Tag: linear algebra

Linear Algebra Bridge Course Returns for Fall 2024

 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.

Global Campus Grows

Whether it’s been covering new education fellowship partnerships, reporting on Michigan Tech’s collaboration with the MEDC, writing about innovative mass timber research initiatives, researching the gifts of adult learners, welcoming new team members, or rushing to keep up with Global Campus Vice President David Lawrence, this blog writer has had a busy year. And while all these initiatives, and more, have been underway, I’ve also had to keep track of Michigan Tech’s new online courses and programs.

Recent Online Programs at Global Campus

For example, in the last year, the College of Business added the online Tech MBA and the Master of Engineering Management. Both are accredited, 10-course programs that, in various ways, leverage your STEM expertise. Whereas the Tech MBA provides foundational business skills, the MEM allows students to customize degrees that merge engineering and business. To promote these programs, Dr. Mari Buche, David Lawrence, and his Global Campus team graciously led several online virtual interest sessions, which were all well attended.

Leadership and learning are indispensable to each other.

President John F. Kennedy

Furthermore, the College of Engineering met the learning and leadership challenge with its Master of Engineering, a professional terminal degree. This degree allows students to focus on either a HEV (hybrid electric vehicle) track or an engineering track. For the engineering track, learners can combine courses from several disciplines. In fact, the master of engineering is ideal for those collaborating with their employer to develop a program to meet specific on-the-job needs.

More recently, the Department of Applied Computing has also added two new programs to its roster: Public Health Informatics and Foundations in Health Informatics. Both certificates can be stacked to form a master’s degree. Like other HI programs, these prepare students for diverse roles in the data-driven healthcare industry. Guy Hembroff, the Health Informatics director, also ensured that MTU’s CHI students have memberships in HIMSS. HIMSS (Health Information Management Systems Society) is a global society. It enables health information professionals to access resources, enroll in seminars, develop networks, search for jobs, and much more. In other words, it gives MTU’s Health Informatics students an edge.

Global Campus Bridge Courses

Bridge courses are short, intensive, preparatory online courses that help learners acquire the necessary knowledge and skills to enter advanced study. This study might mean an undergraduate program, graduate degree, or graduate certificate. Often, bridge courses are for students who are provisionally accepted into a program.

Linear Algebra: A Bridge Course Offered Through Global Campus
Linear Algebra: A Bridge Course Offered Through Global Campus

For instance, in September of 2022, Teresa Woods, Associate Teaching Professor in Mathematical Sciences and Linear Algebra aficionado, taught our first bridge course: Linear Algebra. Her ten-week, asynchronous online course was aimed at prospective students who needed the LA requirement to enroll in MTU’s Online Master of Science in Applied Statistics program.

Woods’ course covered fundamental linear algebra concepts as used in Applied Statistics. Some of the topics included systems of equations, vectors, matrices, orthogonality, subspaces, and the eigenvalue problem.

To learn more about this course, email Teresa Woods (tmthomps@mtu.edu).

Linear Algebra is once again running for the Fall 2023 semester. And there are still a few seats left. Right now, the proposed start date is Sept. 18, 2023.

Newer Professional Development Opportunities

Fundamental Courses and Bootcamps

Global Campus also had the privilege of working with subject matter experts to promote in-demand professional development courses. Also known as continuing education and career training, these courses allow those in the workforce to hone skills, acquire specialized training, develop leadership abilities, and stay up-to-date on current trends.

Currently, Michigan Tech offers both non-credit and for-credit pd courses.

For example, during the summer of 2023, APS Labs rolled out its short, but rigorous course on Diesel Engine Fundamentals. Despite the turn to EV, this course recognized that diesel engines weren’t going anywhere soon. That is, diesel engines are still in light-duty vehicles, medium and heavy-duty trucks; in commercial vehicles (trains, trucks, buses, barges, and boats); in army vehicles; and in generators.

This course was conveniently available in both online and in-person versions. Its goal was educating those pursuing careers in the automotive industry, commercial vehicles, power generation, or related fields.

A Diesel Engine, which was studied in the APS Labs short course for Global Campus
A Diesel Engine

Also, Kevin Johnson, Assistant Teaching Professor, Manufacturing and Mechanical Engineering, lent his significant expertise to summer students. He taught an an intense 20-hour in-person hydraulics bootcamp. In his course, students learned about several topics crucial to hydraulics, such as valves, pumps, motors, circuits, and closed-loop hydrostatic systems.

Upcoming Professional Development Courses

Python for Modern GIS

A person working on GIS with Python, one of the courses taught though Global Campus
GIS Workshop

Furthermore, recognizing the need for more Python professionals in the GIS world, Parth Bhatt (Assistant Teaching Professor / Researcher from the College of Forest Resources and Environmental Sciences) is offering a 7-week, asynchronous, online course for Fall 2023.

His Python for Modern GIS and Remote Sensing course will help students learn beginning and immediate-level applications of Python for understanding and writing simple scripts, automating workflows, and solving day-to-day, real-world geoprocessing tasks in the ArcGIS ecosystem and open-source platform.

Dr. Bhatt, a dynamic teaching professor who lives and breathes GIS, is also on deck to develop online for-credit certificates for his department. Stay tuned for more developments.

And, yes, you still have time to register for Bhatt’s course.

Civil Asset Management

As well, the Department of Civil, Environmental, and Geospatial Engineering has recently added a 3-credit, synchronous online course in Civil Asset Management. This course is taught by Mark Declercq, who brings three decades of valuable, practical civil asset expertise to the classroom. In fact, as Grand Rapids Engineer, Declercq was one of the first experts with boots on the ground during that city’s massive flood event.

Civil Asset Management (CEE 5390) will help students develop long-term plans, as well as the strategic, critical thinking they need to recognize and maintain the value of our all-important civil assets. Declercq also maintains that to develop resilient and affordable solutions and to tackle upcoming sustainability challenges, engineers definitely need Civil Asset Management skills.

Keep Up With Global Campus as We Learn and Grow

In the future, Global Campus plans to offer additional non-credit and for-credit courses and programs. Our goals are advancing the personal development, career goals, and leadership opportunities that come with education. We also recognize the importance of challenging all learners to grow, to think creatively and critically, and to prepare for tomorrow.

We’ll keep you posted as we assist in developing and supporting new programs. For updates, read this blog or follow us on social media.

And remember, regardless of where you are in your educational journey, whether you want to take a course for fun or for your future, it is never too late to start learning.

Anyone who stops learning is old, whether at twenty or eighty. Anyone who keeps learning stays young.

Henry Ford