority to follow.
- Artistic:Artistic occupations frequently involve working with forms, designs and patterns. They often require self-expression and the work can be done without following a clear set of rules.
Work Values
- Achievement:Occupations that satisfy this work value are results oriented and allow employees to use their strongest abilities, giving them a feeling of accomplishment. Corresponding needs are Ability Utilization and Achievement.
- Recognition:Occupations that satisfy this work value offer advancement, potential for leadership, and are often considered prestigious. Corresponding needs are Advancement, Authority, Recognition and Social Status.
- Independence:Occupations that satisfy this work value allow employees to work on their own and make decisions. Corresponding needs are Creativity, Responsibility and Autonomy.
Work Styles
- Analytical Thinking:Job requires analyzing information and using logic to address work-related issues and problems.
- Attention to Detail:Job requires being careful about detail and thorough in completing work tasks.
- Persistence:Job requires persistence in the face of obstacles.
- Achievement/Effort:Job requires establishing and maintaining personally challenging achievement goals and exerting effort toward mastering tasks.
- Innovation:Job requires creativity and alternative thinking to develop new ideas for and answers to work-related problems.
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