MATH443 — Numerical Methods
Introduces scientific computing including root finding, numerical integration, differentiation, interpolation, and solving differential equations numerically.
Learning Objectives & Matches
Compare the error from a numerical calculus approximation to the corresponding error estimate
Perform computations and apply methods of numerical analysis to data.
Examine theories, such as those of probability and inference, to discover mathematical bases for new or improved methods of obtaining and evaluating numerical data.
Compare models using statistical performance metrics, such as loss functions or proportion of explained variance.
Implement numerical algorithms for root finding, integration, and differentiation
Perform computations and apply methods of numerical analysis to data.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Examine theories, such as those of probability and inference, to discover mathematical bases for new or improved methods of obtaining and evaluating numerical data.
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
Formulate mathematical or simulation models of problems, relating constants and variables, restrictions, alternatives, conflicting objectives, and their numerical parameters.
Develop or implement data analysis algorithms.
Conduct logical analyses of business, scientific, engineering, and other technical problems, formulating mathematical models of problems for solution by computers.
Analyze information processing or computation needs and plan and design computer systems, using techniques such as structured analysis, data modeling, and information engineering.
Specify manipulative or computational methods to be applied to models.
Analyze problems to develop solutions involving computer hardware and software.
Implement a numerical approximation to a solution of an initial value problem
Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
Maintain awareness of new and emerging computational methods and technologies.
Direct the analysis, development, and operation of complete computer systems.
Develop or apply data mining and machine learning algorithms.
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Correct errors by making appropriate changes and rechecking the program to ensure that the desired results are produced.
Write new functions or applications in programming languages to conduct analyses.
Perform computations and apply methods of numerical analysis to data.
Formulate mathematical or simulation models of problems, relating constants and variables, restrictions, alternatives, conflicting objectives, and their numerical parameters.
Analyze algorithm accuracy, stability, and error propagation
Perform computations and apply methods of numerical analysis to data.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Verify stability, interoperability, portability, security, or scalability of system architecture.
Correct errors by making appropriate changes and rechecking the program to ensure that the desired results are produced.
Review and analyze computer printouts and performance indicators to locate code problems, and correct errors by correcting codes.
Develop or implement data analysis algorithms.
Evaluate code to ensure that it is valid, is properly structured, meets industry standards, and is compatible with browsers, devices, or operating systems.
Recommend and implement performance improvements.
Verify the structure, accuracy, or quality of warehouse data.
Consult with and assist computer operators or system analysts to define and resolve problems in running computer programs.
Employ and analyze a prescribed method to find a root of a nonlinear equation (with knowledge of the strengths and weaknesses of the approach)
Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Solve computational problems using iterative and direct methods
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
Analyze problems to develop solutions involving computer hardware and software.
Conduct logical analyses of business, scientific, engineering, and other technical problems, formulating mathematical models of problems for solution by computers.
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Formulate mathematical or simulation models of problems, relating constants and variables, restrictions, alternatives, conflicting objectives, and their numerical parameters.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Specify manipulative or computational methods to be applied to models.
Write new functions or applications in programming languages to conduct analyses.
Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
Maintain awareness of new and emerging computational methods and technologies.
Produce a report that contains contextualized numerical results
Perform computations and apply methods of numerical analysis to data.
Report results of statistical analyses, including information in the form of graphs, charts, and tables.
Write technical summaries to report findings.
Report results of statistical analyses in peer-reviewed papers and technical manuals.
Generate standard or custom reports summarizing business, financial, or economic data for review by executives, managers, clients, and other stakeholders.
Examine theories, such as those of probability and inference, to discover mathematical bases for new or improved methods of obtaining and evaluating numerical data.
Specify inputs accessed by the system and plan the distribution and use of the results.
Create graphs, charts, or other visualizations to convey the results of data analysis using specialized software.
Analyze, manipulate, or process large sets of data using statistical software.
Present the results of mathematical modeling and data analysis to management or other end users.
Use scientific computing tools and libraries for numerical analysis
Process large amounts of data for statistical modeling and graphic analysis, using computers.
Maintain awareness of new and emerging computational methods and technologies.
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
Perform computations and apply methods of numerical analysis to data.
Perform system analysis, data analysis or programming, using a variety of computer languages and procedures.
Analyze, manipulate, or process large sets of data using statistical software.
Develop or implement data analysis algorithms.
Analyze information processing or computation needs and plan and design computer systems, using techniques such as structured analysis, data modeling, and information engineering.
Collaborate with computer manufacturers and other users to develop new programming methods.
Select programming languages, design tools, or applications.
Apply numerical methods to solve differential equations
Implement interpolation and approximation methods for data fitting
Analyze conditioning and numerical stability of computational problems
Adapt statistical methods to solve specific problems in many fields, such as economics, biology, and engineering.
Develop or implement data analysis algorithms.
Confer with clients regarding the nature of the information processing or computation needs a computer program is to address.
Analyze information processing or computation needs and plan and design computer systems, using techniques such as structured analysis, data modeling, and information engineering.
Perform computations and apply methods of numerical analysis to data.
Direct the analysis, development, and operation of complete computer systems.
Mentor others on mathematical techniques.
Consult with and assist computer operators or system analysts to define and resolve problems in running computer programs.
Provide staff and users with assistance solving computer-related problems, such as malfunctions and program problems.
Design computers and the software that runs them.
Develop programs to solve scientific and engineering problems numerically
Collaborate with computer manufacturers and other users to develop new programming methods.
Examine theories, such as those of probability and inference, to discover mathematical bases for new or improved methods of obtaining and evaluating numerical data.
Use the computer in the analysis and solution of business problems, such as development of integrated production and inventory control and cost analysis systems.
Perform system analysis, data analysis or programming, using a variety of computer languages and procedures.
Collaborate with others in the organization to ensure successful implementation of chosen problem solutions.
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.
Observe the current system in operation, and gather and analyze information about each of the component problems, using a variety of sources.
Perform systems analysis and programming tasks to maintain and control the use of computer systems software as a systems programmer.
Process large amounts of data for statistical modeling and graphic analysis, using computers.