PhD In Data Science Online

Last Updated on February 11, 2022

There are many challenges facing current and future data scientists, such as managing ‘Big Data’, differentiating between algorithms and models, achieving the right level of mathematical thinking, and shifting to cloud-based infrastructure. This new form of educational assistance must be designed with insight into the challenges faced by practicing data scientists. Hence the PhD in Data Science Online is an online part-time PhD program for busy and self-motivated people who need a flexible approach to doctoral studies suited to their time pressure, geographical location and existing job commitments. It offers structured individual guidance from experts in their field, supported by community participants from different backgrounds and areas of expertise. Each program participant will receive mentoring from a faculty member and technical support from our technology team.

The Master of Science in Data Science is an online program offered by the Ph.D. in Data Science at The Graduate School, San Jose State University. It is a one-year program with a total of thirty-seven (37) units, consisting of nine (9) core units and twenty-eight (28) elective units. The curriculum emphasizes statistical thinking, computational skills and proficiency in big data tools to address real-world business problems using data science techniques from machine learning, artificial intelligence and data analytics.

You may be one of those people who find themselves answering the question: “What can you do with a degree in data science?” With such different specialties and positioning themselves against such heavyweights as Engineering and Computer Science, and with a rising number of data science bootcamps, it often seems to me that our field doesn’t have a strong identity. As an industry, we haven’t made it obvious to the world what we excel at or how much value we add.

phd in statistics and data science online

A Ph.D. in data science gives students deep knowledge of programming, statistics, data analysis, machine learning, and artificial intelligence. The degree combines course requirements in data science and related fields with practical experience and a dissertation. Like other doctoral programs, this degree emphasizes original research, particularly in pure theory, applied theory, and the techniques and tools of data science.

Graduates from online doctoral degree programs in data science can work as researchers, college professors, and senior data scientists. They may build new products, lead research teams, reinvent tools, or craft new applications for existing knowledge.

The Bureau of Labor Statistics projects computer and information technology occupations to grow by 12% between 2018 and 2028, amounting to more than 546,000 jobs. These professionals earn a median annual salary of $88,240.

ata Science has become popular in India. Many people are shifting their careers from different fields to data science and AI. A PhD in data science is very demanding and is considered extremely prestigious. India is realising its importance in industries and now has several institutes offering a PhD in data science. Here are some institutes that currently have their applications open for a PhD in India.

Online PhD in Data Science Programs

Data science is exactly what it sounds like – the study of data. Data scientists look at sets of data and notice patterns that emerge. They identify key information that data presents which may not seem readily apparent at first.

If you are someone that notices the small details while also keeping an eye on the bigger picture, a career in data science may be right for you. If you find trends and patterns in large amounts of data, you may be well-suited for this field.

What kind of job can you expect to have as a data scientist? In the last few years, Glassdoor has continuously ranked data scientist as one of the best jobs to have in the United States. The options for specific jobs are numerous and varied.

For example, one data scientist may work as a statistician and interpret statistical information for the U.S. Department of Agriculture. Another data scientist may be a business intelligence developer for Discover, creating strategies for businesses to make more informed decisions about their company.

Data Science Pros and Cons

As with any financial and length time investment, you should consider both the pros and the cons of earning your PhD in an online data science program.

Pros

Data science is a field that is booming in the twenty-first century. Jobs are plentiful and many companies incorporate data scientists to help boost their sales and offer the best customer experience.

Data scientists typically earn significant salaries compared to some other careers. The median data scientist salary is $98,230 per year (Bureau of Labor Statistics).

Cons

PhD programs can be lengthy and you can expect to devote several years to completing the courses and research required.

While earning your PhD can help you make more money in the long run, you will be spending time researching rather than working and making a paycheck.

All salary data in this table was provided by the Bureau of Labor Statistics.

Choosing to pursue an online PhD in a data science program is decision that must be taken into careful consideration, but there are many benefits to completing a program.

Data Science Curriculum & Courses

Curriculum for data science programs is heavily focused on analysis and research. Examples of courses offered by universities like Dakota State University and the University of North Texas are listed below.

  • Information Systems – This course is designed to help students learn about the role information systems have for businesses and other organizations.
  • Applied Statistics – This class teaches how to use statistical software to study data samples and make inferences based on the data presented.
  • Project and Change Management – This class is designed to help students learn the underlying principles for managing information systems and how to utilize software for project management.
  • Technology for Mobile Devices – Students in this course study the process of developing apps for mobile devices like smartphones and tablets.
  • Advanced Network Technology and Management – This class helps students learn how to work with a model network environment, including how to find solutions for problems with the network.
  • Seminar in Research and Research Methodology – Students in this seminar are asked to develop a research proposal and participate in a research study.
  • Knowledge Management Tools and Technologies – This course introduces students to a variety of technologies including those associated with knowledge management and IT infrastructure.
  • Seminar in Communication and Use of Information – This class explores the roles communication plays at various levels in society.
  • Readings in Information Science – Students in this class study texts which emphasize methodological and theoretical issues.
  • Medical Geography – In this course, students study the correlation between location and health care and work on their own projects.

Exploring the curriculum offered by different universities can help you determine which online PhD program is best suited for your interests and your needs.

Data Science PhD Admissions

Before applying for a PhD program, you will want to ensure that you have all the application materials on hand, including the commonly required materials listed below.

  • Reference letters – You should request these documents well before your application deadline as mentors may not be able to honor a last-minute request due to time constraints.
  • All transcripts – These grades will include both undergraduate and graduate level courses.
  • Letter of intent – Be prepared to explain in writing why you want to enroll in the program and what you plan to do after its completion.
  • Application fee – Fees to cover administrative costs of reviewing your application can add up, so make sure to budget for the costs of each one.
  • Resume – Schools want to know your background in not just education but in the job market as well.
  • Specific program application – Your prospective school will most likely have its own unique application on its official website.

Save yourself the stress of anxiously waiting to receive documents from an institution or mentor in time and compile them well ahead of the due date.

Data Science PhD Careers & Salaries

According to the U.S. Bureau of Labor Statistics, computer and information research scientists earned a median of $126,830 a year. Data scientists as a group earn increasingly high salaries in various industries including research laboratories, government departments, and a variety of companies focused on technology.

Some of the top companies that utilize data scientists are IBM, Amazon, Microsoft, Facebook, Oracle, Google, and Apple. These multi-billion dollar companies are consistently hiring data scientists to interpret the large amounts of data, or “big data,” that is collected via their services.

Data scientists can expect to work in roles where job duties include designing data models, organizing data from multiple sources, and identifying trends in data.

Data scientists use a comprehensive process for gathering and analyzing information including asking questions, acquiring data, storing data, using models to interpret it, and presenting their findings to stakeholders in the community.

According to the Bureau of Labor Statistics, some careers in the data science field include:

CareersAnnual Median Salary
Chief Information Officers$166,770
IT Directors$152,480
Computer and Information Systems Managers$151,150
Network Engineers$116,780
Software Developers$110,140
Information Security Analysts$103,590
Database Administrators$98,860
Data Scientists$98,230
Computer Systems Analysts$93,730
Statisticians$92,270
Operations Research Analysts$86,200

Whatever the job title, data scientists continually earn a significant amount more than employees in other fields.

Data Science Accreditation

Before clicking the “submit” button on your application to a PhD program, you will want to ensure that the university you are applying to is accredited, meaning it is recognized as a legitimate program that offers quality coursework and research opportunities.

If you decide to apply to a program related to computer technology or engineering, the Accreditation Board for Engineering and Technology (ABET) determine which schools offer suitable coursework and requirements for these fields. Also be sure that your prospective university is regionally accredited, the gold-standard for accreditation in the United States.
Search on your prospective schools’ website for information regarding their accreditation status. You will want to ensure that the schools you apply to are regionally accredited so you can get the most out of your PhD experience and your credits will be more likely to transfer should you switch schools while studying.

Data Science Professional Organizations

Joining a professional organization can help to advance your career by connecting you with other individuals who work in the same field.

Professional organizations offer a multitude of benefits, including networking opportunities (which may help to connect you with future employers), and they can also provide inspiration for completing your PhD program, decreasing feelings of isolation that can accompany students.

While some organizations may have a yearly membership fee, the potential gains for job opportunities and professional development through these groups can easily offset those costs.

Financial Aid

Across the nation, the average cost of obtaining a PhD online is between $4,000 and $20,000.  As a student in a PhD program, you can expect to have costs from tuition, books, personal supplies, transportation, etc. Without the time or energy for a full-time or often, even part-time job, you should explore all financial aid options available.

Financial aid for PhD students can come in the form of loans, scholarships, and grants. Grants and scholarships typically do not have to be paid back, but loans are borrowed money which may accrue interest and should be a last resort for students.

Some specific scholarships and grants are designed with scientists, including data scientists, in mind. For example, the National Science Foundation Graduate Research Fellowship is designed to support students who are pursuing research-based doctoral degrees.

Previous recipients include Nobel Prize winners, a U.S. Secretary of Energy, and the founder of Google.

Another common source of money comes from taking on teaching assistant positions within your university or becoming an assistant lecturer. Both positions are great for gaining experience teaching in your academic department while generating income to offset the costs incurred from your years of study.

How long does it take to get a PhD in data science?

It takes an average of 71 credits to complete a PhD in data science. On top of this, students may also have responsibilities to research and/or teach, which can make the process take even longer.

It is not unusual for some PhD programs to take anywhere from four to five years to complete.

Is a PhD in data science worth it?

Whether or not a PhD in data science is “worth it” depends on a number of factors. Do you have the time available for next few years (possibly longer) to invest in this opportunity? Are you motivated enough to complete coursework while also on a shoestring budget?

Search for employment positions you are interested in and take a look at the education requirements employers are requesting. These factors may effect your decision in potentially pursuing an online masters in data science instead.

Can I do a PhD in data science?

Whether or not you complete a PhD in data science depends on your ability to stay focused and motivated. PhD programs are notoriously intensive, and they are not for everyone.

You should have a better reason for applying to a program than simply not knowing what to do in today’s job market.

Universities Offering Online Data Science Doctorate Degree Programs

Methodology: The following school list is in alphabetical order. To be included, a college or university must be regionally accredited and offer degree programs online or in a hybrid format. In addition, the schools offer online data science programs.Capella University

Founded in 1993, private Capella University offers online doctorate, master’s, and bachelor’s degrees. The Minneapolis-based school’s 38,000 enrolled students represent 50 states and 61 countries. Doctoral students account for more than 27 percent of Capella University’s student body.

  • DBA in Business Intelligence – Data Analytics

Capella University is accredited by the Higher Learning Commission.Capitol Technology University

Capitol Technology University is a private university located near the nation’s capital in South Laurel, Maryland. Established in 1927, the university now offers undergraduate and master’s programs in business, computer science, cybrsecurity, and engineering.

Capitol Technology University is a military-friendly school founded by a Navy veteran. It holds the prestigious SC Media Award for Best Cybersecurity Higher Education Program. The school’s annual enrollment is approximately 850 students.

  • PhD in Business Analytics and Data Science

Capitol Technology University is accredited by the Middle States Commission on Higher Education.Colorado Technical University

Colorado Technical University was founded in 1965. This private university offers undergraduate, graduate, and doctoral degrees in business management and technology.

The school has earned the U.S. News & World Report “Best for Veterans” designation, the Council of College and Military Educators (CCME) Institution Award, and recognition as a center of Academic Excellence in Information Assurance and Cyber Defense from the NSA and Department of Homeland Security.

Annual enrollment stands at around 26,000 students.

  • Doctor of Computer Science – Big Data Analytics

Colorado Technical University is accredited by the Higher Learning Commission.Columbia University

New York City’s Columbia University is a private Ivy League research university founded in 1754. It stands today as the oldest university in New York City. Columbia operates four undergraduate schools and 15 graduate/professional schools.

Bachelor’s, master’s, and PhD programs covering business, medicine, liberal arts, technology, and political science are available. Student enrollment at Columbia stands at roughly 33,413.

  • PhD in Data Science

Columbia is accredited by the Middle States Commission on Higher Education.Grand Canyon University

Grand Canyon University is a private Christian college based in Phoenix, Arizona. With a student enrollment of 70,000 students, it is considered to be the world’s largest Christian university.

Grand Canyon University offers bachelor’s, master’s, and doctoral degrees in business, education, health sciences, liberal arts, and nursing. The school offers a total of 200 academic programs throughout its nine colleges.

  • DBA in Data Analytics

Grand Canyon University is accredited by the Higher Learning Commission.Harrisburg University of Science and Technology

Founded in 2001, Harrisburg University of Science and Technology is a STEM-focused institution with campuses in Harrisburg and Philadelphia.

This private university offers bachelor’s degrees, master’s degrees, doctoral degrees, and certificate programs. The nearly 6,000 students enrolled study degree paths related to applied science and technology.

  • PhD in Data Sciences

Harrisburg University of Science and Technology is accredited by the Middle States Commission on Higher Education.Indiana University-Purdue University Indianapolis

Indiana University-Purdue University Indianapolis is a public research university offering more than 225 options for bachelor’s, master’s, and doctoral degrees across 18 different schools. The university’s campus is based in Indianapolis, Indiana.

The more than 30,000 students enrolled pursue degrees in majors like art and design, business, education, engineering, law, liberal arts, medicine, nursing, and social work.

  • PhD in Data Science (on-campus)

Indiana University – Purdue University Indianapolis is accredited by the Higher Learning Commission.Northcentral University

Northcentral University is a private university based in San Diego, California. The school offers a range of bachelor’s degrees, master’s degrees, doctoral degrees, and certificates in business, education, marriage and family therapy, psychology, and technology.

Approximately 10,000 students are enrolled at Northcentral University. The school boasts a 100-percent doctoral faculty.

  • PhD in Data Science

Northcentral University is accredited by the Western Association of Schools and Colleges.Stevens Institute of Technology

Located in Hoboken, New Jersey, Stevens Institute of Technology is a private research institution with an enrollment of approximately 6,125 students. Founded in 1870, the school has been named among the “Best Value Colleges” by the Princeton Review.

Additionally, the Princeton Review ranks Stevens Institute of Technology among its “Top 15 for Internships.” The school’s undergraduate and graduate students represent 47 states and 60 countries. Students can pursue bachelor’s, master’s, doctoral, and certificate programs.

  • PhD in Data Science (on-campus)

Stevens Institute of Technology is accredited by the Middle States Commission on Higher Education.University of Central Florida

Located along Orlando’s Space Coast, the University of Central Florida is a public research university with a student enrollment of approximately 69,525. It offers bachelor’s, master’s, and doctoral programs.

Students can pursue degrees in arts and humanities, business, engineering, computer science, health science, medicine, and nursing. The University of Central Florida has been ranked as a “Best Southeastern College” by the Princeton Review.

  • PhD in Big Data Analytics

The University of Central Florida is accredited by the Southern Association of Colleges and Schools Commission on Colleges.

Getting Your PhD in Data Science Online

Obtaining your doctoral degree in data science is not an easy task, but it is also not an impossible one. If you are serious about pursuing your PhD, talk to experts in the field. The admissions departments at prospective universities can help put you in touch with recruiters who can give you more information about the program.

Joining a professional organization can help you connect with individuals who are working in the field, many of whom will have obtained their higher education degree. With careful planning and the right information to make informed career choices, you can further your education and your sense of accomplishment.

Should I Get a Ph.D. in Data Science?

Is a Ph.D. in data science worth it? Each person must answer that question for themselves based on their own expected return on investment. Nevertheless, many professional and personal benefits come with pursuing a terminal degree in data science. The following list outlines several of these benefits.

  • Qualify for Academic Positions: Earning an online Ph.D. in data science qualifies professional data scientists to take on academic positions, including postsecondary teaching jobs and university administration positions.
  • Transition from Computer Engineering to Data Science: Most machine learning engineers and data scientists transition into the field from computer engineering. A Ph.D. can help smooth that transition.
  • Demonstrate Intelligence and Dedication: The road to a Ph.D. is long and requires dedication. Completing a terminal degree demonstrates to employers that an applicant possesses both the dedication and the intelligence to succeed in a challenging field.
  • Competitive Resume: Data science is a competitive field, and a Ph.D. can help applicants’ resumes stand out. A Ph.D. indicates strong leadership and research skills along with deep technical knowledge.
  • Research Skills: Ph.D. work primarily consists of conducting original research. After completing a Ph.D. in data science, graduates can apply these skills to stay ahead of industry trends and create innovative solutions to problems.

Admission Requirements for a Ph.D. in Data Science

The admission requirements for an online Ph.D. in data science program vary from school to school. However, most schools have common expectations regarding previous education and experience. In general, prospective students should hold at least a bachelor’s degree, and some schools expect applicants to hold a master’s degree.

While a major in computer science, math, or business analytics may increase an applicant’s chances of acceptance, most schools do not list a specific major as a requirement. Some universities do, however, expect students to have completed courses in linear algebra, multivariate calculus, computer programming, and statistics or probability theory.

Typically, applicants need a minimum overall GPA in all previous coursework, often 3.5 on a 4.0 scale. Schools may also require a minimum GRE score, usually in the 70th percentile, as a prerequisite for acceptance into the program.

What Can I Do With a Ph.D. in Data Science?

After completing an online doctoral degree program in data science, graduates can work as data scientists, business analysts, information science researchers, or college professors. Some people may also wish to gain certification in a new data research language, which can open additional career opportunities.

Career and Salary Outlook for Data Science Graduates

An online Ph.D. in data science can lead to careers in analytics, business leadership, and machine learning. The Bureau of Labor Statistics projects the demand for computer and information technology professionals to grow by 12% between 2018-2028. Many computer science careers pay lucrative salaries and offer opportunities to advance with more education.

Some of the highest-paying careers in the field include database administrator, software developer, information security analyst, computer and information research scientist, and computer network architect. Graduates can also work in high-paying jobs in data science. Data scientists who work for federal agencies in Washington, D.C., or in technology firms in Silicon Valley or New York City do particularly well.COLLAPSE ALL EXPAND ALL

  • Professor
  • Data Scientist
  • Senior Data Scientist
  • Computer and Information Scientist, Research
  • Business Intelligence Analyst
PH.D. IN DATA SCIENCE CAREERS: MEDIAN SALARIES BY EXPERIENCE
JOB TITLEENTRY LEVEL (0-12 MONTHS)EARLY CAREER (1-4 YEARS)MID-CAREER (5-9 YEARS)EXPERIENCED (10-19 YEARS)
Professor$61,000$61,000$69,000$86,000
Senior Data Scientist$108,000$121,000$130,000$137,000
Computer and Information Scientist, Research$105,000$103,000$120,000$149,000
Business Intelligence Analyst$59,000$66,000$77,000$85,000
Data Scientist$86,000$94,000$108,000$120,000

Source: PayScale

Continuing Education in Data Science

Data science is a fast-moving field that requires ongoing study to stay abreast of the latest changes. Pursuing continuing education opportunities can provide benefits such as salary increases and new career opportunities.

Earning Your Doctorate in Data Science

Earning an online Ph.D. in data science typically takes about five years. This timeline includes coursework, apprenticeships, research, and dissertation writing and defense.

Most graduate data science programs require 10 courses to complete the master’s component of the program, which usually takes two years. These courses often draw from data science, ethics, applied math, computer science, and statistics. Students may learn to create simulations, run sklearn regressors, optimize data sets, and perform hyperparameter optimization on an artificial neural network.

Once they complete the coursework component of the Ph.D., graduate students can move on to teaching, internships, research, and writing. An online degree may take longer to complete than an on-campus program, since these students often work while going to school. Online students may also spend more time in courses or on writing, since they are less likely to conduct teaching or guided research than their on-campus peers. That said, each online Ph.D. in data science is different and prospective students should consider the individual merits of prospective programs.

Comparing Ph.D. Options

Students can pursue several different types of Ph.D. programs that explore data science, including degrees in business analytics, computer science, and data science itself. While all of these degrees include coursework and research opportunities in the same major fields, their varying emphases differentiate them from each other.COLLAPSE ALL EXPAND ALL

  • Ph.D. in Data Science
  • Ph.D. in Business Analytics
  • Ph.D. in Computer Science with a Data Science Concentration

Online doctoral degree programs in data science offer a variety of course types and topics depending upon faculty members’ expertise and the school’s focus. Due to the cutting-edge nature of data science, the curriculum examines critical topics aligned with current industry needs. Most courses also include an opportunity for students to gain hands-on experience.

Doctoral programs are oriented toward research and therefore include project-based courses, capstones, and writing-intensive classes. These courses explore many critical topics, including databases, data mining, business intelligence, data visualization, and big data integration. Like most other doctoral programs, Ph.D. in data science programs typically conclude with a dissertation.Algorithm Design, Analysis, and ImplementationStudents in this course learn the fundamental techniques required to design and analyze algorithms. Topics include balancing, dynamic programming, and divide and conquer. Learners also examine lower and upper bounds on space and time costs, worst case, and expected cost measures. In addition, students consider a selection of applications, including pattern matching, search trees, disjoint set union/find, and graph algorithms.Computational Methods in AnalysisThis course considers ways to use numerical algorithms to solve classical problems in real analysis. Students focus on optimization problems, along with both nonlinear and linear systems of equations. The course also includes a study of the writing, testing, and comparison of numerical software in problem-solving. Students consider the software characteristics needed to implement these algorithms.Informatics Research DesignIn this class, Ph.D. students learn about the philosophical underpinnings and practical applications of informatics research. Topics include deterministic hypothesis-driven experimental designs, data mining, posteriori research, and quantitative and qualitative research.Visualization Design, Analysis, and EvaluationThis graduate-level course introduces students to topics such as visualization design, interaction techniques, human visual perception, and evaluation methods. Students learn how to use modern web-based frameworks to create visualizations, critically evaluate visualizations, and conduct independent research in visualization and visual analytics.Applied Cloud Computing for Data-Intensive SciencesStudents in this course learn the techniques, tools, and concepts of data science, including parallel algorithms, cloud computing, high-level language support, and nonrelational databases. Learners discover how to apply virtual-machine utility computing environments and the MapReduce programming model to scalable data processing and data-driven discovery for scientific applications.

The Doctoral Dissertation

One of the final steps in the Ph.D. journey is the dissertation, which is an original research project in data science. Typically, academics consider the dissertation to be the most important component of their doctorate, since it shapes their knowledge and specialty in the field. Data science students might research topics such as data cleaning, trend identification, or compositional machine learning. Alternatively, they may research a cross-disciplinary topic such as bioinformatics or the role of data science in renewable energy policy.

The dissertation phase typically lasts 1-3 years and includes research, writing, and defense components.

Selecting Your Data Science Doctoral Program

Students should consider many factors when researching prospective programs. The list below describes a few that may be particularly important to consider.

Staff Credentials

Ph.D. students should consider the expertise, professional reputation, and diversity of the faculty members who teach classes, oversee research projects, and direct dissertations.

Cost/Financial Aid

Cost and financial aid are major factors in selecting a school for many students. Selecting a less expensive program or one that provides a substantial aid package can save students a lot of money.

Concentrations/Specializations

Data science links with other disciplines such as genetics, biomedical science, engineering, computer science, technology management, information studies, and business administration. Consequently, many schools offer concentrations in these areas, as well as other fields.

Program Length

Does the program accept transfer coursework from a master’s degree or other graduate-level study? Or must students complete all required credits at the university? The answers to those questions can determine the difference between a three-year completion time versus a five-year completion time for many learners.

Alumni Network

A robust alumni network can lead to significant career opportunities by allowing learners to connect with top professionals in the data science field.

Online vs. In-Person

Online programs are more flexible and often less expensive than on-campus programs, but they may not include as many networking and research opportunities.

Accreditation

At minimum, students should select a school with regional accreditation. The best programs often hold programmatic accreditation, as well.

Should You Get Your Ph.D. in Data Science Online?

Data science is particularly suited to the online learning experience because of its inherent curricular flexibility, emphasis on technology, and focus on analytics. Students considering an online Ph.D. in data science should consider whether their top choices include limited residency requirements.

Prospective students should also look at the cost of an online degree, which is typically less than that of a traditional program. They may also research graduate career outcomes to determine the return on investment when considering the best path forward.

Accreditation for Data Science Schools and Programs

In the U.S., schools can hold regional or national accreditation, with regional accreditation generally considered the more prestigious of the two. Regional accreditation indicates that a degree-granting institution meets high academic standards with respect to factors like faculty qualifications, academic rigor, and student learning outcomes. There are six regional accrediting bodies approved by the U.S. Department of Education and the Council for Higher Education Accreditation.

Data science programs may also receive accreditation, typically through the Accreditation Board for Engineering and Technology. Programmatic accreditation indicates a school’s willingness to invest in high-quality educational infrastructure for its graduate programs in data science.

Students who attend an accredited school enjoy more financial aid opportunities and greater access to careers after graduation. Learners pursuing a doctorate should take an especially keen look at their school’s accreditation status, since it will affect their ability to pursue opportunities in postsecondary teaching.

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