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Linear Algebra Bridge Course Returns for Fall 2024

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A 3-D representation of Linear Algebra equations.

On Monday, September 16, 2024, Teresa Woods is once again teaching her ten-week, noncredit, asynchronous, online course: Linear Algebra: A Bridge Course for Prospective Applied Statistics Students.

If you’re unfamiliar with the term bridge course, it is a short, intensive, preparatory course. Bridge courses help learners acquire the necessary knowledge and skills to enter advanced study, which might mean an undergraduate program, graduate degree, or graduate certificate. Often, these courses are meant for students who have been provisionally accepted into a program.

Woods’ course is an effective, low-cost option for prospective students who need the linear algebra requirement to enroll in MTU’s Online Master of Science in Applied Statistics program. However, those interested in brushing up on their linear algebra, so that they can later apply to the MSAS program could also take it.

The course’s very practical curriculum covers the fundamentals of linear algebra as they are used in applied statistics. Some of the topics include, but are not limited to, the following:

  • systems of equations
  • vectors
  • matrices
  • orthogonality
  • subspaces
  • the eigenvalue problem

Students will benefit from an interactive learning experience that will make the concepts stick. That is, the course involves helpful instructor-led videos, extensive auto-graded exercises in Pearson’s MyLab Math, periodic review assignments, and regular instructor feedback.

What is Linear Algebra?

Algebra is a broad field encompassing the study of mathematical symbols and the rules for manipulating them. It includes various sub fields, such as elementary algebra, abstract algebra, and number theory.

Linear algebra, a specialized branch of algebra, focuses on the study of vectors, vector spaces (or linear spaces), matrices, eigenvalues and eigenvectors, linear transformations, and systems of linear equations. This foundational area of mathematics has applications in several fields, such as physics, computer science, engineering, economics, and applied statistics.

  • In physics, experts use linear algebra to describe physical systems, including quantum mechanics, classical mechanics, and relativity.
  • In engineering, those working in control theory, signal processing, and structural analysis recruit linear algebra tools.
  • Computer scientists use this branch of algebra in computer graphic creation, machine learning, data mining, and optimization problems.
  • Also, those in the field of economics apply linear algebra when modeling economic systems, analyzing input-output models, and optimizing resource allocation.

What is the Relationship Between Linear Algebra and Applied Statistics?

And, of course, linear algebra plays a key role in applied statistics.

Applied statistics is the implementation of statistical methods, techniques, and theories to real-world problems and situations in science, engineering, business, medicine, social sciences, and more.

It involves collecting, summarizing, analyzing, interpreting, and presenting data to make informed decisions, analyze scenarios, solve problems, and answer questions.

Applied statisticians often use linear algebra to analyze and then visualize data.

Applied statisticians also use advanced techniques, such as machine learning algorithms, to extract insights and patterns from large datasets. They work in a wide range of places: research institutions, the government, business and finance, universities, healthcare systems, and more.

These experts regularly apply linear algebra, primarily because of its ability to handle large datasets and complex calculations efficiently. 

What Are Some Real-World Examples of Linear Algebra and Applied Statistics?

Here are a few scenarios in which linear algebra and applied statistics work together:

  • A statistician working for Netflix might collect and then simplify data on user ratings for various movies. Next, they would represent that data as a matrix and train the model. By uncovering patterns in the ratings, they could then use the model to generate an effective recommendation system. This approach is also widely used in e-commerce sites and music streaming services.
  • Furthermore, a real estate agent might use linear regression, a common method for determining outcomes, to predict how housing prices will increase or decrease in the next year. This information would help them price houses in their portfolio, estimate their commission, and so on.
  • In the healthcare sector, professionals use linear algebra and applied statistics. Principal Component Analysis (PCA) helps reduce the complexity of a large dataset by identifying key patterns and relationships between variables. Through this approach, health officials can then predict and intervene on disease outbreaks more effectively.
  • And, of course, linear algebra and applied statistics work together in several processes involving elections. These include voter segmentation and targeting, predictive modeling, analyzing voting patterns, polling analysis, and redistricting and gerrymandering.

About Your Instructor

Teresa Woods, associate teaching professor in Mathematical Sciences, is helming this course. Woods also advises students and serves as assistant to the department chair.

Woods’ received her Master’s of Science in Mathematical Sciences from Michigan Tech in 2017. Her master’s report “ANALYSIS OF ALEKS MATHEMATICS PLACEMENT TEST DATA” combined her two areas of expertise (and passions): mathematics and educational assessment. That is, she holds both an MS in Mathematical Sciences and an MS in Education (with a focus on adult learning.)

If you take this course, you’ll benefit from an instructor who has considerable experience in teaching, a wealth of enthusiasm for elementary linear algebra, and a rich history in designing and delivering online courses. 

Reach Out if You’d Like to Learn More.

Need advice on whether this course is right for you? If so, please contact Teresa Woods at tmthomps@mtu.edu. Or if you have questions about our online MSAS program, contact Amanda at globalcampus@mtu.edu.

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Online MBAs Grow in Popularity

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Potential online TechMBA® students sharing data visualizations.

45,038 is the number of students enrolled in online MBA programs in the 2020-2021 academic year. For the first time ever, the online student population outnumbered the in-person full-time one (43,740). At last count, in fact, there were 1,095 online MBA programs offered by US higher-ed institutions alone. MTU’s TechMBA® ranks well among this crowd.

Why the rapid increase in both online MBA programs and enrollment? Well, one of the main reasons is that the COVID-19 pandemic changed the education game. At first, universities were forced to offer online and hybrid options. But then they kept rolling these out. In other words, the coronavirus crisis made both prospective students and employers more receptive of online programs. A New America poll also found that the belief in the quality of online learning actually increased by 16% during the pandemic.

Furthermore, 83 percent of the hiring executives in a CNN survey affirmed that an accredited online degree is as credible as an on-campus program. When it comes to online MBA degrees, a survey from the Center for the Future of Higher Education and Talent Strategy Fund had similar findings. That is, 71 percent of employers now view the quality of business degrees earned online as equal to or even better than traditional in-person programs.

So Why Earn MTU’s TechMBA®?

Back in July 2022, in my first blog, I introduced Michigan Tech’s newest online program: the TechMBA®. This program is still going strong. And there are several reasons for both its popularity and credibility.

Accreditation

Only 248 percentage of the 1,095 online MBA programs (less than 25%) offered by US institutions are accredited by the Association to Advance Collegiate Schools of Business. MTU’s TechMBA® is one of these select programs. In other words, the TechMBA® is not only accredited but also respected by industry, business, and STEM professionals. In fact, MTU’s online MBA program regularly ranks as one of the top in the state.

Stem Focus

Michigan Tech’s online MBA is not just business (adminstration) as usual. The TechMBA® is also one of the 24% of US online MBAs that have a STEM focus. That is, MTU’s online MBA degree allows students to leverage their STEM backgrounds and technological competencies. Students develop the fundamental business administration, project management, and communication skills required for STEM-professional roles. These skills qualify graduates for leadership roles in their chosen engineering fields. Those who complete the TechMBA® program are also adept at taking on project management, technical sales, and entrepreneurship positions in STEM-related workplaces.

Flexibility

The US News reports that when it comes to in-person MBA programs, the average age of students is 27. For online programs, however, that age rises to 33.

And 91% of online MBA students even worked full time while pursuing their degree.

What these numbers mean is that online MBA programs, like the TechMBA®, attract older students seeking flexibility in their education. Online learning, for sure, does involve an adjustment period. But there is no need to relocate, readjust your schedule, or leave your job. (There is also no need to frantically dig out from a snowstorm only to arrive to class a late, sweaty mess.)

Smaller, Tighter Class Community

Online learning often means increased interactivity. Research has shown that online learning is as good as if not better than face-to-face instruction. When it comes to peer-to-peer interaction and discussions, online classes may even surpass the effectiveness of their in-person versions. And in a smaller program, such as that of the TechMBA®, there are even more opportunities to connect with peers and instructors. More opportunities to develop those communication skills that are central to leadership roles.

Career Advancement

As early as 2016, Fast Company reported on how several employers began increasing their education requirements. A later CareerBuilder survey revealed that this trend has continued. In other words, an advanced degree may help you not only get that job in the first place but also move up the corporate ladder more easily.

Then there is the matter of salaries. According to a study done by the Georgetown University Center on Education and the Workforce, those holding advanced degrees may earn over 30% more over the span of their career than employees with only bachelor’s degrees.

Strong Return on Investment

Investopedia has noted that MBA graduates who specialize in consulting, finances, and technology management earn the most. And according to one Fortune article, the median salaries for those with MBA degrees are substantially higher than those without them.

The Corporate Recruiter Survey survey (Graduate Management Admission Council) also found that the median 2022 starting salary of new MBA hires was $115,000. And that salary, which is a historically high figure, doesn’t include the median signing bonus of $10,500.

And you also get that ROI faster with an MBA. A recent Wall Street Journal analysis of federal student loan data found that 98 percent of MBA programs leave students with more manageable debt loads than graduates of other programs.

Other Benefits of the TechMBA®

The short list of why you might pursue an advanced degree, such as an MBA, includes the following: acquiring the necessary credentials, pursuing your interests, moving into more fulfilling, impactful roles, gaining additional job security,and increasing your compensation.

But there are other, more personal incentives. Whatever your current degree or desired career path, we’ve summarized some of the advantages for pursuing an advanced degree or earning an MBA degree.

Learn More About the TechMBA®.

If you’d like to learn more about the in-demand MTU’s online MBA degree, come listen to the experts.

That is, Mari Buche (College of Business), David Lawrence (Vice President for Global Campus and Continuing Education), as well as members of the Global Campus team will be holding a virtual interest session on the TechMBA®.

This online event will be on April 11, 2023, at 11:30 AM – 12:15 PM. Please bring your curiosity and your questions.

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Powering the World

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an electric power tower against the blue sky

“It’s an unstable system, but we’re bringing stability to it,” so confirmed Glen E. Archer, Teaching Professor of Electrical and Computer Engineering at Michigan Technological University. While making this statement, Archer is standing in EERC 134, or the Smart Grid Operations Center. In this sophisticated classroom, students attack such topics as interoperability, energy management and emergency control, and system protection; as well as monitoring the connections into MTU’s Energy Management System and the regional grid. And so, so much more. It is, from my starry-eyed perspective, a very cool room.

At this point, the Michigan Tech Global Campus team has been touring the Electrical Engineering Resources Center (EERC) and picking Archer’s brain for the last hour. This room is the last stop on our educational tour.

As he speaks, my attention is divided between the brilliant, glowing grid on the wall and the energy and experience of Archer. He clearly has a passion for the important work and research that transpires in MTU’s electrical engineering classrooms and laboratories. And even more of a passion for electrical power engineering itself.

Which brings me, once again, to his earlier comment. He had mentioned that power engineering jobs might not seem particularly trendy, but those employed in this field have very important work to do. And much of this work is done behind the scenes. “Maybe the humble, unsung heroes of the engineering world,” I suggested. He didn’t comment, but smiled.

Power Engineers: Working Wherever the World Needs Them

Electric power engineering, a subfield of electrical engineering, is dedicated to all things electric power: from its generation, transmission, distribution, conversion, utilization, and management. The electrical apparatus and components associated with these systems, both large and small (wiring, cables, circuit breakers, fuses, switches, converters, vehicle drives, and so on), also fall under power engineering. Depending on their specialty and educational pathway, electric power engineers may work with electric power systems, power stations, solar voltaic cells, wind turbines, and electrical grids.

Electric power engineering may also go by other names, such as power engineering, power system engineering, power management, and power systems management. Its engineers are found wherever people and organizations need power, energy storage, renewables, and intermittent power sources.

Some Electric Power Engineering Workplaces

  • Utility companies
  • Manufacturing plants
  • Engineering Firms
  • Infrastructure related to the oil and gas industry
  • Other industries
  • Airports
  • Hospitals
  • Residential complexes
  • Schools
Industrial Power Plant

Filling a Shortage of Electric Power Engineers

Although they may not outwardly seem flashy, careers in electric power engineering have the advantage of being both flexible and mobile. Or to put it another way, the knowledge and competencies that power engineers acquire on one job may be transferred to another. This versatility means significant career choice and mobility, both within and between organizations as well as in workplaces throughout the world.

That is, as more countries transition to renewable energy sources and advanced technologies and invest in more infrastructure, the global demand for electric power engineers will likely increase. Some experts even believe that there is a definite shortage right now.

According to a summary of the Global Energy Talent Index Report, “power companies everywhere are struggling to balance talent shortages with changing skills.” The writers continue to say that there is a “looming skills shortage of engineers in the power, nuclear, and renewables sectors.”

What does this shortage look like? The GETI document confirms that as many as 48% of power professionals are concerned about an upcoming skills crisis whereas 32% believe the crisis has already hit the sector. 28% contend that their company has been affected by a skills shortage.

There are three main causes of this crisis: massive retirements, an aging workforce that requires upskilling, and a need for more workers with training in new power electric technologies. The report states that 13% of power workers are 55 years and older whereas 17% are between 45 and 54.

Confronting Upcoming Challenges

In short, both United States and the world need power engineers to not only fill these gaps but also address present and upcoming challenges.

In this nation, one of the biggest issues facing American engineers is contending with an outdated American grid in need of both repair and replacement. This aging grid can cause reliability problems, power shortages, and other complications. However, electric power engineers face other challenges, which affect the United States and beyond.

Improving Energy Storage

A photovoltaic system, otherwise known as a solar panel array.

Increasing the capacity and efficiency of energy storage systems is one key concern. To enable the widespread adoption of renewable energy sources, electric power engineers must develop better and more cost-effective energy storage solutions.

There is a need to improve the performance and efficiency of battery technology, which is essential for the large-scale energy storage. The excess electricity generated by renewable sources can then be used to help meet peak demand or provide back-up power during outages.

Increasing Grid Reliability

As electric grids integrate with more renewable sources (such as wind and power), power engineers must ensure grid stability and reliability. They must also develop solutions for reducing grid congestion. And create strategies for maintaining system stability and resilience in the face of climate change, extreme weather events, cyber-attacks, and other potential threats.

In fact, right here at Michigan Tech, Dr. Chee-Wooi Ten (Electrical and Computer Engineering), has spearheaded an impressive, interdisciplinary research team since 2010. This group contains members from the fields of statistics, business, engineering, and computer science. Its goals are advancing power engineering and developing strategies for improving power grid cybersecurity, grid reliability, interdependence, and sustainability.

Integrating Smart Technologies

Smart technologies are helping to make electricity consumption more efficient. For instance, smart meters allow utility companies to track and measure electricity consumption in real-time. They also enable consumers to monitor and adjust their own energy usage. Automated demand response systems can also reduce or increase electricity consumption according to fluctuations in the grid. And then there are advanced distribution management systems for utility companies to monitor and manage their electric grid in real-time. These can detect outages, schedule maintenance, and react to changing electricity demand.

There is a need for power engineers to understand these technologies and develop ways to integrate new smart systems into the existing grid. These strategies might include implementing communication protocols, creating intelligent control systems, and developing cybersecurity policies.

Ensuring Cybersecurity

Cyberattacks on the grid are not just the stuff of movies. For instance, in 2022, Russian cyber-hackers targeted Ukraine’s power grid. And in 2016, hackers chose a Florida power utility as their mark. The result: pumps ran continuously, causing not only waste but also physical damage. And since 2018, the US has been fending off Russian cyber-attacks on critical infrastructure.

Cyberattacks on electrical grids, then, can cause major disruptions and blackouts. It is obvious that one of the responsibilities of power engineers is improving the cybersecurity of the grid. This task is also one of the main objectives of Dr. Chee-Wooi Ten’s CIResilience team.

Addressing Environmental Concerns

Power plants, especially coal-fired ones, generate substantial emissions. And the cooling and operation of these plants require sizeable amounts of water. In fact, the power sector is the largest industrial power user. Therefore, a main engineering challenge is lessening the environmental impact of electric power systems, including reducing emissions and water consumption, improving efficiency, and minimizing waste.

Pursuing Electric Power Engineering at Michigan Tech

In short, as the world’s population continues to grow, the demand for electricity will increase significantly. Additionally, global citizens are requesting more sustainable and environmentally friendly energy infrastructure. Engineers may answer these calls by developing renewable energy sources and technologies as well as reducing electricity consumption and improving power efficiency.

If you’re up for these (and other) challenges, Michigan Tech offers several educational routes in electrical power engineering. For instance, there is a 13-credit undergraduate certificate in Electric Power Engineering and a 15-credit Graduate Certificate in Advanced Electric Power Engineering. Both of these certificates have been designed with consultation from experts from electric utilities and industry. In other words, students receive the knowledge, skills, and aptitudes that working electric power professionals regularly apply in their careers.

And, of course, there is the 30-credit MS in Electrical and Computer Engineering, with a Focus in Power Systems.

Whatever your preferred educational or career path in power engineering, Michigan Tech can help you get started.

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