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 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.