Mathematics & Statistics
Optimize complex systems and processes to build streamlined operations. Engineer experiments that sift signal from noise, converting data deluges into strategic information.
Career Tracks in Mathematics & Statistics
Click on a track to learn more about its key functions, the types of problems you might work on if you choose that track, and the short- and long-term focuses of roles in that track.
// 001 // Data Science // 001 //
// 001 // Data Science // 001 //
Data Science
extract usable insights from data, driving informed strategies and solutions in various industries
- Extract meaningful insights from complex and diverse datasets.
- Use advanced statistical and machine learning algorithms to forecast trends, make predictions, and optimize outcomes.
- Create innovative solutions through data-driven methodologies.
- What is the optimal feature selection strategy for this model, and how can we use techniques such as Lasso or Ridge regression to identify the most relevant variables?
- How can we use ensemble learning techniques such as bagging or boosting to improve the accuracy and robustness of our models?
- What is the optimal hyperparameter selection for this model, and how can we use techniques such as cross-validation of grid search to optimize our performance metrics?
- How can we use deep learning models such as convolutional neural networks or recurrent neural networks to analyze complex data such as images or time series?
- What is the optimal sampling strategy for this dataset, and how can we use techniques such as stratified sampling or bootstrapping to ensure representative samples?
As a Data Scientist, you’ll have the opportunity to work across a multitude of domains, using your expertise to build models that drive decision-making in everything from finance to healthcare to energy.
Working closely with business teams throughout the company, you’ll develop an understanding of the business context and fundamentals. You’ll become an expert in your domain and gain a deep understanding of how data science can be used to accomplish business goals.
You’ll collect, move, manipulate, and clean data, preparing it for analysis and modeling. Your models will usually cover all four model types: descriptive, diagnostic, predictive, and prescriptive. You’ll build classifiers such as random forests, support vector machines, and gradient-boosted trees. To accomplish this, you’ll need knowledge of advanced mathematical, statistical, and machine learning techniques.
Some Data Scientists must also know how to write production-caliber code, ensuring that their models can run on real-time data and give real-time results. But even if you’re not responsible for deploying your models in production, you’re still likely to need technical skills to build advanced models.
Data Scientist; Artificial Intelligence Data Scientist; Statistician - Data Scientist; Data Scientist - Images; Data Scientist - Forecasting.
// 002 // Statistics // 002 //
// 002 // Statistics // 002 //
Statistics
contribute to evidence-based research and innovation across diverse domains
- Design experiments and craft studies and surveys that generate high-quality data for analysis.
- Use advanced statistical modeling techniques to make predictions, explore relationships, and identify causal factors.
- Apply statistical and mathematical expertise to unravel complex patterns.
- How can we use survival analysis techniques such as Kaplan-Meier or Cox proportional hazards models to analyze time-to-event data?
- What is the optimal experimental design for this study, and how can we use techniques such as factorial designs or Latin squares to reduce variability and increase efficiency?
- How can we use mixed-effects models to analyze longitudinal or clustered data and account for within-subject or within-group correlations?
- What is the appropriate effect size measure for this analysis, and how can we use techniques such as Cohen’s D or Odds Ratios to interpret our results?
- How can we use Bayesian hierarchical models to analyze complex data structures such as spatial or network data, and incorporate prior information to improve performance?
As a Statistician, you can work across a variety of industries, from healthcare to finance to government agencies and national labs. In this role, you’ll perform a variety of different functions, depending on the domain in which you work. At its core, the role of a statistician involves collecting, analyzing, and interpreting data to help organizations make informed decisions and solve complex problems.
You’ll typically begin projects by collecting and preparing data, and performing exploratory data analysis. This will involve cleaning, organizing, and integrating datasets from various sources and often in differing formats. You’re likely to use programming languages like R or Python, along with specialized statistical platforms such as SAS or SPSS to wrangle and manipulate data.
Once cleaned and standardized, you’ll create visualizations and perform initial analyses to identify trends, patterns, and anomalies in data. Once you gain a rudimentary understanding of the data, you’ll apply more advanced techniques such as regression analysis, hypothesis testing, time series analysis, or more elaborate methods like multivariate analysis or Bayesian inference. You’ll need to be adept at selecting the appropriate statistical methods based on both the nature of the data and the nature of the questions being investigated.
Increasingly, working as a statistician will also require the incorporation of machine learning techniques. Methods such as random forests, support vector machines, or even neural networks are used in the modeling process. As a Statistician, you’ll likely need to balance the complexity and interpretability of these methods, especially in regulated industries in which model explainability is nonnegotiable.
Your work is likely to require communicating your findings to both technical and nontechnical audiences, as decision-makers will need to understand the reliability and applicability of your results. You’ll need to create clear, visually appealing reports that summarize your results in an accessible manner. You’ll also need to explain the implications of your analyses, as well as their uncertainties and limitations.
Working as a Statistician, you might also be involved in the design of experiments, or the design of surveys to collect new data. This requires knowledge of experimental design principles and sampling methods. You might frequently deal with sensitive data, requiring transparency in the selection of methods as well as protections for data privacy. Given that statisticians work across many industries, you’re likely to collaborate with subject matter experts, learning field-specific concepts from them (or on your own) and figuring out how to translate statistical techniques into given contexts.
Statistician; Applied Statistician; Statistical Scientist; Statistical Programmer; Research Scientist - Statistics.
// 003 // Operations Research // 003 //
// 003 // Operations Research // 003 //
Operations Research
Use mathematical models and advanced analytics to optimize complex systems
- Use mathematical modeling and analysis to optimize business processes.
- Leverage mathematical and statistical techniques to simulate business scenarios.
- Design and implement optimization algorithms and decision-support systems.
- What is the most effective way to use linear programming techniques to optimize production schedules and minimize costs?
- How can we use queuing theory to model wait times and optimize staffing levels in our customer support division?
- What are the most effective ways to use metaheuristic optimization algorithms such as genetic algorithms or simulated annealing to solve complex optimization problems?
- How can we use data envelopment analysis to evaluate the relative efficiency of different production processes and identify areas for improvement?
- How can we use fuzzy logic modeling techniques to handle imprecise or uncertain data and optimize complex systems such as logistics networks or manufacturing processes?
As an Operations Research Analyst, your goal will be to optimize the operations of companies by analyzing data and designing new operating procedures based on the results of your analyses. You’ll use models, algorithms, and simulations to analyze and optimize complex systems such as transportation systems, networks, supply chains, and manufacturing processes.
In addition to analyzing existing processes, you’ll work on designing new procedures that will help companies operate more efficiently. You’ll work closely with engineers, business leaders, and data scientists to conduct stakeholder interviews and analyze data. You’ll build simulations to understand the effects of proposed actions on processes to find optimal solutions and quantify the costs and benefits of each alternative.
Operations Research Analysts use a variety of mathematical and statistical techniques to optimize the processes they investigate. This role may require advanced modeling skills or the ability to use computational software to run analyses and simulations. Among the many techniques from which Operations Research Analysts might draw are linear programming, integer and dynamic programming, stochastic processes, and simulated annealing.
Operations Research Analyst; Operations Consultant; Principal Operations Researcher; Decision Analyst; Data Scientist - Operations.
// 004 // Statistical Quality Control // 004 //
// 004 // Statistical Quality Control // 004 //
Statistical Quality Control
ensure every product meets quality standards through meticulous analysis
- Utilize statistical methods to analyze production data, identify trends, and detect anomalies in manufacturing processes.
- Create efficient sampling strategies that accurately reflect the reliability, safety, and quality of products without compromising production capacity.
- Identify root causes of quality problems using statistical tools and recommending corrective action to prevent recurrence.
- What statistical methods can we use to identify the root cause of the recent increase in defect rates?
- How can we adjust the sampling strategy to ensure we are effectively detecting variations without overburdening the production process?
- What trends are emerging from the process capability analysis, and what do they imply about our production process’s future performance?
- How does the introduction of new technology and/or materials impact the statistical models we use for quality control?
- How do changes in environmental conditions within the manufacturing facility affect product quality, and how can we mitigate these effects?
Working in statistical quality control and analysis, you’ll use statistical methods to predict and eliminate potential flaws in production processes before they become large-scale problems. You’ll implement systems that increase efficiency, reduce waste, and ensure specified levels of quality for products. By applying techniques such as control charts and process capability analysis, you’ll identify variations that could signify a problem, allowing for real-time corrective actions.
You’ll develop sampling strategies that accurately assess product quality without disrupting the manufacturing flow, and optimize production processes to meet both quality and quantity demands and ensure compliance with regulatory and industry standards. Your work will require the continual adaptation of quality control measures to accommodate new materials, technologies, and processes.
To reduce variability in production processes, you’ll implement statistical methods to identify and eliminate sources of variation, ensuring products conform to consistent quality standards. Similarly, you’ll enhance process capabilities by using statistical analysis to improve manufacturing processes within specified tolerance levels. You’ll also work to ensure the reliability of products by analyzing failure rates and patterns, so that the design of manufacturing processes can be updated as needed.
Statistical Process Control Engineer; Quality Engineer; Quality Control Scientist; Quality Control Testing Engineer; Quality Control Analyst.
// 005 // GIS Analysis // 005 //
// 005 // GIS Analysis // 005 //
GIS Analysis
Reveal spatial connections in integrated data streams
- Perform complex spatial operations and analyses to solve geographic problems.
- Organize, maintain, and update geographical data within GIS databases to ensure data accuracy and accessibility for analysis.
- Address the challenges of data compatibility and precision in multi-source GIS projects.
- How do we balance the level of detail in our maps without oversimplifying the data or overwhelming our computing resources?
- What strategies can we use to improve the accuracy of predictions made using spatial modeling?
- How can we update our GIS databases more efficiently to reflect real-time changes in the environment?
- What are the most efficient algorithms we can use to speed up the processing of large datasets?
- What additional spatial layers or data points could enhance the depth and utility of a given GIS project?
As a GIS (Geographic Information Systems) Analyst, you’ll harness the power of spatial data to map out solutions that have applications across numerous industries. You’ll analyze geographic and environmental data, combining spatial data from various sources and formats into a cohesive GIS database, ensuring consistency and accuracy across different datasets and types. You might assess land use patterns, demographic trends, and environmental constraints, creating models that inform agriculture, urban planning, utility management, or disaster response.
Some of the challenges that you might encounter in your work include data integration, in which you’ll combine spatial data from various sources and formats into a cohesive GIS database, with different datasets needing the same consistency and accuracy for effective merging. Resolution issues might also arise, especially when combining different datasets for analyses. There may also be use cases for real-time data processing, in which real-time data such as weather conditions or traffic flow needs to be incorporated with other GIS data.
Once the data is ready for analysis, you’ll utilize GIS software and algorithms to analyze spatial data, identify patterns, and create models that predict trends. You’ll perform complex spatial operations and analysis, such as overlay analysis, buffer generation, and network analysis, to solve geographic problems. You might design and produce maps or other visual representations of this data, communicating geographic information clearly to technical and nontechnical audiences and users alike.
GIS Analyst; Geospatial Analyst; GIS Data Analyst; GIS Compilation Analyst; GIS Spatial Analyst.
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